Fancy Store-Bought Dirt

Pinker's NYT Magazine Article About Morality

We read the paper version yesterday; you can read the on-line version here.

At one point the article mentions three hypothetical situations that most people supposedly find immoral. My immediate reaction was a complete lack of objection to any of the three. (Admittedly, my eyes glazed over a critical detail in one of the three. I fervently defended my original position even after catching the important detail: That might be an example of some psychological effect whose name I can't think of (oversimplify a bit and call it stubbornness).)

Julia agreed with me about the lack-of-immorality in the flag case and the dog case. The flag case might have been a moral transgression depending on what standard of conduct the protagonist would have otherwise claimed to uphold.

(Reminds me of something our rabbi told us in Judaism classes over a year ago, that I'll do my best to recount adequately: It's wrong to violate certain Jewish laws/traditions, if and only if you believed in their validity to begin with. So if you assert from the outset, for example, "kosher dietary restrictions are silly"... that's your choice and life goes on. But if you believe that kosher is theoretically correct, yet fail to live up to it in practice, then you've transgressed. Does this make sense? But you could argue that this distinction doesn't apply to any moral rules about treatment of other people.)

I argued with her at length about the brother-sister incest case. It's unclear how much of this was devil's advocacy, how much was rationalizing a stake I'd taken, and how much is what I really believe. I think the two best arguments against brother-sister incest are the risk of pregnancy (you can't just hand-wave this risk down to zero in a hypothetical, no matter how much contraception is involved), and the premise that lots of childhood/adolescent sibling interaction would be really squicky if "these two people can never have sex ever" weren't a ground rule.

The article also mentions two competing flavors of the train problem, that most people will throw a switch to kill one person instead of five, but won't kill that one person with their bare hands (i.e. shove that person in front of the train) to spare five people.

I sort understand why people reflexively draw that distinction, but the way people pigeonhole things is ridiculous in light of simple physics. If you won't use your bare hands but will throw a switch, then what about the case where you save the five people by firing a pistol at the one person? (Railroad switches don't kill people, people kill people.)

[As you know from past moral philosophy posts, I'm in the distinct minority in claiming that you shouldn't even throw the switch. My defense of this is almost exactly the same as what I infer that people say in objection to killing someone with their bare hands. Despite what I claim in theory, in practice I'd probably throw the switch, pull the pistol shove the fat guy, or whatever it took. Unless I just froze.]

Fortunately, Scissors Has Developed an Immunity to Iocane Powder

WHY WHY WHY WHY WHY?

You have exactly three options for your starting move. As game structure goes they're all analogous: You could call them asphalt, bagpipe, and chrysanthemum and not change the game itself one bit.

It is, therefore, rather unlikely that any one of those three options merits the phrase "stalwart players have come up with a strategy," much less the label "how to win."

But hey, some company won a big business deal with scissors once. And now that I think of it, I once saw some guy win a huge pot with 5d 4s on televised World Series of Poker. (OK fine, I looked it up.)

My Favorite Dice Paradox

(Internal monologue in the car this morning: "Is it too soon to care about Week 15 fantasy football?" "Yes, because even aside from injuries you don't know who you're facing." "But why would that matter. Regardless of the opponent I'm just maximizing expected scoring.")

You probably already knew this but in a two-player game where margin of victory is unimportant, comparing the "expected" payouts tells you a lot less than you might think.

For example, consider three nonstandard six-sided dice. One has two 6's and four 2's on its faces; one has 3's on every face; one has four 4's and two 0's.

The first die has an expected roll of 3.3, the second 3 (obviously), the third 2.7. But if your opponent had the second die (the all 3's), and you wanted a higher number, for a quick ten points which one of the remaining dice would you choose?

You saw what happened there, right? Once you've convinced yourself that {4, 4, 0, 0, 0, 0} < {3, 3, 3, 3, 3, 3} < {6, 6, 2, 2, 2, 2} in the long run, add another die to the mix, this one with three 5's and three 1's. How do you expect that one to do against the others?

Paul gets comment of the month. That was quite the typo (and of course his main point is dead-on)

Word Stacks

An exercise for the reader is to tell me (through memory or research) what two seven-letter words were involved in the story, from Word Freak, of a Scrabble game whose first play was a seven-letter word and whose second play was a seven-letter word that also made seven two-letter words.

Earlier this week Julia and I finished a game in which I slipped AXONS under TOGAE. (For one of the ancillary words ET became ETA, but since TA itself is a word I think this still counts as 5/7 of the Word Freak thing.)

The Limits of Stipulations in Philosophical Problems

I think I might be gravitating to the "one box" camp for Newcomb's paradox. But I should tell you how I got there.

Julia, like nearly every intelligent person, disagrees with me about the track/switch "kill one man to save five" problem. She's surprised that once my own life is secure, I'm unwilling to be an agent of death. (I suppose anyone who knows that I'm not a pacifist -- e.g. that I continue to support what the U.S. is doing in Iraq -- should be many times as surprised.)

My immediate answer -- not my whole answer, but so instinctively first that the rest is just rationalization -- is that ground rules be damned, I reject the 100% certainty that it's a case of five innocent people dying versus one innocent person dying.

So what if the ground rules become absolutely ironclad?

Then my answer to the switch problem becomes really lame, though it continues to be my answer. (It's not nearly as lame as the people who'd let their entire basement hideout be massacred because they were too wussy to smother one baby.)

This got me to thinking about other ground rules that I find suspect. For example, even in the usual formulation of prisoner's dilemma (where players have a dominant strategy that works to the other player's disadvantage) I am the most outspoken advocate I know of the correctness of the "nice" option. No matter how hard you stipulate that this is a one-time game, in practice different flavors of it can and do come up frequently. The world as a whole is better off if everyone consistently cooperates, and if everyone realize that the world as a whole [etc. to infinity].

Although you'd think Newcomb's paradox stems from a game that you personally play just once (apparently billions of other people have played it though, for the Great Predictor to have amassed such a track record?), something similar might be at play here: Think of sustainable development, and of various free rider problems. (I wonder if they cover Newcomb's paradox in those "Green MBA" programs...)

One caveat: Several years ago at a New Year's Eve party thrown by geeks, for geeks, I overheard someone (whom I'd never met and have never seen since) mention that unlike his friends, he carries grudges from strategy game to strategy game. That is, if you screw him over in one game (think of Diplomacy and the like), he'll remember it. That guy apparently wished to use his openness about such grudges to his advantage, as a deterrent.

I think if you're playing a strategy game that you don't (can't) take payoff calculations personally. The best long-term reaction to that guy I overheard would be just to refuse to play games with him.

(So the paradox is that I advocate screwing people over when you're playing for fun, yet being "nice" when you play for money! This must be what I think given how fervently I advocated the "Friend" strategy in that old game show Friend or Foe.)

Time Morality Quiz

Take it (via Fark).

I find problems 1 and 2 to be slam-dunk easy (can you guess from my other political views how strongly I value the right of self-defense?).

Like everyone who's ever taken a college philosophy class I've had plenty of opportunity to think about (and discuss) the trolley problem and its variants; I tend to be one of the few people in the room (sometimes the only one) who opposes throwing the switch.

The Time quiz doesn't include the "famous violinist" problem (nine months of detaining one man so that another might live: one of the most thinly-veiled allegories in this realm); my answer to that one is consistent with pro-life principles.

(For what it's worth, related to practical sociopolitics rather than abstract philosophy, one of my five biggest regrets in life is having been so vocally anti-abortion over the years. Since I somehow doubt that I personally have talked anyone out of having an abortion, that outspokenness has easily done more harm than good.)

I Solved a Volokh Puzzle!

Got this one right away. (As did basically every commenter.)

Replay!

I just sent my wife a link to the news about baseball GMs voting for instant replay. That left stuck in my head the glorious sound a pinball machine makes when you hit the replay threshold (or succeed at the 10% chance of a freebie, on those machine gracious enough to include that option).

It's been so long since I played pinball. Even the concept of "extra ball" is fond memories.

377-377

Have you ever had a Scrabble game end in a dead draw? I don't think I ever had, but there's a first time for everything.

Also, that makes twice in one week where I needed the leftover tile bonus/penalty to avert a loss.

Thomas the Sudoku Engine

The identity of the U.S. sudoku champ (pictured in the linked-to article) won't surprise anyone who read Jason Z's travelogue e-mails from Prague a few months ago.

Mechanism Design

Today's exercise for the reader:

1. Read as much as you can about the work that won the 2007 Nobel Prize in Economics.

2. Think about eBay, and the last-second sniping everyone talks about.

In theory last-second snipers should not affect a second-place auction; more importantly, if you understand the structure of those auctions then those snipers shouldn't affect you. Yet last-second bids are not only prevalent but also part of the conventional wisdom. Why? ("Market inefficiency" is an easy answer but how likely is it to be true?)

The best answer I can come up with: If last-minute bids become the perceived norm then buyers collectively will come out ahead of where they would have been. eBay probably has more buyers than sellers. (Ironically, all the people who get outbid at the last minute and say "I would have bid more" have only themselves to blame for bad tactics, even if those bad tactics were part of a plausibly good overall strategy (of rent-seeking?).)

Mutually Assured Destruction was a Suck-Out Artist

Do you fully comprehend how incredibly lucky we are that the world as we know it still exists despite the nuclear arms race of the Cold War?

I probably mention this dozens of times but this is one of the many things that could have gone wrong but didn't. (If you know what was going on as of the instant the Soviet warning system reported a supposed U.S. missile launch, what odds would you lay that nuclear holocaust would ensue?)

Silly Math of the Day

(See, not all of my posts lately are about fantasy sports. (Oh wait, this one actually is if you notice the direct mapping.))

A science class has an even number of students (2n for some positive integer n) and a 50-50 male female ratio. Those students are assigned randomly into lab partnerships. (Process doesn't matter but if it helps you visualize: Pick two students at random - they're partners. Pick two more students at random from among the ones who are left. Repeat until the two remaining students become partners.)

As a function of n, how many male-female partnerships do we expect?

Silly Arithmetic Relic

Read my mind and tell me: In what context did I just solve for the fraction 161/180?

(Hint: Public education is involved but it has nothing to do with a 180-day school year. Don't think of the denominator as exactly 180. Instead, think of someone who's perfect at computation (i.e. they have a calculator) but inept at understanding certain mathematical principles, like rounding.)

it always does come full circle

Only five minutes instead of a day, but the joke in this Fark headline led me to this Wikipedia page, which refers to the same Fark thread.

The Difference Between an Angle-Shoot and a Cheat

Yesterday some co-workers were in a pool tournament and with the game on the line one of them called a table scratch on the other (it was indeed a table scratch), took ball in hand, and sank the 8-ball.

Earlier in the game, the scratcher's teammate had chosen not to enforce a table scratch. Whether that's relevant is an exercise for the reader.

Bathroom Tile Math

I believe this problem has long since been solved, and it came up several "sit-down meetings" ago, but Z's comment to a baseball post reminded me that we do have some cool math geek readers here.

Consider infinitely many rows of tiles in a triangle pattern: The first row has one tile, second has two tiles, nth has n tiles.

Which positive integers can('t) be formed as the sum of two or more consecutive rows of tiles?

(Henceforth "number" describes only positive integers.)

Two consecutive rows can form any odd number greater than 1. Any odd number is expressible as 2i+1 for some i, and if i > 0 then you use the ith row and the (i+1)th row.

Three consecutive rows can form any proper multiple of 3 because i + (i+1) + (i+2) = 3i + 3 = 3(i+1).

More generally any odd number of consecutive rows can form any multiple of that odd number greater than half the square of that odd number.

Four consecutive rows can form any 2mod4 number >= 10. Six consecutive rows can form any 3mod6 number >= 21, eight consecutive rows can form any 4mod8 number >=36.

More generally, any number that can be expressed as the product of an even number and an odd number can be represented by consecutive rows. If 2E > O then use O rows whose average is E. If 2E < O then use 2E rows whose average is O/2. (For a quick 10 points why will you never see 2E == O?)

We've covered every odd number greater than 1 and every even number expressible as the product of an odd and an even. The only even numbers not expressible as the product of an odd and an even are powers of 2.

An exercise for the reader is to prove that NO power of 2 can be expressed as the sum of N consecutive integers.

Probability Theory of the Day

Also feeling pangs of regret must be the San Francisco cab driver who drove Murphy and Kamal from the airport to their hotel. Hoping to get out of the $55 fare, they told the driver that if they caught Bonds' record home run ball, they'd give him a couple thousand dollars.

"He turned me down, man," Murphy said.
--Yahoo! Sports

I think the actual probability that Bonds would hit his record-breaking home run that night, AND that one of those guys would catch it, was a good deal less than 55 in 10,000.

"What do you do for a living?"

"I drive cabs... AND I chase inside straight draws."

Mathematical Misconception of the Day

Five friends gather for a marathon bridge session. They want to play ten rubbers, such that each person has each possible partner for two rubbers and sits out two rubbers. Moreover, the two times any given partners play together must NOT both involve the same pair of opponents.

I spent much of this morning convinced that these criteria were impossible to meet (but not sure how to prove it). But then I realized exactly how to do it and felt stupid.

(Hint: The more instinctively you know the best way to set up a five-person round robin, the more you're at risk of falling into a mental trap.)

A Devil's Advocate Defense of Point Spreads

In theory, gambling based on point spreads (as opposed to straight-outcome betting) should not only reduce the magnitude of harm of gambling-related "fixes" but also make certain kinds of cheating easier to detect if someone actually crunches the numbers.

Consider a corrupt referee who needs the home team to win by at least five points and who does something to cause the home team to win by six points instead of by four. In abstract, yes, this still ruins the integrity of the game, but on purely outcome-based analysis what has he really changed? (If, on the other hand, he needed the home team to win and did something corrupt to cause the home team not to lose...)

As for catching the cheats: You may remember the chapter in Freakonomics about suspicious results in sumo wrestling. Couldn't one design a similar study involving, say, NBA games with a final score within 2-3 points of the spread? (Or within 2-3 points of the over/under?)

Unless players, coaches, and refs were chronically acutely aware of the exact spread, you wouldn't expect much discontinuity in stat trends involving games barely on either side of the line. (You would expect bits and pieces of discontinuity between games some team barely lost and games it barely won.)

Some interesting questions:
1. For all NBA referees, what was the average distribution of fouls in games in which
a) a home underdog barely covered?
b) a home underdog barely failed to cover?
c) a home favorite barely covered?
d) a home favorite barely failed to cover?

2. For NBA referee X, what were those distributions?

3. For all NBA refs, on average how many fouls were called in games in which the teams {barely hit, barely missed} the over?

