Thread: Is this right?
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Old 08-22-2007, 02:55 AM
MarkGritter MarkGritter is offline
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Join Date: Jan 2005
Location: Eagan, MN
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Default Re: Is this right?

Yup, it's correct.

T7532 vs. 8543 vs 6542: We can estimate that other players are drawing to 12 and 13 outs so it should be something like 27/39*25/38 = 45.5% chance of them both bricking. (Not quite accurate.)

To get the right answer, we can count the two-card cases where the T loses by hand. There are 39 cards left unspecified so there are 1482 possibilities (like pokenum says)

9x: 4*38
7x: 3*38
6x: 3*38
2x: 2*38
A[T987]: 4*13
K[T987]: 4*13
Q[T987]: 4*13
J[T987]: 4*13
T[T987]: 3*12
8[T987]: 3*12
5[T987]: 1*13
4[T987]: 2*13
3[T987]: 2*13

That gives 801 ways to lose, which is just what pokenum says, 45.95% chance of winning.

Last-draw equities against two players drawing one tend to flatten out because there is a substantial chance for each player of bricking quite badly.

For example,
532 vs 8543 vs 6542: 21% to win
742 vs 8543 vs 6542: 20% to win
T532 vs 8543 vs 6542: 25% to win
T9532 vs 8543 vs 6542: 41% to win

Unless an opponent is pat, a live draw will have substantial equity. Drawing four to a deuce is still 10% to win against these two draws.
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