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Old 12-17-2005, 02:24 AM
PseudoPserious PseudoPserious is offline
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Join Date: Oct 2002
Posts: 151
Default Re: Is Acey Duecy a +EV game

Count the number of cards that win your bet. W
Count the number of cards that lose your bet. L
Count the number of cards that hit the rail. R
Count the total number of cards. T

You win 1 bet W/T of the time.
You lose 1 bet L/T of the time.
You lose 2 bets R/T of the time.

You have a neutral bet when W/T = L/T + 2R/T

So, when the number of winning cards is more than the number of losing cards plus the twice number of rail cards, make the maximum bet possible.

When the number of winning cards is less than the number of losing cards plus twice the number of rail cards, make the minimum bet possible.

In a fresh deck, there are 6 rail cards and 50 total cards. A little substitution gives you 2W = T + R, so you need 28 winning cards to break even. This corresponds to a 7-gap between the rails (3-J). So, the only profitable bets (in a fresh deck) are 2-J, 2-Q, 2-K, 2-A, 3-Q, 3-K, 3-A, 4-K, 4-A, and 5-A.

Overall, the game is only +EV if you make the above calculations better than your opponents do.

PP
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