4. For NBA referee X [...]

Here's the only Freakonomics post I could find that mentioned the scandal. Somebody mentioned the difficulty of detecting a cheating ref whose actions could nudge the outcome to either side of the spread. Well... just look for refs with a relatively high frequency of "outlier" games (e.g. visiting team got more foul calls than usual) correlated to close calls where the outlying trend worked to the benefit of whichever team barely covered.

Meanwhile Mark Cuban is an outstanding business leader. I should have guessed he would write something like this (but both the position and the eloquence still surprised me).

Math of the Day

Combinatorics can involve some messy computation. All the more reason to keep it simple(r) whenever you have a chance.

Barry Bonds has not started 16 of the 91 games that the Giants have played so far this season. There are 260,462,895,672,871,000 (260 quadrillion) possible combinations of games that Bonds might have “chosen” to miss. For example, Bonds missing Giants games # 88, 4, 62, 18, 22, 23, 61, 2, 91, 54, 87, 10, 58, 19, 65 and 83 is one such combination.

Of those combinations, 1,200,635,647,008,340 (1.2 quadrillion) involve each of the three Giants games that have been nationally televised on ESPN this season, as well as any other set of 13 non-ESPN games. In other words, the probability that if Bonds were picking 16 out of 91 games at random to miss, it would so happen that all 3 of the ESPN games were included among those 16, is 1,200,635,647,008,340 divided into 260,462,895,672,871,000, or about 215-to-1 against.
--Nate Silver, Baseball Prospectus Unfiltered

Those numbers seem plausible but I don't think many humans have a good sense of whether hundreds of quadrillions are the right order of magnitude. In a perfect world you could solve this problem without numbers that large. In fact, you can solve the problem int his world without numbers that large.

This problem is equivalent to three friends each drawing (without replacing) a ball out of an urn that contains 91 balls, 16 black and 75 orange. The probability that each of the three friends draws a black ball is:

16/91 * 15/90 * 14/89

(If the first friend draws an orange ball then we know our condition is false. If the first friend draws a black ball then the number of balls and the number of black balls have each decreased by one, etc.)

According to Excel (don't bother with a calculator!) that's 3,360 out of 728,910. Six-digit numbers are still difficult for a human to put in perspective but at least they're not quadrillions.

(And yes, consistent with what Nate said, about 215.9 to 1 against.)

Oh, if you're being truly anal about problem equivalence, you can have 91 people in a line, each of whom will draw a marble without replacing. Three of those people are friends, and they happen to be at places within the line that correspond to the ESPN games on the Giants' schedule-to-date.

Poker Hand Flashback of the Day

"What's more annoying, hearing about somebody's fantasy team, or hearing about his bad poker beats?

Nate Silver: Fantasy Team. Surprisingly not close. With the bad beat story, you can usually just tune it out and be done with it, but with someone talking about his fantasy team, you're usually expected to produce some coherent reply."
--Baseball Prospectus all-star game live chat. Nate is known elsewhere as Nate Tha Great.

An old roommate is getting married in two days. Several friends are in town for this, including Chad (the best man at my own wedding). He and the Mrs. are staying at our place, just as they did before our wedding.

(Friday night Chad and I stayed in the same hotel where most wedding guests stayed. The previous two nights Julia stayed at her parents. Because we had a one-bedroom apartment then (now a two) I slept on the couch those nights.)

The nights Julia was away I ratcheted up the stakes a bit in the on-line poker. If this was all about the last days of bachelorhood then there are certainly worse ways to mark that passage.

Anyhow: No Limit cash game, [mumble] stakes. Hero had A6 suited in the big blind. Some people limped and/or folded. Button min-raised. Hero called, anyone else still in the hand called.

The ragged flop (let's say it was T63) gave Hero second pair and a backdoor flush draw. Hero led with a half-pot bet, Button min-raised again, Hero called. Two players left.

Turn was a 6. Hero check-pushed. Button thought about it a bit. Hero felt a rush of anticipation and turned his attention to other tables. A few seconds later Hero noticed a shocking lack of stack at the original table.

(Villain called with AA. Naturally the river was the other ace. [There's only a 33% chance the link is apt. My suit was red.])

One More Anniversary Oddity

This is (at least) the second year in a row that R. spent his June 16 involved in bachelor party festivities, among a group of friends for whom the highlight of a bachelor party is an especially intricate board game.

Do I Underrate How Surprising or Groundbreaking This Is?

Benford's Law

"In many data series a surprising number of entries begin with the number 1, and the number 2 is also more common than a random distribution might suggest." --Tyler Cowen

You might not have thought of this (I hadn't) but in hindsight it makes total sense. Pick a random integer and see what happens with the digits of the numbers between 1 and that number. For example, in the tens digit you see a 1 ten times before you see other number, a 2 ten times before [etc.].

The interesting question for any given set of data is whether the law is applicable. It probably is, but think about conditions (upper or lower bounds, whether the data in question is better thought of as a sequence of digits than as an n-digit number) that would make it inapplicable.

I hope everyone realizes that the second parenthetical reason above is why lottery numbers decidedly do not follow Benford's law.

Even if there was a lottery setup that sort of applied to Benford's law -- e.g, if a lotto drew just one ping-pong ball from balls numbered sequentially from 1 to some three-digit number and thus the first digit was more likely to be 1 than any other number -- this would tell you absolutely nothing about whether 101 was more likely to appear than 102, 102 than 103, etc.

While we're here: Take a lottery that involves drawing six balls (without replacing) numbered from 1 to 99. Assume the balls have been properly randomly shuffled. THINK QUICK: Which outcome is more likely, 1-2-3-4-5-6 or 48-40-1-79-72-93? (If you get this wrong I will sigh sadly and die a little inside.)

This is all very interesting (I claim) and very easy to understand if explained correctly but it doesn't get nearly enough coverage. I'm embarrassed to admit that until the Marginal Revolution entry I'd never heard of Benford's Law, nor intuited the same result.

Uh Oh

Poker-style betting rules for golf.

The funny thing is you can do this with just about any multi-round contest (c.f. the Backgammon doubling cube (shout-out to Dan Harrington)) but it's so perfect for golf on so many levels, I'm surprised nobody thought of it sooner.

Iron Dragon: Worth A Hot Poker to the Eye?

I'll admit I'd wanted to learn how to play Iron Dragon. That said... six players, including four of us newbies, made for five hours (even after reducing the victory condition from 7 major cities + 250gp to 7 + 125gp) worth of pain. The really frustrating part was the opportunity cost of playing this one thing instead using that same time to enjoy three or four games with the other half of the party.

(Have I mentioned how big a Trans[location] snob I've become? Simple and elegant tactical games are your friend.)

The rest of this post is basically for Greg (or any other Iron Dragon connoisseur out there).

So for someone who claims to be all about efficiency (I enjoy wonkish stuff about logistics or operations research, and despise manual processes that take linear time), it turns out the games at which I do the worst on my first play-through are the efficiency games -- the ones where your levels of production snowball out of past production.

I went third. Since my initial cards had some nice synergy involving Fish, I planned to start in the top left corner of the board (what I thought of as "northwest" until I noticed that the compass on the game board was a bit askew, so technically more like NNW). As it happens that's exactly where the first two players BOTH went. So I started out in Old World (bottom right of the board), with some high-risk, high-reward strategy involving Wands. I ended up having to cut all the way across the bottom of the board, and it was a long time before any other player's moves became remotely relevant to what I was doing.

(If it weren't for our "you can borrow anything from the bank as long as you eventually pay back double (and don't use the borrowed funds specifically to hose an opponent)" house rule, I'd have probably been dead in the water, reduced to several turns in a row turning in cards until I got something I was capable of doing.)

Eons later I actually got out of debt and ostensibly came in fourth (I had seven major cities plus 55 gp when the game ended, though I'd just made a huge delivery; fifth place had fewer gp but was about to pass me; sixth place was still in debt). Ironically the one city I didn't connect was the "K" city smack in the middle of the board.

(If it weren't for the Rainbow Bridge event I probably couldn't have made it to the top-right-corner city either.)

Anyhow, my post hoc understanding of the game is way, way different from what I assumed at the outset (though still quite different from what other players made it out to be). Unless I'm missing something huge, this is NOT a game of immediate adversarial maneuvering (yeah, sure, other people will hog the most direct routes to the places you get to last, but that zig-zag route costs you, what, about 6-8 extra gp? pshaw).

On the contrary, I wonder whether the best strategy (maybe even the only strategy if you don't have that "borrow from the bank" house rule) is to tacitly cooperate with one or two opponents: Build adjacent to each other (and rent each other's track) so that early on you have access to a whole bunch of cities without needing to burn precious capital laying track you can't afford yet.

Full circle: from the TransEuropa on the other side of the apartment I heard an otherwise very smart person ask, half-jokingly, why bother to build at all if everything you play helps everyone else as well as yourself. Very amusing way to miss the point (of Trans, of Settlers, and of a lot of similar games): OF COURSE you're helping [some] other people at the same time you help yourself. Part of the trick is to get yourself into a position where you're helped as much as possible by other people (read: fewer things FAIL to help you than fail to help other people).

What Am I Playing Lately?

Moai

Leap of Faith

In both cases the music is especially soothing.

Brain Teasers 101

Post a brain teaser whose answer is very simple (but not immediately obvious). Examples, which many of you have probably heard hundreds of times:

1. You're in a room with two doors. One leads to freedom, the other to torture. (Obviously you want freedom.) There are two guards here, one of whom always tells the truth, the other of whom always lies. You know that to be the case (it's unclear how you know) but you don't know which is which. You're allowed to ask either guard (but not the other) ONE question, and only one, after which you will choose a door. Devise a question from whose answer you can pick the correct door with 100% certainty.

2. You have three boxes of marbles. One contains only blue marbles, one contains only red marbles, and one contains both blue marbles and red marbles. One is labeled "BLUE MARBLES," one is labeled "RED MARBLES," and one is labeled "BLUE MARBLES & RED MARBLES." However, you happen to know that all three boxes are currently mislabeled. The good news is, you can figure out which label belongs on which box by drawing just ONE marble from one box. Explain how!

3. You and several other contestants are invited to a game show taped on the set of The Price is Right. However, this show consists entirely of spins of a wheel. Until the game is won, contestants will take turns, each getting one spin. If a spin lands on "$1.00" (assume that any given spin will hit that square with 1/20 probability) then that contestant wins $10,000 and the show ends immediately. Otherwise, that contestant goes to the back of the queue and the next person spins. (Assume the outcome of each spin is independent of the outcome of any other spin.) When the initial queue forms, what's the best spot in the line and why? (Hint: Your initial impression is probably exactly right but the trick is to see, mathematically, why it's right.)

4. (In theory this one is more difficult but I hope it becomes clear why I put it here.) Big Tex plays a lot of hold em poker: Hundreds of hands a day every day for the last several years (at a casino where the dealers are known to be 100% honest). Despite the reputation of some poker players, you know him to be 100% a man of his word. Big Tex wins a huge pot with pocket aces. He turns to you (watching on the rail) and says "Okay, that was hand zero. The next hand I'm dealt will be hand 1, then hand 2, etc. Now, you know the odds of getting pocket aces on a hand." [N.B. 4/52 x 3/51 = 1/13 x 1/17 = 1/221.] "I want you to write down on this post-it note the NUMBER of the hand on which I get my NEXT pocket aces. Fold it up and I won't open it until that hand. If you're right I'll give you $10,000." What hand number should you write and why?

False Epiphany of the Day

Wow. I'd been aware of "the long tail" as business jargon but
this post severely deflated my interest the main purveyor of that piece of jargon.

How best to simplify it's findings? Let's see...

If you choose a bunch of characters at random (one of which is a space) then the length of intervals between spaces will follow a power law. WHO KNEW?!?

(Hint: No matter what characters your monkey just typed, you have exponential waiting time until the next time the monkey hits the space bar.)

This Game Is So Wrong

I don't mean morally wrong: I have no objections to pretending to wipe out the human race with a viral pandemic. But this game has inaccuracies in multiple disciplines:

GEOGRAPHY - Western Europe has no airports? (I give a free pass to the low population levels and "one airport per continent" statuses because those are obvious simplifications.)

GEOPOLITICS - Countries wouldn't sealed off their borders until after 100,000 people [in this game, 1/6 of the human population] had already died over two months?

BIOLOGY - If thousands of people contract a virus, and several weeks later that virus mutates into something else, the virus's transformation would instantly affect the instances those people previously contracted?

COMPUTER INTERFACE DESIGN - The virus definition screen and the world map can't possibly be on the same screen at once?

It's a most annoying game, about which the most annoying thing of all is how much time I spent on it yesterday. (The only way I can "win" is to reduce the virus to zero lethality before everyone shuts down their transportation, then bide my time until it somehow migrates to Western Europe, at which point you drop the hammer on fatal symptoms. You have to get to Western Europe before it occurs to them to seal that border. This ends the world by about Day 90 but doesn't get me anywhere near the high scores.)

Hey, I Know That Guy!

The alphabetically last member of the U.S. Sudoku team, that is.

I don't think Jason Z. and Mike Develin have ever met each other, which is funny given their common interests and how many mutual friends they have. I'm jealous of both for playing particular mind games well enough to represent our country.

Speaking of the latter (by the way, doesn't Rex Grossman sort of look like him from the neck up?), his January 25 quick hit sounds like exactly the type of practical advice my father-in-law the engineer/inventor would give. Meanwhile, he's exactly right about his February 5 rambling.

I'm lucky to be a relatively healthy person so that I have the luxury of taking sick days on a somewhat lower threshold of actual sickness than most people have (yet still without using many). I can't stand it when sufficiently sick people are out in public (especially on airplanes!). But then I'm evolving into one of those people who thinks that people don't use Purel nearly frequently enough.

(I'm still a clutter-messy person, though I'd like to claim not a germ-messy person. But enough of this: How on EARTH did I get here all the way from congratulating Jason Z.?!)

The Princes of Florence

This game seems to combine the best elements of Funkenschlag with the best elements of Puerto Rico. At the moment I'm head-over-heels smitten with Trans Europa, which means that at the moment Rio games seem gratuitously complicated to me; that said, this one is worthwhile.

Once you know how to play this, it seems really straightforward, despite how fiendishly complicated it seems when encountering the rules cold. OVERSIMPLIFICATION of the rules (with some finer points left out):

Your goal is to get prestige points. The best way to get prestige points is for someone in your court to complete a work. (You also get prestige points from buildings, redundant landforms, and satisfying criteria on Prestige cards, though these are ancillary to the central thrust of the game.)

There are seven rounds; each round has an auction phase and an action phase.

