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poker math question

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deathstar   United States. Dec 05 2017 13:37. Posts 103

Say we have A5s and want to know the chances that the board flops a gutshot.
Whats the chance we flop 32x 42x or 43x with a5s?

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 Last edit: 05/12/2017 13:47

Stroggoz   New Zealand. Dec 05 2017 20:05. Posts 3922

probability was the area of math i didnt study

I imagine this is a simple combinatorics problem. Havn't done this in a while, but you represent all possible flops as the sample space, there are 22,100 of them i think. Then represent flopping a gutshot as an event.

The formula will look like P(A) = A/S, where P(A) is probably of the event of flopping a gutshot, and A=size of event, S=size of sample space.

ill use combinations instead of permutations, so order doesn't matter.

the sample space of all flops is 52!/(3!x49!)=22,100

Can't figure out the event of flopping a gutshot right now.

I was GTO in 2007 -wobbly_au 

deathstar   United States. Dec 06 2017 19:25. Posts 103

Your math is weird Stroggoz. That's some event horizon mathematics.

 Last edit: 06/12/2017 19:26

deathstar   United States. Dec 07 2017 02:58. Posts 103

50*49*48=117600
117600 different flops


Stroggoz   New Zealand. Dec 07 2017 06:29. Posts 3922

sure, its 117600 different flops if order matters, but it doesn't. there is no difference between AdKdTs and TsKdAd. there are 6 ways to order every flop, and therefore you divide 117600 by 6 and get 22,100. well actually, you dont since i wasn't counting 2 cards in my hand


I was GTO in 2007 -wobbly_auLast edit: 07/12/2017 06:30

Oly   United Kingdom. Dec 12 2017 09:41. Posts 3569

(12x8x46+12x43x8+40x12x8)/(52x51x50)

Whatever that is. This excludes flopping straights.

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