poker math question

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?

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.

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

50*49*48=117600
117600 different flops

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

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

Whatever that is. This excludes flopping straights.

I don't think it is even worth knowing because the chances are probably 5% or a lot less.
If you wanted to know if an As/10s would have a high chance of flopping a straight or flush draw or top pair, then I would be interested.

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combinatorics is hard

anyways flopzilla says the odds are about 7%. But i think that might be the odds of it happening without something bigger happening?

((4*4*44)/6)/19600)*3

this seems like it would be right to me but that total about 15%...

23x = 4/50 * 4/49 * 44/48 = .6 (excludes 4's)
2x3 = 4/50 * 45/49 * 4/48 = .61
32x = same as 1
3x2 = same as 2
x23 = 46/50 * 4/49 * 4/48 = .63
x32 = same as 5

all of that * 3

= 11%

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