Auction: you acquire a landform, a Builder, a Jester, a recruiter (reuse someone else's already-played artisan/scholar), or a Prestige card.

Action: you do up to two things from among completing a work, adding an artisan/scholar to your court, building something, adding a Freedom (makes works more valuable, see below), or getting a Bonus card that (when played with a work) might make that work more valuable.

Each artisan/scholar is associated with a particular building, a particular land form, and a particular freedom. When you complete a work with that artisan (by playing that card from your hand -- each person starts with three but you can only use any given artisan once), the value of that work depends on the answers to these questions:

1. Have you build that building?

2. Do you have that freedom?

3. Do you have that landform?

4. How many Jesters (if any) do you have [Jesters improve artisan morale: Jesters need to fetch a high price at auction to prevent a degenerate all-Jester strategy]?

5. How many artisans do you have (counting both the ones in your hand and the ones you've played)?

Based on the above, each work has a Work Value that you can claim in either Prestige Points or money. Prestige Points are how you win but if you go broke you'll end up s.o.l.

My first and only time playing, from memory:

1. Park; built a Workshop and completed a work (took the Prestige). I know now how shortsighted and pointless that was but at this point none of us really knew what we were doing.

2. Lake; took a freedom and another artisan.

3. Prestige card; another freedom and completed a work (took the money)

4. Builder; built a University and an Opera House

5. Jester; drew an artisan and completed a work

6. Another Park; took a freedom and completed a work

7. Another Lake; took a bonus card (very useful one as it turned out) and completed a work

Despite thinking I was losing badly I ended up winning.

We've Played So Much Trans Europa This Month

Also, we were in L.A. taking care of our niece and nephew as a birthday present to their mom (while their dad took their mom on vacation).

Our six-and-a-half year old nephew played two rounds of "the train game," one as Julia's teammate and then one holding his own cards (which he never did show anyone) and choosing moves completely for himself. He successfully connected some green (ex-Soviet) city with Budapest(?), got his tracks networked, and went to Bilbao all by himself. (We didn't announce any scoring but he'd have done especially well had his selfish Madrid-holding uncle actually helped him on the westward drive.)

The point is this is a very easy game for even a six-and-a-half year old to understand (and play a round), yet still engaging enough not to bore my science grad student and Ph.D. friends.

Oh, and our 10-year-old niece won both of the first two rounds she played, and had the patience to play one particular overarching game all the way to the rulesheet-specified end.

(The Trans Europa/America points system is similar to Hearts in that you're trying to avoid being charged points, indeed to have the fewest whenever someone hits a specified milestone.)

Trans Africa

Pro: Brazzaville and Kinshasa just a double-line track away from each other.

Con: The southern group of cities might be too bunched together. (Jo'burg, Capetown, Durban, [...]?) Mabe just give South Africa (and its surroundings) the Florida (non-Jacksonville) treatment and make that group be Luanda, Lusaka, Harare, Maputo, Dodoma, Gaborone?

Cecil Rhodes would surely disapprove.

Anyhow, we now own Trans Europa, and over the weekend I made a homemade map identical to the Trans America layout. As soon as I get around to finding playing cards w/five different color backs, we can replicate Trans America using tracing paper on that homemade board.

(And really once you have the concept down and an free easy source of printable triangular (NOT hex!) graph paper, you can design a map of anywhere you want.)

The Ultimatum Game

Have you read about this?

Two anonymous parties interact only once. One is told to split an amount of money; the other then either accepts or rejects that split. If the second player accepts the split then players divvy up that money in the specified ratio. If the second player rejects then both players get nothing.

I just took a sex of your brain test (apparently I'm quite masculine, including 11 out of 12 on a surprisingly difficult spatial test) that had the ultimatum game as part of it.

They asked how you'd propose to divide 50 pounds if you were the first player in the ultimatum game. I made a snap gut decision (incidentally, the dollar is weaker than I thought it was but not strikingly so).

So yeah: 50 pounds. Divide it up, knowing that an anonymous person would get to accept the offer (you get what you allocated to yourself, other person gets the rest) or reject the offer (you both get nothing). Make your call before you read on.

I demanded 35 pounds (thus offering 15 pounds). I wince at how much money I seemed to be "leaving on the table" but did feel somewhat risk-averse about whether an anonymous person would just hose me out of spite.

Two Games

Play within your browser. Requires Java but does not require any emulation.

Montezuma's Revenge (this site has another, vastly inferior, MR instance that unfortunately has a much higher Google PageRank).

JezzBall

The Year 2100 Is Not A Leap Year

Years divisible by 100 (but not by 400) are not Leap Years. Since 2000 is divisible by 400, it came off as an application of the Leap Year rule instead of an exception an exception.

This thwarts what I'd previously thought of as a nifty calendar fact: At least between 1901 and 2099 there's a repeating 28-year cycle of day to date.

Questions for astute readers (based on a trivia question I wrote that was returned to me, probably correctly):

1. Why is it a 28-year cycle, rather than 27 or 29 or 14 or some other number?

2. In particular, how many days over a period of exactly 28 years (some time between 1901 and 2099) will it be Friday the 13th?

The answers to both are fairly simple.

LOL Dimeaments

If you were at the deathbed of a woman you secretly loved all your life but whom you never had the courage to tell and then she tells you that she secretly loved you all these years, what a great opportunity that would be to practice your "poker face."
--Dan Liebert, Verbal Cartoonist

At the bank today I changed a twenty into two rolls of dimes and ten ones. No questions asked, though I can't immediately think of any legitimate, non-business use for two rolls of dimes. Even the illegitimate uses just scream out for better herbs and/or higher stakes.

Wikipedia used to have a donkament page; it now redirects to a list of poker jargon that doesn't even include the term. (The phrase "LOL donkaments" and variants used to be in vogue on certain 2+2 message boards. Right when I stopped reading those the meme was being run into the ground.)

Anyhow, I claim that even for home play ring games are better than tournaments. Your mileage may vary, but the only real hassle with a ring game is making change, while tournaments involve getting everyone to show up (sort of) on time, keeping track of when blinds should go up, reaching a consensus on whether to allow rebuys and when, prize structure, etc. Then the whole thing comes down to five people each having about ten times the big blind worth of chips, pushing if you're the first in with a decent hand, and hoping for the best.

(Note to the wife: Yes, that last sentence sounds like a claim that poker is about luck. Really it's that a particular structure of poker has decisive luck.)

One time I drove eight miles to play cards with friends. After I got there we spent 45 minues watching the Colts and Patriots (Thursday season opener) and waiting for critical mass. Very first hand was set over set. I calmly walked right out the door (they caught up with me to collect the buy-in) and went over to the office to write trivia questions. In a rink game that'd just be a rebuy (admittedly in a tournament with rebuys that would also just be a rebuy).

(I've often driven 35 miles to play cards with friends near Stanford. One of two things is true: Either that same hand would have given me a one-and-done after a 35 mile drive, or the distance I drove would have affected how I played a hand.)

I know someone who strongly prefers tournaments to ring games because he believes he's a much better tournament player than ring game player. Such people do exist (Phil H., for one) but I'm not convinced, hand-by-hand, that ring play is all that different from how you'd play the early stages of a rebuy tournament. That said, apparently (before the big U.S. crackdown on on-line poker), the tournaments at the leading on-line poker site were much softer than the cash tables.

Brain-Dead Story Problem of the Day

From one end of I-40 to the other troopers across eight states will be out in record numbers to keep the highway and drivers safe. [...] Under the program state troopers will be positioned every ten miles along I-40.
--Troops out in record numbers along I-40

Length: 2554 mi
Miles km state
155 249 California
359 578 Arizona
373 600 New Mexico
177 285 Texas
331 533 Oklahoma
284 457 Arkansas
455 733 Tennessee
420 675 North Carolina
2,554 4,110 Total
--Interstate 40 on Wikipedia

"The Highway Patrol said they couldn't say how many troopers would be on the roads [...]" --ibid

CAN YOU?

I did learn something from this exercise: The easternmost part of I-40 is so circuitous that the shortest distance from Barstow, CA, to Wilmington, NC, is actually 30 miles shorter than the length of I-40. It dips through South Carolina.

An Anecdote About Prodigy-Based Movies

Thinking of quasi-scholastic pursuits turned into movies reminded me: (I've probably told this a million times but to me it never gets old.)

1992 High School Chess Championship (Lexington, KY). [I played in the Open division despite being eligible for the Under 1600. They actually had trophies just for people like me, and I took home a trophy for having one of the N best results (4.5 of 7: D L W D W D W) among under-1600ers who "played up" into the Open.]

One of the championship contenders was Josh Waitzkin, whose dad had just written the book about him that would later become the movie. After Waitzkin lost badly in some climactic game, a joke circulated around the floor that the sequel would be called STILL Searching for Bobby Fischer.

Child's Games: A Strategy Guide

The rock-paper-scissors reference reminded me: I've been sitting on this one since our visit to the niece and nephew ten days ago.

Clue Mysteries (obviously not to be confused with the original Clue): My first strategic act was a clear mistake. Visiting the police inspector is a waste of time. Once you've visited enough people to unqiuely identify a suspect (if everyone you talked to were truthful), the probability that they're all telling the truth is way more than the probability that you'd beat your N opponents in a race.

Franklin Goes to School: When you answer a question correctly (or not), one square is at stake. Compare to the spinner variance and the card drawing variance. So much luck is involved that this is a flimsy framework within which to read elementary school questions off a card to kids who don't think of themselves as being quizzed.

Pet Detectives (card game): This is a great simpler case of Canadian fish. The best strategy just seems to be a good memory. If I knew more about what the different outcome cards did, I could recommend going for either the "cheaper" pets or the "costlier" pets.

Mario Party: The key to victory is stealing other players' stars, by an overwhelming margin. Coins are just the intermediate step of being able to afford to ride a vicious dog or whatever else it takes to steal those stars.

One somewhat strategically interesting game-within-a-game is "Same Is Lame." I assume table talk is discouraged, but the more obvious you can make it that you're always going to press the same button, the better you'll do. (If everyone knows "Matt is always pressing B" then nobody gains anything from also selecting B. To be sure, this would result in a standoff if four players settled on unique buttons, but hey.)

A Disappointing Meta-Disappointment

I was all set actually to solve the "Sudorku" in this past Sunday's Foxtrot, except that for some reason I was dead certain that 252/36 wasn't an integer for spurious reasons relating to the fact that 2 * 6 = 12. Then I actually bothered to type "=252/36" into the cell of a spreadsheet.

Apparently I'm the worst number theorist ever.

I missed the specific brainteaser but worked out the general case a day later

(But now I think the general case is actually easier to solve aside from the fact that it's so much more more confusing to explain. Anyhow, we had dinner Tuesday night with a family that has twins in eighth grade, one of whom stumped us. You've probably seen the specific version somewhere.)

N soldiers (but only one feeble lantern) are traveling at night when they reach a mountain bridge that all N of them (N > 2) need to get across. From past experience they happen to know with complete certainty that:

1. Each soldier can cross the bridge alone in a specific amount of time (either direction, always the same time interval). Without losing any generality you can sort those times from fast to slow and represent them as x[0], x[1], ..., x[n-1], where x[i] <= x[i+1].

2. If two soldiers cross the bridge together, they'll always take exactly as long as the slower one would have taken crossing alone.

3. The bridge cannot hold more than two people; it would fall apart and kill all three (or more).

4. Nobody can so much as stand on the bridge without being in immediate proximity of their light source (that one feeble lantern, which as you might guess will keep going back and forth) or else that person will misstep in the dark (or, if standing, lose their balance) and fall to a grisly death.

5. There is no hidden way to conjure up more light sources, circumvent the bridge, or anything else that would make this a lateral thinking puzzle rather than a math problem.

6. Luckily for them, the instant one or two people finish crossing the bridge, anyone making the opposite crossing can grab the light and immediately be recrossing with no time lost in the transfer.

Now, give me both the strategy that always minimizes their time to cross, and the formula that expresses (in terms of x[0], x[1], ..., x[n-1]) that time. It can be a conditional formula (it very much is conditional) but you have to describe the conditions precisely.

Some time soon I'll write up my answer (I'm confident I'm right; whether I succeed at a rigorous proof is to be seen) and put it in the extended entry.

UPDATE: Inelegant solution posted (I idly wonder how many points it would get on a Putnam problem - 6 of 10?). Oh, and if you just want a brainteaser that's tricky without being confusing, then here you go:

Same facts as above, but it happens to be four soldiers. A takes 1 minute, B takes 2 minutes, C takes 5 minutes, D takes 10 minutes.

Base cases:
N=0, time = 0 (no crossing is necessary)
N=1, time = x[0] (one crossing)
N=2, time = x[1] (one crossing)

N>2: One crossing is not enough, in fact the lantern now has go back (and be carried by at least one person), so there's a maximum net gain of one person for each pair of crossings until the final step. So for N>2, we need at least 2(N-2)+1 crossings [also known as "2N - 3"].

A reasonable plan for N>2 is for the fastest one to hold the lantern all the time and escort the others one by one. That strategy has time x[n-1] + ... + x[1] + (N-2)*x[0], where the last term is the sum of all the return trips and the other terms are the individual forward trips.

I believe it's easy to prove that any successful maneuver with more than 2N-3 crossings has some easily eliminated redundancies, though I'll "leave that as an exercise to the reader," with mild regret that I didn't find an elegant way to nail that part of it.

Anyhow, when N=3 the best you can do is x[2] + x[1] + x[0]; any possible set of crossings is exactly that fast, or slower. So we have well-known solutions for N=2 and N=3.

Now what if for a given value of N soldiers, we already knew the general solution for N-2 soldiers?

There are two ways to simplify the N problem to the N-2 problem by getting the two slowest soldiers across the bridge first:

Either 0 escorts (n-1) and (n-2) one by one -- taking time 2*x[0] + x[n-1] + x[n-2].

Or, 0 escorts 1; n-1 and n-2 cross together; 1 takes the lantern back -- taking time x[0] + 2*x[1] + x[n-1]. Whichever of those two is faster depends on whether the average of x[0] and x[n-2] is greater than x[1].

(Example: The canonical form of the brainteaser is four soldiers, where x = [1,2,5,10]. They can do it in 17 minutes, not 19, because 2 + 2 < 1 + 5.)

The proof that "move the two slowest guys first to simplify the problem" is efficient involves these particular points:
1. To pull this crossing off most efficiently, the slowest two guys only cross the bridge once each. Any other way of doing it could be rearranged more efficiently by having them switch roles with people who cross just once.

2. Thus there's no way for the existence of the two slowest guys to make the subset of the other N-2 guys crossing go any quicker.

