flush probabilities all in

[jack1234]

ok, simple one for all you math geniuses out there:

in holdem for advanced players Sklansky puts the chances of making a flush with suited hole cards around 6.5% (p.310). Now I'm a no limit player mostly (both tournament and cash), so this affects me mainly on all in situations where 5 cards are seen and raising all in, say the last 2 or 3, with Ax suited is sometimes necessitated due to massive blinds. My math always puts it higher than this (around 9.5%), so can someone lay it out for me please? i guess the complete sitution in mind is something like all in hu with A9s v AK, so breakdowns for flush would be useful as well as total probabilities.

cheers

[switters]

you will make a flush with suited cards when the board has 3, 4, or 5 of your suit. you can compute each of those possibilities and add:

C[11,3]C[39,2] / C[50,5] = 5.77059%
+ C[11,4]C[39,1] / C[50,5] = 0.60743%
+ C[11,5]C[39,0] / C[50,5] = 0.02181%
-----------------------------------------
6.39983%

pretty close to Sklansky's number...


from twodimes.net, the straight-up chances for A9s to beat AKo:

cards win %win lose %lose tie %tie EV
Ah 9h 483500 28.24 1152589 67.31 76215 4.45 0.305
As Kd 1152589 67.31 483500 28.24 76215 4.45 0.695

so, you will win or tie about 1/3 of the time you are all-in with A9s vs. AKo, and your opponent doesn't hold the K of your suit...

-switters