Fancy Store-Bought Dirt

FREE RIDE LOTTO

"We pay you to play!"

(Tag line is slightly misleading, as full truth would be "We usually pay you to play.")

A negative-sum (to the customer), but fun, game based on the structure I set out in the extended entry below.

$5 lottery ticket, with a greater than 70%(!) chance at cash back. Six digits, color-coded to emphasize that order is relevant, so a million values that are equally likely to come up.

Six air machines in sequence, each with 10 balls labeled 0-9.
1. Draw a grand jackpot number (one ball per machine)
2. Without replacing, now draw a "little jackpot number": one ball from each of the first four machines
3. Without replacing, now draw a last-chance combo: one ball from each of the first two machines

DOLLAR RIDE: If the first digit of your ticket does not match the first digit of any of those three prize numbers, then your ticket is redeemable for both $1 and a new ticket (randomly generated number) in the next drawing. (This will be true of 700K of the million possible ticket #s.)

TEN-DOLLAR RIDE: If your first two digits match the last-chance combo then your ticket is redeemable for both $10 and a new ticket (randomly generated number) in the next drawing. (This will be true of 10K of the million possible ticket #s.)

$500 PRIZE: If your first four digits match the "little jackpot number," your ticket is redeemable for $500. (This will be true of 100 of the million possible ticket #s.)

$25K PRIZE: If your first five digits (but not the last digit) match the first five digits of the grand jackpot number, then your ticket is redeemable for $25,000. (9 in 1M)

$250K GRAND PRIZE: If all six of your digits match the grand jackpot number then you win $250K (1 in 1M).

According to Excel, this would be a 12.5-cent expected profit per purchased ticket sold if the first two prizes were $6 and $15 rather than {$1 + ticket} and {$10 + ticket}. Since most of the winnings are awarded as tickets rather than cash, the actual expected profit per purchased ticket is an exercise for the reader.

Note that you have a 16.8% chance of getting the "Dollar Ride" five times in a row (bringing your net outlay back to zero, for a literal freeroll).

Posted by Matt Bruce at February 6, 2008 11:37 AM