So the strategy:
Until there fewer than four guys left, get the slowest two guys at a time across. In each case, have the fastest guy escort them both if he's fast enough to make up for the second-slowest guy, otherwise have the fastest guy escort the second-fastest guy (and that guy bring back the lantern) otherwise.

The formula:
If N is even,
min(2*x[0] + x[n-1] + x[n-2], x[0] + 2*x[1] + x[n-1]) + min(2*x[0] + x[n-3] + x[n-4], x[0] + 2*x[1] + x[n-3]) + ... + x[1]

If N is odd,
min(2*x[0] + x[n-1] + x[n-2], x[0] + 2*x[1] + x[n-1]) + min(2*x[0] + x[n-3] + x[n-4], x[0] + 2*x[1] + x[n-3]) + ... + x[2] + x[1] + x[0]

Ambiguity Aversion as a Built-In Swindle Protector

Read about the Ellsburg Paradox here (first post of four). The basic scenario: I have an empty urn and some red marbles, white marbles, and black marbles. First, I put a red marble in an urn. Second, I flip a fair coin; if it comes up heads I put a white marble in the urn, if it comes up tails I put a black marble in the urn. Third, I flip that fair coin again, same consequences. Finally, I give you a choice among these four games:

A1. Draw a marble from the urn. If it's red you get +2, else you get -1.
A2. Draw a marble from the urn. If it's black you get +2, else you get -1.

B1. Draw a marble from the urn. If it's red or white you get +1, else you get -2.
B2. Draw a marble from the urn. If it's black or white you get +1, else you get -2.

If you're astute at probability then you should notice that all four of these potential games have an expected payoff of 0, and moreover that A1 and A2 are functionally equivalent just as B1 and B2 are functionally equivalent. The "paradox" is that despite all that, most people polled will strongly prefer A1 over A2, and B2 over B1. (In both cases simplifying the problem to "red vs. not red" so that the outcome of the coin flips is irrelevant.)

Now, if you know what these probabilities are, and you're confident that your calculations are correct, of course you should have no preference. I assume that the people who do have a preference have this gut feeling that there's a trick involved, and so are gravitating to the simpler scenarios to minimize the chance of being fooled somehow.

Of course, some function of your risk aversion may cause you to prefer the A1/A2 odds over the B1/B2 odds (or vice verse).

Poker Ban Thoughts (By Request)

If you live in a U.S. state other than Nevada then depending on your jurisdiction on-line poker for money was probably already illegal. That said, I exceeded the speed limit over various stretches of 880 and 580 on my way to work, this morning and every morning.

A bill that specifically forbids using particular monetary sources to fund on-line gambling is a lot like (there are so many ways to mangle this metaphor, especially by holding onto it too long)... imagine that the technology existed physically to prevent cars from exceeding the speed limit of the road they were on. Requiring this technology would be some kind of dystopia.

There's a hardcore strain of political philosophy which insists that you should either enforce a law rigorously or repeal it. I'd be strongly in favor of repealing either speed limits or gambling bans but I'm not holding my breath for either one. In lieu of that, everyone should remember that there are only so many law enforcement resources available, and using them to go after Internet gamblers is farcical (unless we already won the Global War on Terror and I hadn't noticed).

As for me, it's been almost a month since the night that I uninstalled Party software at 5 a.m. I haven't looked back.

Funniest Phrase Ever

Courtesy of someone who sent e-mail to Bill Simmons:
Little League World Series of Poker

RuSTLING CARRIE(D) BEAtINGS

The card player in me can only dream of ever getting hands as sick as the tiles I got just now.

This Is Why A Formal Ban on On-Line Poker Will Pass Eventually

It would be a horrible law enacted for all the wrong reasons, but still:

"I just lost $600. My mom is going to kill me."
--this post, subject line "My life is over." I thought it was a troll but the original poster is apparently 18 years old and serious.

Does Anurag Dikshit Look Like Me?

The 10th richest man in India obviously has darker skin than me, and South Asian features rather than Ameriwhitey. Aside from that I'm startled by the resemblance, though I could just be hallucinating this.

Cash Out In Style

Apparently on-line poker is some serious booty.

Poker Thread of the Day

I laughed, I cried...

The premise of the first post is comparable to a quiz-bowl player bragging on a message board that he got five tossups in the same game once. The rest of the thread speaks for itself.

Before the original post, I knew that the original poster was widely despised and maligned (perhaps unfairly for all I knew). But I think you can easily see why.

Amusing Poker QOTD

Quoting from this post (about a No Limit game with $200 buyin and $1/2 blinds)...

(emphasis added for mockery's sake - feel free to bother to answer his final questions)

typical situation for me in AC. guy is MP (TAG, not a great read since its early) raises to $20. I call with 77 on the button, incredibly loose drunk guy calls in SB.

How can I even play a hand at a full ring table if its not tens+,AK+?

They Don't Spread Omaha in Omaha

On a cursory search they don't spread anything in Omaha proper. You can play Hold Em (but not Omaha) in Council Bluffs.

They don't spread Texas Hold Em in Texas, either, unless you're at an "unofficial" card room or on a boat. (Or unless I just didn't look hard enough.)

Chicago is probably played at home games throughout the Windy City.

Fun Little Math Puzzle

Consider a 128-team tournament. (Oh, I've been considering a 128-team tournament a lot lately...) Of course you know those teams could play seven rounds of power-matching without teams of unmatched record ever facing each other.

Now suppose 56 rooms are available, which means each round at least 16 teams have a bye. Suppose someone asks you, "Can't you just stretch out the same 7-round schedule to eight rounds, giving each team one bye?"

Prove as elegantly as possible that, in fact, you can't do this.

(That is, it's impossible to schedule 128 teams for an 8-round, 56-game-per-round tournament where each team gets one bye and each game features teams with exactly the same record.)

Although I already have a correct(?) and reasonably brief proof, I'm sure someone can nail this much better than I did. Bonus points if everyone who hears the explanation (even the math-phobic) immediately understands its correctness.

Poker Quote of the Day

I'm a student at FSU and a major in mechanical engineering. So, im 20, and i know all the mathematics there is to know in the world. I've mastered calculus down to a science. So basically, yeah i get statistics.
--this guy, who can't understand why he isn't winning at live poker

I'm not even sure which claim amuses me more between "i know all the mathematics there is to know in the world" and "I've mastered calculus down to a science."

Card Forum QOTD

(From an obvious spam posting)

"sorry for my bad english i am the french"

This same forum had a running "BUSTO!" meme ("BUSTO!" = lost all your money; don't forget the caps and the exclam) that, thanks to an anti-bot capcha prompt somebody got, is now apparently a running "BUTSO" meme.

My New Favorite Opening Paragraph

As genre (non)fiction goes this is pure quality:

I think Small Stakes could use a little nonfiction prose now and again to spice up a place filled with bad advice, uninteresting hands, petty drama, and dry strategy. So here's what happened to me tonight leading up to the largest pot I've ever been involved in live.
--Private Joker

OMFG

Play video games against your pet.

I'd also love to compete against celebrity animals and quasi-celebrity animals. Pretend to be a lizard and get Nardo from Is Full of Crap to chase you.

Proof That On-Line Poker Is Rigged!

This is hilarious.

Every time I write about the curiously widespread belief that poker is rigged, I want to append "TINC," though my sense is not enough people would get the reference.

The Doggie Check-Raises!

So cute!

Party Poker runs ads on the video feed in our office building's elevators. In one, this very large dog (collie? husky?) has cards in front of him. He taps his front paw on the table twice (the part I hadn't previously noticed), then cut to some sort of graphic, then he pushes chips in with his snout.

The fact that it's a check-raise makes me especially amused. Now if only Party allowed user-defined avatars, or at least made it possible to have a canine avatar.

Silly Little Math Puzzle

Four (4) golf buddies are on a business trip and take time out to visit a five-course resort. They have enough time to play three (3) rounds of golf but no more than that.

Their first choice was to stick together as a foursome and try out three of the five (5) courses. Unfortunately, this is a popular resort with plenty of tee times on all five courses for a twosome to join another twosome but no space for a foursome to stick together.

As these are competitive types they get another idea: Why not a round robin tournament? Since they have time for three rounds, each of them can get a match in against a different opponent. So how hard could it be to figure out a schedule where in the span of three "rounds" they each face each other once, and each of them gets to try out three of the five courses?

In fact, as their math geek buddy immediately told them, it's impossible to schedule them a full round robin in three rounds without making at least one of them play the same course more than once. Exercise for the reader: Explain as simply and elegantly as possible why that's so.

Basketball (And Card) Thoughts

Nobody else at the card table from last night seemed to notice my called shot on the end of the Texas game. ("But here it comes [...] there it is [...] yep.") Since the host has Texas ties he was too busy being elated.

Then he had to come back to the table and deal the turn.

Two things that will happen often when people attempt to play PLO8 (pot-limit Omaha hi-lo, 8 qualifier) in person:
1. Button deals (just) two cards to everyone, then a pregnant pause.

2. Someone asks how big a pot-sized bet/raise would be and two other people disagree on the correct answer.

Back to the hoops, I'm sure a million people have mentioned it but the biggest upset of the night in my opinion is that after the postgame display J.J. Redick put on, Adam Morrison still managed to out cry-like-a-girl him.

Games From My Birthday Bash

Wow, this is almost two weeks ago now. Thought I'd blogged this but apparently not. (Thanks to everyone who wished me happy (belated) birthday. Not at all necessary to do so but appreciated all the same.)

The biggest hits of the party were the Trivial Pursuit Pop Culture edition (w/DVD) and the card game Guillotine. On the latter I pulled out a sweet unexpected (at least I didn't expect it until the opportunity arose) victory that involved bringing Day 3 to an immediate end just when I'd taken the lead. Woo Scarlet Pimpernel card.

Turns out we had quite a French nomenclature theme to the played games (Milles Bornes and Carcasonne also). And I killed Dr. Lucky in the Foyer with the monkey paw, long after the game seemed to reach "up for grabs" status. The field did muster four Failure points but would have needed eight.

Contrary to Popular Belief, Tuesday Was Not a Geek Holiday

Maybe some misguided math people thought of it that way, but when they say March 14 what they really mean is 22 July.

The Natural Tendency to Assume Something is Rigged

I suppose it's not that much worse than other cases where people overreact to the appearance of clustering caused by true randomness (localized cancer scares, et al), but it's still funny how often it happens.

Really funny quote from a poker-themed bulletin board today. I'll paste the whole thing but be a sport and click here anyway and then click on an ad or two:

People who think [well-known poker site] is rigged are thinking waaay too small.

So, shhhhhhh...

Scrabble Problem

Here's a bitmap of an Excel rendition of the board at the critical point. (Yeah, could've just taken a cell phone picture of it, but why do something that simple?)

It's the protagonist's turn and he is trailing, 297 to 328, but has a sweet rack of ADILNST. (One can also figure out the opponent's rack since both players have 7 letter but no other letters remain. Note that both blanks have already been played.)

I'm about to find out the best play myself (I'm almost dead certain there is one) but I played something less than the best. In addition to finding the best play yourself, an exercise for the reader is to reconstruct how the game actually came out.

(Specific plays, not just "protagonist loses.")

Answer(s) as appropriate in a couple days below the fold.

Apparently no win-by-force existed after all (i.e. couldn't find a bingo despite the great tiles and opportunistic hanging tiles).

I got 32 for the triple word score "lands" (turning "hove" into "hovel") but she pwn3d me with "quey" ("ag" into "age") for 36 and the insurmountable lead. Note that "queue" also ices it for her.

Two Card Game Variants

These are both from Mike Develin*, one of which I'd long since known of but never actually played, one of which seems to be very new.

*- In the midst of a five-year paid math fellowship also deeply into bridge.
1. Creights. If you like Uno this is a thousand times better. More of a party/social game than a strategy game but there are some tricky decisions especially involving 3's and devious ways to induce/avoid shuffle pressure.

2. "Endgame Poker": 2-4 players are each dealt 13 cards and play eight leads of a generic trick-taking game (must follow suit if you can, discard anything if you can't, nothing is trump). Once each player has five cards left, best poker hand wins. Despite the victory criterion and name of the game this is very much a bridge strategy trainer rather than poker strategy per se.

Signs That Cards Are On The Brain

ESPN.com just showed a headline "All Hail the Flop." From the accompanying graphic it seems to be about basketball, though that wouldn't have been my first guess.

Several weeks ago two ladies were talking in an elevator and one of them asked, "You folded that?" From context they were talking about some article of clothing.

The main Starbucks I go to both have big signs that say "[something] Station" that I always parse as "calling station."

Empathizing and Systematizing

Blah blah take these tests blah blah small sample size blah psychobabble quack.

(Me: EQ = 26, SQ = 40. Very much not a woman, but not nearly as much of a man geek as everyone knows me to be.)

How High Would You Have to Be To Enjoy This?

Although I've never used drugs in my life (that you know of - and anyway heaven knows all the caffeine more than makes up for eschewing the illegal stuff), I could actually see myself doing this after a bit too much chemical alteration. It wouldn't even take that much.

Geek Malfunction

I went over to set up my password for a new piece of software. The trip would have been perfect had the song stuck in my head been the Super Password theme; instead, I realized after a few seconds it was actually the Scrabble theme.

Therefore my new password was an inadvertent double entendre that made Chuck Woolery guffaw.

The Better You Are At Math, The Less Risk-Averse You Probably Are

Read this article and answer the various questions honestly.

I nailed the quiz questions and went with each bigger risk, bigger expected payoff option.

For a quick 10 points, name a particular card game that I might also happen to find interesting.

Good Reading About Bad Beats

One of you is on a downswing (you know who you are). That run you complained about, five times in a row having a pocket pair that lost to an inferior pocket pair, is about a 3000 to 1 misfortune.

(Well, 3000 to 1 on those particular hands. A bit less unlikely that you'd have such a sequence at some point or other.)

If you like commiseration (or Schadenfreude), the Beats, Brags, and Variance forum on twoplustwo.com is nifty. It entertains you without making you think very hard.

On the other hand, Tommy Angelo has a great essay on this theme, called Sympathetic Vibrations. All poker players Everyone should read this and aspire to that attittude in life, not just poker. All non-poker players should read this and aspire to write as well as Tommy Angelo writes. (Read his other articles as well.)

Quick Scrabble Report

I forgot to blog this the previous time (though I have available a spreadsheet with final board and moves), but thanks in part to the Z remaining in the bag until the bitter end, she beat me last time, 319-317.

This time we used exactly as many Triple Word Score squares as Double Word Score squares (six apiece). Also, I only got to take 14 turns, resulting from our unusually lengthy (for us) words.

From my 12th move on:
RELATION (and IN), going down the column just to the left of the middle column, 63 points for me.

RELATIONS (and SQUIRMS), 26 points for her.

THREAD off the "R" in RELATIONS, after I looked forever for a bingo (rack was BLTHED#) but couldn't find one; 21 points for me.

IRONIC (and ID), upper right Triple, 30 points for her.

BET (and ET), upper middle Triple, 17 for me, knowing full well she had one letter left and would end the game somewhere random.

She got 3 points with her last E and the "LU" left on my rack pulled us within 347-307.

Oh, other Triple Word Score words: FIRST (left middle, going down), AVERT (bottom left, going across), WIFE (bottom middle, going down, she got 42 for a word that will soon describe her), and ZING (right middle, going down).

Business Brainteaser

Consider the 20 years (80 quarters) from 1991 through 2010. What business logic led to the distinctions you see below? (i.e. what do "Foo" and "Bar" mean?)

Foo:
1991 Q2 and Q3
1994 Q1
1994 Q4 through 1996 Q3
2000 Q1 through 2001 Q4
2002 Q2 and Q3
2005 Q1
2005 Q4 through 2007 Q4

Bar:
1991 Q1
1991 Q4 through 1993 Q4
1994 Q2 and Q3
1996 Q4 through 1999 Q4
2002 Q1
2002 Q4 through 2004 Q4
2005 Q2 and Q3
2008 Q1 through 2010 Q4

Technically Bar (as seen above) but essentially Foo:
1993 Q1, 1994 Q3, 1999 Q1, 2002 Q1, 2005 Q3, 2008 Q1, 2010 Q1

Silly Game Theory Problem: 5 players, Case 1

(See the post immediately below this one for the statement of the main problem.)

Suppose P1 takes the aces of spades; P2 the ace of hearts; P3 the ace of diamonds. (So far, suits haven't lost any generality.)

On first pass I'm reasonably sure P4 should take something like a 7 6. (Which suit is another matter, with perhaps surprising complications.) Explanation below.

If P5 takes kings, P4 will go for 76 suited and P3's aces crush everyone (but 76 suited still surprisingly robust). With optimal poker players and game theorists, the idea is that P4 knows that P5 knows this.

Example (P5 takes Kings): P1 and P2 are in sad shape. P3's aces are around 39%, P4's 76s around 22%, P5's kings around 16.7%. Note that in this line, it's important that P4's suit matched P3's suit, since the best P1 or P2 can do is suit their own ace. The suits of the kings don't make a big difference.

Example (P5 takes AKs): With the pocket pair, everyone's best chance (other than their own suit's flush) is the best non-ace unique overcard they can grab. (Further research suggests that 66 does slightly better than 77 here, probably related to 4-straight boards.)

Contrast the above to:
P4 takes the case ace, P5 takes kings and crushes everyone.

P4 takes a king, now P5 can't do Ax(s) without P4's kings crushing everyone. But if P5 takes KK himself, P4 has disincentive to prevent P3 from AA. Best for P5 seems to be 66, which is just like the above only with P4 and P5 switched.

If P4 takes the 6d and P5 does something weird like Ts 9s, then P4's best play is another 6 even though it allows P3 to get AA (and crushes P5). This is partly because P4's first card isn't the same suit as the case ace (making the threat to let P3 get AA more credible).

Silly Poker Game Theory Problem

N people decide to pool some money for a one-hand, winner-take-all, "everybody is all in" Hold Em poker showdown.

But instead of dealing the down cards randomly, they decide that they'll have a two-round serpentine draft (fantasy sports style) to see who gets which downcards. Then the other cards will be shuffled for the dealing of the board. (They draw lots for draft order.)

Assume that they are experts at both poker and game theory and that they draft optimally (and expect the same from each other). Oh, and also U(w) = w, so nobody's worried about minimizing variance. What result?

N = 1 is nonsensical.

N = 2 is trivial. Both end up with pocket aces and probably chop.

N = 3 is somewhat interesting. If P1 takes an ace then P2 is in a bind: At least one of his opponents will have AA. He's better off with 76s against {AA,AA} than he would be with Ax against AA and some other Ax. (I believe 76s is his best possible hand against competing pairs of pocket aces. 25% equity; KK are about 20%, with lower pairs about 22%.)

N = 4 seems to result by force in four flavors of AKs, unless I'm missing something really subtle.

N = 5 is extremely tricky (before that, nobody can take KK without giving someone else a chance at AA; here, though, KK is a monster against four flavors of Ax). More on N > 4 later.

Optimal Wishing: Part 2 (Your Djinn as Chit)

Thinking over Richard's comment (below) led to a brainstorm:

If I am allowed to disclose to the world that I have a wish-granter, then in theory I could auction off my wishes to the highest bidder and thus get ample compensation without actually spending any of the wishes.

In theory.

In practice, perhaps a wise djinn would forbid this alternative just as it's forbidden to wish for more wishes. Also, the highest bidder might be someone whose wishes I would find monstrous. If there is a bidding war between (say) the Bill Gates Foundation and the Saudi Arabian monarchy, game theory might come into play depending on whether the Gates trustees see my selling to the Saudi monarchy as a credible threat.

If you are allowed to seek outside help for your wishes then you should probably bargain with some entity that has ideals similar to yours*, tremendous collective intellect, and a whole lot of money. (Harvard qualifies on at least two out of those three.) Then they compensate you personally and are, one would think, in close to ideal position to draft the wishes as cleverly as possible.

*- Though if you do use your N wishes to cure N forms of disease, chances are you'll become as rich as you're supposed to become from at least one of those patents. Richard's comment about how the patent system should work is dead-on, though I know enough inventors to realize that it doesn't always work as it should.

Anyhow, we're reasonably smart people ourselves. Let's assume from this point on either that our djinn forbade us from outside help once his existence was known (hmm, does speculation like this reduce the chance of one of us finding a djinn from epsilon to "epsilon over N"?), or that we were the people asked to draft optimal humanitarian wishes.

(From this point on, all my best ideas involve spontaneous genetic mutations anyway, one advantage being that you don't have to worry about the logistics of worldwide distribution of dosages of medicine.)

Optimal Wishing: Part 1 (Money)

(Inspired by the Twilight Zone episode The Man in the Bottle.)

Not that this is remotely likely to happen to you, but if you were granted N wishes (with the usual "Can't wish for more wishes" restriction) and warned of the side effects of poorly defined wishes, would you be up to the task?

One's immediate selfish temptation is to wish for money. (I don't mean that "selfish" as pejoratively as that sounds. There are things that one wishes for with the primary aim of improving one's own life, and things that one wishes for with the primary aim of improving the world.) However, such a wish may be very unwise no matter how much you ask for.

The problem in TZ is that the wishers failed to account for their tax burden. The problem in the real world is much more important: Where did the money come from?

Remember that it's impossible to increase the world's wealth by increasing the currency supply. (Otherwise of course the U.S. treasury could instantly solve everything.) If you wish yourself some vast amount of currency, you'll devalue that currency and make a tiny bit worse the lives of everyone else who has that currency. Maybe you don't care about those people whose lives you've made a tiny bit worse, but at the very least this flagrantly violates categorical imperative.

You can opt instead to wish that money be transferred from some specific source (where it's not being used well) to yourself. Perhaps some corrupt African president, or the Walton family (but not Bill Gates: with his charities he's putting his wealth to extremely good use), or best yet the Harvard endowment. Good luck explaining to interested parties how the money got to you and why that's just. To be sure, they wouldn't have the power to resist you (can you wish that the transfer be purely voluntary: this seems to produce free will contradictions) or undo the transaction, but at the very least there's some serious ostracism to deal with.

(The corrupt African president in particular embezzled from foreign aid and/or charities; now, the money wouldn't have gone to its real causes anyway, but all the same can you sleep at night knowing that your money not just could have gone to starving Third Worlders but in fact was earmarked for them before the acts of theft that indirectly enriched you?)

For personal monetary enrichment, the only palatable option I see is to wish to win a lottery. It's still a zero-sum transaction (the granting of the wish, that is) but here the people who "lose" are people who can't possibly make a claim of entitlement to the dumb luck of winning instead of you (or winning more than they won).

Now, in the case of vast sums of wealth that you believe are misappropriated, you can certainly wish for a reallocation that makes the world better off, and if you're arrogant enough to think you'd yourself do a better job of resource allocation than you could even wish to be put in charge of that particular fund. ("Genie, make me a benevolent dictator over the Harvard endowment, so that this money actually makes the world a better place instead of just sitting there collecting interest.")

That said, I suspect one can easily describe material improvements that would improve the world much more than reallocation of currency ever could. For example, imagine a world where the Green Revolution had never happened; if you were to wish for Norman Borlaug or someone like him to breed better wheat, the difference you'd make would be so vast that it's hard for currency reallocation to even compare.

So that's about all I have to say for money, aside from an ethical question: Suppose you first wished to discover yourself a cure for cancer ("a cure for cancer" is shorthand here for generic wishes along those lines; we'll explore world improvement wishes much more precisely later), and second wished to be granted a patent on your work. You made the world a lot better place with your first wish, then greatly enriched yourself with your second wish, though it's hard to say convincingly at whose expense. Is this morally justifiable? Depends of course on how soon someone else would have discovered what you discovered, but maybe it's not so simple.

Anyhow, don't wish for money: You can do so much better. More when time permits.

Yet Another Scrabble Post

Based on post-mortem on-line searches, apparently there is no seven-letter word that anagrams to "E-SALADS." (I wonder whether anyone had that idea in the dot-com era, maybe if they were drunk or high.)

Given that six letters (if ending in "S") would be enough to hit a triple word score, SALADS was fine with me.

RETAKES also seems to be the only seven-letter word made of those particular letters. I had no place to hang it, though, and only a "C" on which to build an 8-letter word (and the C would need to be at or near the beginning of the word). I almost played CASKET, with the K landing to the right of a triple word score, but decided to pass instead.

Beloved obligingly made CHIT, except that as far as I could tell I still had no place to hang RETAKES. Took a chance and played TAKE for 13 instead of STAKE for 42. Redraw to get a rack of STEER-U-#. At this point every S or blank either had already been played or was in my rack. Although post-mortem search turned up "SUETIER", there's no way I'd have thought of that. Instead I casually played the "U" somewhere random and got to play STYRENE on the next turn.

107-point play (50 + 30 + 27), decidedly greater than the eventual margin of victory.

One cool side-light to this game was the minimalist vine of horizontal plays going up the upper right doubles: HI (also making "EM" to get twice the mileage out of the triple-letter score), MI, XU.

She got to make GROWS (TO, AW) and YE (TOY, AWE) on consecutive turns, which was pretty slick, plus REED (OR, NE, DE) as the game's third play.

Scrabble Report

She got both WIZ and HUNK onto triple word scores but he cleared his rack with EMITTING and got QANAT onto a triple word score.

(Six triple word scores in all; others were ORA, OWE, and PULSE.)

A Google search on qanat + "Brian Ulrich" revealed one hit, but it was this weird login-only news site that no longer had those terms after all.

7 Cards, So Many Possibilities

Analysis follows of a game of chance (and skill), if that's your cup of tea.

Seven players. Ante is 0.25 units, bring-in 1 unit, small bet 2 units, big bet 4 units.

Hero brings in with (Ah 6d) 2d
P1 calls with (xx) Qs
(fold)
P2 calls with (xx) 2s
(fold)
(call)
(fold)

5.75 units in the pot.

Three calls, no completes. Forgive me for not remembering the dead cards. At least three were black and none matched my ranks.

FOURTH STREET:
Hero (Ah 6d) 2d Ac
P1: (xx) Qs 3h
P2: (xx) 2s Kd
Other player: something non-threatening

Hero bets, P1 raises, P2 re-raises, other player folds, Hero calls, P1 caps, P2 and Hero call. Hero plans to check-fold 5th if it's not an A, 6, or 2.

About 7 big bets in the pot.

FIFTH:
Hero (Ah 6d) 2d Ac As
P1: (xx) Qs 3h Th
P2: (xx) 2s Kd 2h

Hero bets, strongly representing the AAA he does indeed have (or bare minimum aces up). P1 and P2 both raise, representing hands that beat aces up even though clearly neither of them has a made straight or made flush. Hero caps, opponents call.

About 23 19 big bets in the pot.

SIXTH:
Hero (Ah 6d) 2d Ac As 9h
P1: (xx) Qs 3h Th 8d
P2: (xx) 2s Kd 2h 2c

P2 bets, Hero calls, P1 raises. (Aside: It's obviously physically impossible for P1 to have a full house right now. The only other way he can already beat AAA is if he has J9 down and is psychic.) P2 raises, Hero caps, P1 and P2 call.

About 39 31 big bets in the pot.

SEVENTH:
P2 bets (to the surprise of nobody). Hero ... ???

(Partial Spoiler - nothing revealed in the link should surprise you.)

Spot the Random Walks

Like Alex, I was 3 for 3 on this survey and correctly forecast the stock's future price on two of the three.

Spotting a random walk is actually extremely easy. Predicting the future price of a real stock is basically extrapolation unless I missed some subtlety.

Poker Fallacy of the Day

(Actually of a few days ago.)

So with time on my hands the other day (having made a reservation at the Apple Store's Genius Bar for an iPod issue), I browsed the poker books at a local Barnes & Noble. They had two books on Omaha, one each by Warren and Cappelletti, neither of which stood out as worth buying.

One of those books, in describing the different flop textures relevant to Omaha-8 (i.e. the hi-lo split), explained that if there are two or more low cards on the flop then "high hands are devalued" because so many people will stay in for their potential low.

Before reading on, think a bit about why that statement is in one sense sort of close to accurate, though in a more important sense almost 180 degrees wrong. (And if it's obvious to you -- top of the morning, Nate and ZD -- then pardon the overexplanation after the jump.)

The trivially correct part: Well, duh, you'd rather your high hand take the whole pot rather than take half of it.

Why it's almost laughably wrong: The best high hand will still take at least half the pot, if not the whole thing. (Rarely will two people tie for best hand. Unless the board includes like KQJT, but we're talking about lowish and low flops anyway.) The best low might take half the pot, though if two or more people are both in on a low it's likely A2 vs. A2 (or A3 vs. A3 if a 2 is on the board), so they're fighting over half the pot. (Or none of it, if two low cards flop but the third low card never comes.) Let them fight as you waltz home with the other half. The bigger the pot gets, the bigger your profit from that arrangement.

(If you're in a situation where the high depends on a draw hitting or missing, say set vs. flush, then of course all the people chasing low give the hand that much more expected profit for both you and your high rival, even though only one of you will realize the profit that particular time.)

The nugget of truth it does contain: People who wisely stay in for their low (i.e. hands like A236, not so much hands like A2JJ) sometimes back into a straight.

(But if a straight is fatal to you, then you were vastly overestimating your high hand chances, split pot or no split pot. Flush draws and sets shrug off those low straights. Omaha isn't the kind of game where flopping "top pair" gives you much.)

DISCLAIMER: I am by no means an expert Omaha player. The last time I sat down (figuratively) for PLO8, from late position I cold-called a mid-position player's pot-raise while holding (AKT)9. Yes, I've heard the "never play a hand with a 9" rule of thumb. As a guideline it's very useful. And yes, I realize that the third spade worsens my hand even more than it would appear, to say nothing of the AK combo making it less likely that a second-nut flush would pay big. Anyhow, the flop came QJ8 in three suits. He pot-bet, I max-raised, and his AAKx never knew what hit him.

(Kind of a silly expression, since when the chips went my way, the reveal showed exactly what hit him. With the all-in already in place, the Q turn scared me for a split second before I realized that he probably had basically what he did turn out to have. The river was some generic low card, i.e. not third of a suit and more relevantly not an A, Q, or T.)

Robo Rally

We played one of the best games ever last night. I feel a little guilty, since although it was Paul who bought the game, he may not realize until reading this that we played it, all while everyone in his household slaved away at Berkeley quiz practice.

All that and the slow service at an Indian restaurant (whose fantastic food more than makes up for the service and odd ambiance) caused Mike to miss Arrested Development, leaving him to hope Paul taped it.

In any case, it's hard to think of a game that rewards spatial thinking more cleverly. Robo Rally's target audience is probably 12-year-old boys but I can't think of another game that works so well for young and old, for deep thinkers and people-at-a-party.

(Most games that work well at a party can only reward high-level strategery so much. But a chess mentality really does benefit you in the long run for Robo Rally, even as in the short run everyone is in the same boat and getting in each other's way and so on.)

Here's an on-line review. Given who created this game, I'm surprised I've never heard it come up in a trivia question (at least not that I remember).

Also, you can create your own boards!

I'm Even Geekier Than I Thought I Was

I really can't get into details without compromising confidentiality, but some things I've taken for granted knowing since I was about 10 were apparently less well-known than I thought, even to the geekiest among us.

Just to make this post not competely useless, I'll pose a general question for comment: How proficient were you at board games as a kid? Feel free to be as specific or general as you wish.

Game Theory and Dirty Dishes

[Note: All the work you see here is "home grown," though I assume that a standard game theory textbook would mention something like this in passing. If it reaches the same conclusions I do then bully for me; if it reaches different conclusions then my work has some subtle flaw.]

[Note #2: At the moment I think my household has at most a negligble number of dirty dishes; if I'm wrong I'll do them tonight just to thwart any real-world relevance of this problem. Re the continuation, there's certainly no ongoing "big fight" that I'm aware of.]

Morgan and Chris are two roommates with a lingering problem. Their dirty dishes cause them disutility, but the act of washing their dirty dishes is also unpleasant, though admittedly they'd both get utility out of their dishes being clean.

Suppose this were a game with one "round" per day of simultaneous action, where each player must decide each round either to do the dishes or not to do the dishes. The game may last arbitrarily many rounds, ending when (and only when) at least one player decides to do the dishes.

Each player's payoff is R - D - W(?), where D is the number of days on which neither player does the dishes, R is some constant reward that comes from the dishes finally being done, and W is some constant that reflects the unpleasantness of doing dishes [decrement W if that player finally decided to do the dishes; decrement W from the payoff even if the other player also finally decided to do the dishes that day].

Is it strictly in either roommate's best interest definitely to do the dishes on day 1 (i.e. D = 0)? If not, for the optimal mixed strategy, with what probability would you do the dishes on day 1?

You can also prove that the size of R is irrelevant; there's an easy way to do so and a hard way to do so.

The easy way to prove R's irrelevance: No matter who actually does them, the probability approaches 1 that at some point the dishes will have been done.

The harder way:
At the optimal mixed strategy, your roommate's payoff will be the same regardless of whether your roommate does the dishes or refrains from doing so.

X = R - W = pR + (1 - p)(X - 1)
= X - 1 + p (R - X + 1)

1 = p (R - X + 1) = p(R - (R-W) +1)

p = 1 / (W + 1)

So if you and your roommate have some unpleasant task, where each passing day that it goes undone makes your life worse but doesn't make the task any more unplesant, ask yourself: "Which would be worse? Doing it myself or having it go undone for N days?" Once you find the N where it's breakeven, then you can use the formula above (plus some random number generator) to decide from day to day whether to hope your roommate does it or just go ahead and do it yourself.

With one change this becomes the "Who apologizes after the big fight?" game. Now, if one person apologizes unilaterally then that person loses W and the other person gains W; if they apologize at the same time then there is no W and their payout is just -D for however many days passed before the apology.

Some algebra follows that I've handwritten but don't feel inclined to blog. Unless my computation is wrong I get W(p-squared) - (2W+1) p + 1 = 0.

Quadratic formula time.
a = W
b = 1 - 2W
c = 1

It gets messy (which I hope just means I botched something, since you'd think there'd be an elegant solution), but if the disutility of giving a unilateral apology matches the disutility of two days going by with no apology at all, then you should apologize with probability .5; if it matches the disulity of three days going by, then you should apologize with probability .232408 (that is, the quantity 6 - 1 - sqrt(13) all over 6).

Of course you have more than just one opportunity per day to apologize. You could treat this as the disutility of 72 hours (instead of 3 days) going without an apology, and with each passing hour you'd apologize with probablity p (very small) and do nothing with probability 1-p.

Very interesting things happen as you go from hours to minutes to seconds (i.e. let the time interval per round approach zero).

Silly Poker Puzzle

A card maven offers you a proposition: Given a fair, 52-card deck he will play one game of Texas hold em against you, with these provisos:

1. His hand contains the ace of spades and ace of hearts.
2. The ace of diamonds is out of play (discarded face-up).
3. You may choose any two of the other 49 cards for your hand.
4. The remaning 47 cards will be shuffled and five of them dealt out as usual for the board.

Instead of any rounds of betting, he will simply give you $3.00 if you either win or chop, and charge you $1.00 if you lose. In fact, as a token of good will he'll throw in a penny just for playing. (So, he'll give you $3.01 if you win or chop, and charge you $0.99 if you lose.)

Should you play this game? (Assume either that you're risk neutral or that you can play it arbitrarily many times.) If so, which cards should you choose?

(Spoiler follows.)

You should play this game and select the T9 of clubs. This is your only positive-equity choice.

The straight, flush, and two-pair draws give you a better chance than you have of setting any particular pocket pair. Clubs are obviously the suit with the best flush potential. As for straights, you want at least four real possibilities. JT or higher is inferior because the AT straight is extremely unlikely to come but 98 or worse is inferior because you're a bit more likely to be counterfeited even if you hit two pair.

(982 flop, T turn, T river and suddenly his AATT beats your TT99.)

If you've read this far you obviously know what counterfeiting is. Like when you're holding 55 against a T75 board. When another 7 turns, someone holding A7 gets really aggressive, and then a T rivers and your set 5's don't play. Don't you hate it when that happens?

Oldie but Goodie Problem

If you weren't already familiar with this math problem, you should be.

Prove that in any group of 6 people, there must be either a group of 3 people who are all mutual friends or a group of 3 people who are all mutual strangers. (Some assumptions: Friendship is symmetric — if I'm friends with you, then you're friends with me; and any two people are either friends or strangers.)

First solution is by far the best; I was gratified to see that someone had long since beaten me to it.

The Castle Tower Problem

The puzzle-blogging is a very welcome addition to Volokh.com. Go read today's entry (which I've seen via the main page but have yet to read comments) and try to solve it on your own.

Then read my comment (which may be a good solution or may be inferior and hand-wavy) and the Volokh.com post's comments, in either order.

LEMMA: Each hour on the hour, each guard will be at a tower.

PROOF: Each guard walks at a pace that takes him exactly around the perimeter in exactly one hour. The only event that causes a particular guard to deviate from his original speed/direction is an event that gives some other guard that exact same speed/direction from the exact point where the original guard was that instant.

REMARK: The relative order of the guards around the castle is constant, since they never pass each other (only meet each other and turn around).

A consequence of the remark is that at 1:00 there are 12 possible configurations of guards. Either they're all back where they started, or each guard N is at tower N+i (for some i between 1 and 11, with the appropriate modular arithmetic on the edge cases). At midnight each guard would be at tower N+(12i), modulo 12, except that obviously 12i is zero mod 12.

The Old Woman and the Airplane

This problem is fantastic.

I haven't fully read the comments, but I've seen enough to realize that a lot of people are dead convinced of something they're wrong about. I had the right answer but with a subtly flawed proof-by-induction constructed before seeing any of the comments:

GOOD ATTEMPT AT ELEGANCE:
When the old lady gets on the plane, she has one option that will guarantee that the last passenger gets the correct seat (she sits in her own); one option that guarantees that the last passenger gets an incorrect seat (she sits in that passenger's seat); and N-2 options that put some succeeding passenger (whichever passenger's seat she took) in the same position she was in.

Each time somebody's correct seat is open, that person doesn't affect the problem; each time somebody's incorrect seat is open, that person is equally likely to guarantee one outcome or the other, with i-2 other possibilities that just postpone the decision point.

BAD ATTEMPT AT INDUCTION:
You can prove by induction that if there are two or more passengers (counting the old lady) then the last passenger's correct seat is open with probability 1/2.

Case 2 passengers: She sits in her own seat with probability 1/2 and the other passenger's seat with probability 1/2.

Proof that "the N-passenger case has probability 1/2" implies "the N+1 passenger case has probability 1/2":

Consider passenger N+1 as (without loss of generality) the second person through the door, just after the old lady. Now there are three possibilities for where the old lady sits:

1. She sits in her correct seat, as does everybody else. This is also true in the N-passenger case, so passenger N+1 doesn't affect the problem.

2. She sits a seat that is neither hers nor passenger N+1's. Then passenger N+1 sits in the correct seat and thus neither the passenger nor the seat impacts the rest of the problem.

3. She sits in the N+1 passenger's seat. But then that passenger sits somewhere random, just as the old lady would have.

FLAW: The N+1'st seat makes it more probable than previous that the old lady would sit in a wrong seat.

My First Sudoku Composition

Done during a 2.5-hour meeting. Those of you who solve these, feedback is encouraged on difficulty, quality, and aesthetic appeal. I know there's exactly one solution; it's unclear whether all listed numbers are necessary for the solution's uniqueness.

UPDATE: Posted incorectly the first time, now fixed.

Fundamental Theorem of Poker

Every time you play a hand differently from the way you would have played it if you could see all your opponents' cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose.
--David Sklansky, The Theory of Poker

Sometimes a hand illustrates this principle really amusingly, even if it doesn't flatter me much.

Worth noting:
1. The non-round numbers resulted from a four-way chop when neither a bad pair nor overcards could beat the board's J-over-6 boat.
2. I don't usually raise with garbage. Once in a blue moon, though... so cough and roll your eyes, and take my pre-flop raise as a fait accompli (though whatever it might have advertised is worth considering on the flop).

So we have a T22 flop for two players. He and I can both be pretty sure neither of us has a 2. I've advertised a good hand, and now here I have top pair, bad kicker, and am bet into. What now?

Well, what does he have and with what probability? Maybe 2/3 of the time he has a T, and chances are he has me kicked (why call a pre-flop raise with T6 or worse... well, I guess if a myopic player were suited...), though the pair on the board gives me anywhere from 3 to 19 chopping "outs". Other possibilities are underpair (anything from 33 to 99 is plausible), overpair (unlikely: you don't cold-call JJ or better in the small blind, gotta raise that), or overcards. (Or garbage, but...)

Anyhow, after mulling this hand over a long time I stand by going in over him, because of the two opposite FTP mistakes he could make: He could mistakenly call with an underpair thinking I have overcards, or he could mistakenly fold with a good-but-not-great kicker thinking I have him kicked or have overpair. (What if he doesn't "mess up"? Well, obviously I don't mind if he folds an underpair - certainly better than if I folded to his bet, and if I just called what happens on the turn and river? And if he calls a mediocre kicker... well, there's the chopping outs.)

So sadly enough he had what he had (AT), and obviously if I knew he had that I wouldn't have gone in. Fundamental Theorem again. (Or an ironically appropriate fate for raising garbage?)

Obligatory EV:
In real life he has 82% (77% win, 11% chop).
If he had KT: 76 (64-24)
If he had QT: 70 (53-36)
If he had JT: 65 (43-46)
If he had T9: 61 (34-54)
If he had 99, then I'd have 91%.

***** Hand History for Game 2568664697 *****
30/60 Tourney Texas Hold'em Game Table (NL) (Tournament 15013538) - Sat Aug 20 18:41:49 EDT 2005
Table Table 14435 -- Seat 3 is the button
Total number of players : 9
Seat 2: matt979 (831)
Seat 3: wavetown (230)
Seat 4: stevelandis (861)
Seat 5: Renegade75 (1135)
Seat 6: Justasbob (361)
Seat 7: ZZ350 (775)
Seat 8: Dash4Cash7 (2190)
Seat 9: te999 (590)
Seat 10: KIKASVMAX (1027)
stevelandis posts small blind (15)
Renegade75 posts big blind (30)
** Dealing down cards **
Dealt to matt979 [ Tc, 7d ]
Justasbob calls (30)
ZZ350 folds.
Dash4Cash7 folds.
te999 folds.
KIKASVMAX calls (30)
matt979 raises (169) to 169
wavetown folds.
stevelandis calls (154)
Renegade75 folds.
Justasbob folds.
KIKASVMAX folds.
** Dealing Flop ** : [ Td, 2h, 2c ]
stevelandis bets (210)
matt979 raises (662) to 662
matt979 is all-In.
stevelandis calls (452)
** Dealing Turn ** : [ Js ]
** Dealing River ** : [ 3s ]
Creating Main Pot with $1752 with matt979
** Summary **
Main Pot: 1752 |
Board: [ Td 2h 2c Js 3s ]
matt979 balance 0, lost 831 [ Tc 7d ] [ two pairs, tens and twos -- Js,Tc,Td,2h,2c ]
wavetown balance 230, didn't bet (folded)
stevelandis balance 1782, bet 831, collected 1752, net +921 [ Ad Ts ] [ two pairs, tens and twos with ace kicker -- Ad,Ts,Td,2h,2c ]
Renegade75 balance 1105, lost 30 (folded)
Justasbob balance 331, lost 30 (folded)
ZZ350 balance 775, didn't bet (folded)
Dash4Cash7 balance 2190, didn't bet (folded)
te999 balance 590, didn't bet (folded)
KIKASVMAX balance 997, lost 30 (folded)

Sudoku Chindogu

Are you good at solving those newspaper puzzles but never entirely sure that your solution is 100% correct? After you've already done the logic once, do you find it tedious to recheck every row, column, and square? Does it feel like a waste of time manually to check your chicken-scratch against the published answer?

Your problems are solved! Just download this spreadsheet and type in the digits that you've just handwritten. In just 162 keystrokes you'll know for sure that everything represents appropriately.

Innumeracy of the Week

One thing I forgot to mention in the "complaining about TV shows" posts a bit below here:

GSN had a special "Comedians vs. Pros" poker game in which at one point two of the pros got into a pre-flop all-in showdown with KK against ATs (68% to 32%). An ace flopped and no help came, eliminating the guy with kings and prompting the commentators to describe the heartbreak of a "bad beat." WTF?

Even if you succeed 68% of the time, you will fail 32% of the time and that's just life. If your favorite baseball team is on the road, and with two outs in the ninth inning the other team's .320 hitter gets a walkoff two-run single instead of making an out to end the game, was that a bad beat?!

The more people propogate the mistaken notion that a 32% outcome is a "bad beat," the more bad play (and worse yet whiny reaction) will result.

To be more rigorous, you could call hitting a 32% outcome a "bad beat" if the prevailing player had bet in such a way that he was getting less than 2-to-1 odds, though in this particular case I think enough chips were already in that the ATs guy had at least his 68-to-32.

(It's nice to see the down cards and see the posted odds, but poker coverage is still woefully incomplete until the graphics department finds a snazzy way to include position and chip count, more importantly until the commentators explain why a given hand is so much better if 3 players are left than if 10 players are left.)

If you were to completely ignore pot odds, implied odds, et al, my platonic conception of a "bad beat" would exclude any outcome that had more than a 10% chance of happening. My dividing line is something like rivering a gut-shot straight draw (4 in 44).

I Had Odds

More East Bay poker: Fourth of nine, despite only having three four interesting decisisons.

Tabletalk held that I was tighter than usual tonight. If so then either I've been really loose in the past or I had unusually bad cards tonight, since I certainly bet a few hands harder than the particular cards justified.

Two pocket pairs all night (not counting the critically short-stacked hand). Fortunately one was aces on the button after cutoff went in (with nines). The other was 44 in a bad position and would have been heads-up had I called or raised.

Only one particularly interesting early hand for me. Limped UTG+1 with QJs. Folds to the BB, who checked heads-up. KQ9 flop. He pot-bet, I pot-raised, he called. Blank turn. Check, check (I had him on Kx, Jx, or Tx, the former more likely than the others, JT just scary enough that I couldn't pull the trigger on a bet). Blank river. He bet a little less than half the pot size. I wanted to raise to push out his bad king kicker -- but if he called or reraised with a good kicker or (more likely) two pair... anyhow, I called and he had to show his T2. [By the way, I think signature hands associated with specific poker celebrities get way overplayed.]

Called an all-in bet (by UTG+1) with A8s as big blind. $12.70 to win $17.70. He had AQo and it held up. That was probably bad.

Folded T9s on the button after BB re-raised me all in. Odds were about 1.6 to 1 but pairs (J or higher) were just too likely for me to have that.

On the first bubble hand, no SB; same BB as listed above. Called his all-in reraise with AQo, getting 1.76 to 1 (or, $74 to $42) and covering him by $6 (blinds about to increase from $2/4 to $4/8) with us as the smallest stacks. He had QQ - even at that, 30% instead of 40% isn't a disaster, not even as bad for me as facing AK, but just worse than 1.76 to 1.

So with my last $5 (minus ante) I actually got QQ on the button. Blinds called/checked. Axx flop: Bet, fold, and A4o eliminated me.

I'm not sure how much I should factor in bubble pressure to my second-guessing. Obviously I like my win-the-whole-thing chances better with 1/3 of the chips (3-way) than with less than 1/6 of the chips (4-way).

Poker: East Bay Style

7th 8th of 10. Hadn't driven to a no-limit tournament in what has to be over a month. I don't think I missed the feeling of driving back empty-handed. Notable hands to follow.

First showdown, featuring the two players who'd been loosest in the early going (though both might be a bit passive). I've probably badly misremembered the betting. UTG+1 limped, button raised, limper called. Kc Tc 6d flop. Bet, raise, call. Blank turn. Bet, call. 6c river. They ended up both in, AcJc eliminated by TT (river flushed but also boated).

Above-average pair for me in the BB (1-2 blinds). Tight, slightly passive UTG+1 raised to 7. I made it 15. He called, then checked an all-undercard flop. I jammed, he folded.

Two hands later I gave the 15 back to him: With 97s on the button I became the third limper. SB folded, BB (UTG+1 above) raised to 8 (entered the hand w/stack of 18). Fold, fold, I called. He jammed this flop with his last 10. Even though none of my outs hit, I'm glad I had the 3:1 (though barely). (Of course since I was actually expecting something like this, you could say I didn't have the odds, though the tiny chance he had what he did have (or worse) seems to make it okay for me.) Maybe a bad pre-flop call. Do you put 6 into a 15 pot with suited semi-connectors, facing one-on-one against a tight player who raised as BB? I'd have position on him, I guess, which can be nice.

Second showdown was KK eliminating JJ, all in as of the all-undercard flop.

Third showdown, AKs BB doubled up on AQs UTG (one of the big stacks), the BB going all-in on UTG's pot raise.

Fourth showdown, my own penultimate hand. 2/4 blinds, I'm BB entering the hand with 35.50 (counting the 4BB). Folds around to loose-aggressive SB (33 counting the 2SB), who makes it 15. I jam with AJo, he immediately calls with ATo and drops an s-bomb when he sees my hand. But a T flops.

With 2.50 left and 2 to SB, I put in my last chip against the BB and one limper. My A8o didn't flop anything useful.

So You Think You Know Tic Tac Toe

A few questions to waste your time test your knowledge.

Since I'm too lazy to make a clever graphical user interface, let 1 thru 9 represent the squares of a 3x3 board with 1-2-3 top row, 4-5-6 middle row, 7-8-9 bottom row.

1. X opens with 1. How many non-losing moves does O have? Describe O's non-losing move(s) succinctly.

2. X opens with 5. Same questions.

3. After the opening sequence 1-5-9, describe O's non-losing move(s) succinctly.

4. After the opening sequence 4-9, X has one move that wins with best play, four that lose with best play, and two that draw with best play. Which moves are which?

5. Up to this point, it's been implicit that X "wins" by completing three X's on a row, column, or diagonal; that O "wins" by completing three O's in a row; that the game ends when either of those happens or when all nine squares are filled without a three-in-a-row; and that if there is no three-in-a-row then a draw results. Oh, and of course that X and O take turns putting their own symbol in an empty square.

Let's keep the same game structure and terminating conditions but mess around with the goals. That is, a game still ends with three X's in a row or three O's in a row or nine squares filled; of those three conditions, one maps to "X wins"; one maps to "O wins"; one maps to "draw." (For example, three X's in a row means O wins; three O's in a row means it's a draw; a filled board without three in a row means X wins.) Of the six possible variants along these lines, is any of the six not a draw with best play?

(I believe all six are drawn with best play. Five years ago I proved this, at least rigorously enough for my own satisfaction, though I don't think I held on to the scratch paper with such "proof.")

Deuces, Short-Stacked on the Button

Joon and 13 of his friends each played at least ca. 80 minutes of NL tonight. Two more players (at least one of them really good) played at least an hour. I clocked in at about 75 minutes.

If you've read previous poker entries you know I'm relatively reluctant to blame bad luck, certainly compared to a typical poker player. That said... you'd think it's good to have the two maniacs to your immediate right and the passive-ish* player whose bets too closely match his hand strength (at the expense of probability theory) to your left. But it's not your night when your bets are consistently big-raised by the two tightest players at the table.

*- First time I'd shared a table with him but I stand by my quick assessment. Case in point, on an early hand he flopped quad eights in a two-player showdown and after a bet, big-raised all in rather than even bothering to slowplay.

Once tonight I won the blinds betting on the button.

One other time I defended my BB against an aggressive SB, pot-reraising his... {raise of the amount that would have been a pot raise against both blinds but against me alone was slightly less than a pot raise though more than a min-raise.}

Twice tonight my SB got me to a battle-of-the-blinds flop, with one hand one but a small net gain. (Pot bet, call, pot bet, fold; check, check, min bet, big raise, fold. On the former in theory a flush hit on the turn; on the latter, the lowest flop card paired up on the turn.)

Once tonight I limped into a four-way flop with suited connectors but folded after an unpromising flop and a big bet.

My descent from a peak of ~52:
As BB with KJs, called a short-stacked button's pre-flop bet; with a flush draw, called his all in bet leading to something like this hand. None of my outs came and he doubled up.

At ~38 and on the button with AKo, big-raised the opening bet to my immediate right. BB re-raised us both all in (I barely had him covered) and the original bettor folded. Despite the Bayesian analysis, I put him as too likely to have AA or KK for the call to be worthwhile. With AKs I'd have called.

At ~26 in EMP, I bet the pot with 88 and the strongest tight player at the table raised all in (covering me) from a SB.

At ~19 on the button with deuces, I bet the pot (still 7) and BB raised me all in. My call was a stupid gut feeling (stupid because I was wrong) that he had overcards. I spent the drive home wondering whether he'd have folded his 99 against an all-in bet to begin with. Even against random overcards, 22 isn't nearly enough of a favorite for that not to have been just a bad play.

Maybe the previous folds were too weak-tight.

Which Investment Would Have a Greater EV?

A. The purchase of stock in Party Gaming (incorporated in Gibraltar)

B. The deposit of real money in a Party Poker account, subsequently used in games on their site

Both of those rely on the enthusiasm of poker novices for the site in question. The question may just be academic; I certainly have compelling uses for my short-term liquidity. I do have to admit that both A and B are tempting though.

How to Bust Twice in Five Hands

...in a NL game that in theory doesn't even have rebuys.

0. Start with 40 in chips, .10/.20 blinds, 10 players

1. First hand, two to the right of the button, open with .60 .70 (the pot) in late position, take the blinds (up to 40.30), including the BB of a relative novice.

2. Second hand, three to the right of the button, open with .60 .70 (the pot) in late position on connected suited. After the aggressive, loose-early-but-tight-late player one to the right of the button raises to 1.20 1.70, tight-passive button raises to 6.206.00, novice SB inexplicably calls, and BB folds, call the 6.20 because of pot odds.

After an Axx flop gives you outs and aforementioned novice SB bets .50 (one little red chip) into a 24.50 pot, raise all in (that's 34.30 more). After only the tight-passive button calls you (with AKo), suddenly realize that you can't tell your red suits apart and instead of this coin flip you actually face this sketchy drawing hand.

(I actually had reasonable folding equity there: Suppose my button had KK or QQ instead of AK. Even so, maybe the novice SB had Ax and would have recklessly called me, who knows.)

When nothing hits, gaze longingly at the .40 you have left.

3. Four from the button, again with no earlier bets, make the all-in min-raise with A9o. Watch as everyone folds to the BB, who (correctly) calls before even looking at his cards. Watch him turn over two undercards, one of which hits.

(Watch the rest of Spurs-Pistons with the sound down, then futz around on your host's wireless connection, in theory writing quiz questions but in practice still licking your wounds and not actually accomplishing anything.)

With the blinds up to 2/4 (50-cent ante) and eight players left, seize the opportunity when the novice player has to leave on urgent business and an animated discussion ensues over how to continue. After paying her half the original buy-in, take over her 25 worth of chips with her (now you) one left of the button.

4. Fold 72o after a bet somewhere on your right.

5. Call AQs when the smallest stack goes all in and the biggest stack promptly goes all in over him. Mistakenly believe you stand much better pre-flop than you actually do (though of course you're still the favorite). Rejoice that the flop pairs your ace and gives you a flush draw. But curse the jack (non-club) turn and useless river card.

My ride never had (or claims never to have had) a hand better than 88, though he did manage to improve from 40 to a peak of 60. On his penultimate hand he was SB, folds all the way around to him, and with 42o he tried to push around an extremely tight BB but bet too much and was pot-committed when that tight BB raised him all in. No pair, but neither undercard hit. After supposedly getting several X2o in a row, by the time he was BB again he had 1.00 left over after his blind. UTG called, big stack raised all in, he called for a dollar more, UTG folded, and big stack hit the Q on his Q4s.

What Was The Best Board Game Available in 1985?

Going back to the games update (many posts below this), given just how recent the best board games are, it's interesting to think of people in their (our) 30s being game geeks given the comparatively fewer options available in childhood.

So we have the titular question: What was the best board game available 20 years ago? Long before Settlers, Puerto Rico, et al...

Scrabble is one possibility, still the best game of its kind by such a wide margin that I don't think there's been a serious attempt to make a better word/board hybrid in awhile. But perhaps Scrabble seems to deserve its own category.

Monopoly is tried and true, and probably a better multi-player option than Scrabble. I'd be a better person if I'd played more Monopoly, if only to gain better haggling skills (Settlers itself is often a good negotiation exercise).

What else might be in the running? Stratego (very underrated in my opinion; in contrast I find most other war-themed board games overrated)? Scotland Yard?

Chess, checkers, backgammon, et al, technically fit this category as well, though they too seem to be something other than a "board game" in the narrow fashion that this post seeks to define the term.

Gaming Report

Haven't had one of these posts in awhile - hadn't gotten together with friends for board games in awhile either.

Ticket to Ride: (twice, 5 players each time)

I'd never played this before but thoroughly enjoyed it and caught in quickly enough to what's going on. This seems like an ideal party game because the board's interesting, the play is strategic but won't come close to making your head exploded, and hey -- colorful choo choo trains!

Strategically this seems to boil down to efficient resource acquisition and not much else: Average as close as possible to 2.0 drawn cards per turn (i.e. almost always resist the temptation to do something other than drawing two cards) and you'll do fine.

The extra-ticket-drawing endgame decision is an interesting wrinkle that I can't fairly assess yet: Our first game I kept two really easy routes, focused way too much on completing them quickly, and then drew more routes (kept two, completed one, got blocked out of Chicago). Our second game I kept three long but compatible routes and eventually completed them all, building a comfortable lead that stood up (albeit closely) in the end.

It's not unclear to me whether there are situations in Ticket to Ride where you'd be wise to play a move that sabotages an opponent without helping yourself much.

From all those Settlers of Catan games, holding a big stack of colored trains was unnerving in that I kept expecting the Thief to strike and the remembering that there's no analog to that in this game. For pure gamesmanship I wonder whether that makes Ticket strictly inferior to Settlers. But then I really really like Settlers and am mildly surprised that it seems not to be as popular as a few years ago.

Acquire: (5 players)

I've come to despise Acquire but I want to do well at it just once, just as proof of concept. Most times when I do poorly at a game I assume I'm misplaying it and can adjust my game (c.f. various poker posts - I'm not one of these people who wrongly blames bad luck when he actually played badly), but specific to Acquire I swear I have the worst luck.

The last N times I've played I've started two corporations and been majority holder in both, plus one minority ownership wherever it was convenient for me to be second buyer. Naturally the corporations getting all the action have each time been the four I had no part of, while "my" three languish. Three corporations, for each of which some other player at the table also has incentive to help it, but I don't get the right tiles and my would-be allies either also don't or get the right tiles for higher priorities.

Killing Dr. Lucky (5 players)
It is what it is, the representative Cheapass Game. Fun to play, useful for unwinding.

Tigris & Euphrates (4 players)
After Paul left we needed a four-player game, though playing your first T&E ever with a 10:30 p.m. start time might be biting off a lot. At least, I screwed the pooch pretty badly on particular tactical blunders.

For all the insane assortment of tiny pieces (obviously T&E is deeply incompatible with any household of pets or young children), the premise turns out to be simple and elegant... okay, maybe not simple, but elegant all the same.

There's a chance this is the best game I've ever played, though I'd need to play again to see where I'd rank it compared to Settlers or Carcassonne. Although the deciding factors of a T&E game are the warfare, I suspect that there's an underrated implicit-collaboration aspect of T&E, where different players with leaders in the same kingdom vaguely resemble two players sharing a Carcassonne city. Trying to compare an internal strife red-tile showdown with the scramble for Carcassone farm dominance probably takes the analogy way too far.

I'm not sure how much I regret our failure to play Puerto Rico. As much as other people swear by that game, the fact that I forget everything I ever knew about it between different times playing it makes it hard for me to join that bandwagon.

Of my actual favorite games, our failure to play Carcassonne may have broken a small streak, while our failure to play Settlers continued a streak. Next time we need a game for 3-4 people I'll seriously push a return to Settlers.

(One of the Settlers expansions was just horrible. Exploration was involved if I remember right. I think that one might have been so bad that it killed the whole Settlers experience for some of my peers.)

Poker: Mojo Restoration

Until tonight I'd never eliminated two players on the same hand. Tonight it happened twice. I went through some absurdly bad cards in the early going (whole lot of easy folds at least) only to get great ones at opportune times late.

The second of the two happened with four players left out of 14 (all of us "in the money") and me on the button.

With a total chip universe of 560 (by one metric), reconstruction suggests that we entered the hand with:
SB = 130.50
BB = roughly 69
UTG = roughly 85
Button = roughly 275.5 (almost but not quite half of everything)

4-8 blinds plus 1 ante on this particular hand. UTG folds. With 16 in the pot I put in 30 (a raise of 22) on KQs.

SB (sometimes loose, often aggressive, despite those tendencies generally goes with EV over variance) raises all in.

BB (frequent pot-stealer, makes about the same bets with a variety of hands) calls all in.

Here I am with KQs, and the decision whether to bet 99.5 to gain roughly 231.5. My read is that BB has a legit hand, some better than average pocket pair (I hope not AA or KK). SB could have just about anything.

I guesstimated myself at 35% 25% (typo), usually not enough to justify 2.3-to-1, but this was a chance at a knockout punch, where worst-case I still have about 25% of the chips. Biggest think I can ever remember taking in poker.

Looking it up, of a few of the plausible combinations, I could be anything from 24.1% EV (facing AKs and tens) to 13.7% EV (facing AA and TT) to 38.6% EV (facing JJ and TT) to (as it turns out) 37.1% (facing A5o and TT).

I'm mildly surprised in hindsight that BB had exactly the hand I'd have wild-guessed for him. SB had a worse hand than I should expect (my guess would've been either a pocket pair or something like A9s). It's kind of amusing that the third best pre-flop hand actually has the best EV of the three. Anyhow, Q on the flop and no help to anyone on the last two.

--

With about 85% of the pot (in fact, where I don't have exact chip counts above, the estimates result from assuming I ended up with .85 exactly) the heads-up was undramatic. For posterity, after a few mutually tight hands (fold or bet-fold) I had 86s as BB when he called. I checked. Flop gave me a flush draw only (T42 or something). He bet, I raised all in, he called with J9s (hearts all around). Not only didn't the flush draw hit, but I got a 6 on the turn just for a quick and merciful ending.

--

My big turning point came not only after we merged tables with 10 people. All four of the first eliminations had happened at my original table, including the guy who got sent over to balance us at 6-6. (Both of us running short, my KTs as SB caught a king -- two of them actually -- against his button BB 88 when pre-flop I raised and he went all in (see second comment below, correcting my mismemory).)

At the same blind/ante levels, interesting contrast moving from table-for-five to table-for-ten, especially if you're one of four people whose table had had about 55% of the chips.

UTG I limped with QQ. Player to my left (who I had barely covered) min-raised. Very short-stacked late-position player raised all-in such that pending the action to my left, I'd need to put in at least 13.50 more with 24.50 already in the pot. When I exactly called the all-in bet, player to my left also went all in, immediately and with great gusto. Seemed likely we all had monster hands, high pocket pairs or AK.

Worst plausible case I'm 14% (Aces vs. Kings vs. Queens). Even second-best pair I'm only 17.5%. Of course best pair I'm golden, and as it happened I was 45%, turning into 100% when nothing on the board helped anyone ever.

(The short-stack was very self-critical of going all in with 55. At the time I thought it was justifiable - have to try to double up sometime, and why not triple up - though now I do agree it was a poor play.)

--

After the first one-two punch but before the second, some serendipity led me to get back in the head of the most risk-averse player I know. After several easy folds in a row, mixed with ill-timed steal attempts (at least the re-raises were multiple enough and aggressive enough to keep me out of further trouble on particular showdown hands), I was antsy and going into UTG though to myself "if I get a monster I'll bet big."

There's a meme involving sucker players who go all-in early with AKs. Sure enough, I saw my AKs and played like a sucker and went all-in UTG with it. Post-hoc rationalization was that if nobody had anything then I'd take the blinds no matter what I bet, while if someone did have something why not make them decide if they felt lucky? The blind-to-stack ratio for whoever might call me was almost exactly enough to justify a 46% EV.

Sure enough, my favorite risk-averse player agonized over his hand, finally calling JJ, only to see a K on the flop.

--

My original table had at least two "novices" (only relative to the people I keep seeing game in and game out). One ended up quietly dwindling to nothing. The other was very gregarious though ostentatiously unclear on various concepts, e.g. wanting to be reminded the exact order of poker hands. That plus beginner's luck suggested ringer to me, calling station tendencies aside. (Actuary, as table chatter revealed.)

That beginner's luck decidedly ran out before I could accept that this was indeed a novice calling station rather than a ringer, though my hands were so terrible that this particular opponent's skill level wasn't much of a factor for me.

Poker: You Don't Want Him On Your Left

My carpool mate sat directly to my left at poker last night. We didn't actually see the draw for position as I'd driven him on a quick side errand for allergy medication after he was surprised that the host's roommate had a cat.

5th of 9 for me (3rd of 9 for him), a hand or two to follow.

My second-best downcards of the night were 88 as SB on a hand where everyone folded to me. I believe if you're small blind and the folds come all the way to you then you should min-raise regardless of your hand. Alternatively, fold anything so embarrassingly bad that mucking it face-up might amuse people, and min-raise the non-worst hands.

My min-raise was called. 679 rainbow flop, my bet was called. Another 6 on the turn, my check[-raise] was checked. (Maybe it was check-check, then bet-bet.) Ten on the river, we end up all in, he has 82o, we chop. I had 92% EV pre-flop, "only" 83% once we both had the same outside straight draw. In the long run of course I hope he keeps playing that way.

--

My best downcards of the night were QQ as SB on a hand with three limpers. I raised the size of the pot (not very much, it was still early) and got BB to fold but all three limpers called. Kxx flop, I checked, checks all the way around. x on the turn (no pairs on the board, maybe a flush draw somewhere), I bet small, two folds, button raised me, I put him all in (the rest of my stake being about 1.5x what had been in the pot), he folded. Interesting question is what all the limpers had.

--

I had 66 on the very first hand (or close to it). I bet in a middle position, my carpool mate called, everyone else folded.

345 flop, I bet, he called. Random medium turn card (jack?), I checked, he bet, I called. He tabled talked something like "You checked? So if I bet you'll fold, right?" Something like a king on the river. I checked, he bet, I folded. If he's to be trusted then he had A2.

That hand cost me about 3/8 of my stake off the bat. With overpair and outside straight draw, I don't regret being in. When he bet on the turn I might have considered going all in but pure person-reading intuition was that he had me beat and I'd actually need the straight rather than the pair. Even in that case, pot odds / implied odds kept me in.

--

The QQ hand brought me back up to exactly original stake but after that I had several orbits worth of obvious folds. My only other worthwhile hand all night was 22, in SB (again). Notably loose player bet UTG (both he and my carpool mate were betting all night, mostly stealing) and I big-raised him. If he reraised me I was willing to go all in pre-flop and take my chances on the coin flip. But he called.

Axx all-diamond flop, I checked, he bet enough that my staying in the hand would commit me to all in. I doubt he hit a flush. He might have hit an ace. My best guess is AK with a diamond or KQ with a diamond.

--

With five players left I wasn't critically short but was shortest stack by a wide margin. (I had about half the original stake, everyone else had at least 175% of theirs.) With A5o as SB and folds around to me, I raised and was put all in.

By probability I should fold that. It doesn't dominate crap hands nearly so much as it gets dominated by Ax (x>5) or pocket pairs. But I called and 77 knocked me out.

Four pocket pairs (shown above). Two or three other times I bet a decent hand pre-flop and everyone folded. Other than that, a whole evening of unplayable crap. Unless you like playing J9s UTG when your stack is getting low. Who knows? Maybe that hand was my big opportunity (no flop, so no way of knowing).

Weekend Gaming Recap

Much to Julia's chagrin, I had poker in the East Bay Thursday night (for once, not very far to driver!), poker in Mountain View Friday night, and board games at Stanford Saturday night.

(Here, "poker" means no-limit hold 'em tournament: single table with 10 or 11 players, each of whom starts with 40.00 units of chips (a direct multiple of the buy-in), no re-buy, money split between the top spots.)

I'd already dissected my Thursday losing hand with Nate via e-mail. Friday's game nearly became a work of short non-fiction (and may yet do so, if I ever have sudden free time), but I haven't really had time for so much as a blog entry. Details, possibly sketchy, in the extended entry...

Saturday we generally played Carcassone and I discovered to my surprise and joy that I can now "see" the farming intrigue unfold and plan accordingly.

Thursday:
Long story very very short, a Q76 flop (after someone raised the minimum UTG and many people called but nobody raised) set my 66 but also set Joon's 77. My all-in over Joon's big raise proved costly. As Nate put it, "If you don't go broke here, you played it wrong."

Friday:
In stark contrast to Thursday's table, this one had three first-timers and so (you'd think) ample opportunities to increase one's stack.

Hands I still remember...
ATs (I limped in from an early position; there might have been some pre-flop action) flopped a flush. Somehow the post-flop betting was two-way, with a big raise called but not pushed all in. Another heart (king) on the river, and this time it did become all in, much to the misfortune of Mr. QJs. Fortunately for him he had me covered.

75s flopped a flush draw on KQx (KQ-spades). According to Joon I small-bet on the flop, a play he found questionable compared to either a big bet or a check. He's right, except I don't remember betting at all. I just remember there being 4-way action. 5 of (not-spades) on the turn and the short stack to my left went all-in. Fold, fold, and the stack/pot/opponent situation led me to calling on gut instinct. (No idea what I expected him to have, I just read him as a novice player.) Turns out he had an inside straight draw (AJo), and so I had the advantage just because my 5 paired. River didn't change anything.

For a long time I had easily the biggest stack but no worthwhile cards to do anything. (Maybe I could have bluffed some, but the funny thing about calling-station novices is that bluffing doesn't chase them.)

KK under the gun (incidentally, Joon says on the hand where I lost Thursday, UTG was KK; I don't know if he literally knows this or just read the guy for it), I limped. Other callers, a small bet, a raise by the guy who'd had the worse flush than me. I made a big raise (from 6 to 30) for all the obvious reasons but then the guy whom I'd raised over tried to say "all in" out of turn, before the two still-live players between us. If that doesn't scream "AA" I don't know what does. Of the two still-live players, one of them called before Mr. AA got his all-in in for real. (Entering the hand he low 70's in chips and I had in the 120's.)

Ugly situation, because he couldn't possibly not have AA (unless he had QQ and were an atrocious player, or was telling strong as an obscenely good player), and yet... 30-some more chips to win close to 150. Even if he did have AA to my KK, I liked my chances enough that the slim chance he didn't have it was enough for me. Sure enough, he had it (the novice guy had AJ (suited at least, if I remember right), and very nearly caught a J-7 straight) and no high cards came to the board.

Lots of hands later it was four of us competing for a net gain of +80, +40, +20, and -20, respectively. Host to my left: Tight, but neither especially passive nor especially aggressive. Generally the shortest stack, a result of card quality rather than skill. He'd almost bit the dust on A6 against big stack's KK, only to catch an ace on the river. Big stack across from me, his AA against KK having made up for the inferior flush. Playing pretty loose, trying to push us around, generally most successful against the calling station on my right. Speaking of whom, all night he had some of the best luck I'd ever seen; the less said there, the better, since for all I know he's secretly some poker wizard. I can tell you he was second stack as of when 5th place went out, but short stack a few hands later.

(He and I had an all-in showdown where my KJs caught nothing against his 77. I was shocked to see that I had him covered, albeit barely; I had to triple up on my next action to go from life support to second stack again.)

Two competing strategies here: Either be extremely tight and hope that Mr. Calling Stations' inevitable demise happens sooner than later, then fight David for second place; or continue to play to win, big stack's chip lead aside, and run the risk of being out of the money.

Naturally, big stack went all-in UTG when I had 66. (My new least favorite hand to play?) This time, KJ versus pocket pair went to the kings, as he got one on the flop and one on the river (and paired 4's on the board for a boat).

Furthermore, I learned from David Saturday that my favorite calling station had actually finished second. (David told me about the hand that eliminated him but I didn't remember very long.)