Omha8 Probability Q

[EasilyFound]

What is the probability that the flop will include two low cards, setting up a low draw? I tried to search, but there were way too many answers. I'm hoping someone just knows this and can give the answer. I know it will depend on how many low cards you hold in your hand, but assume you hold two or three. Just an approximation will do. Thanks.

[MickeyHoldem]

when you have 2 low...
how many flops help us:
2 low + 1 high = 6c2 * 16 * 20 = 4800
2 low with a pair = 6c2 * 2 * 4 * 6 = 720
so... chance to flop draw = (4800 + 720) / 48c3 = 0.319

when you have 3 low, its a little more complicated...
how many flops help us:
2 low that you dont have + 1 high = 5c2* 16 * 20 = 3200
1 low you have, 1 you dont + 1 high = 3*3 * 5*4 * 20 = 3600
2 low you don't have with a pair = 5c2*2 * 6*4 = 480
1 low you don't paired with 1 low you have = 5*6 * 3*3 = 270
1 low you have paired with 1 low you dont = 3*3 * 5*4 = 180
so... chance to flop draw = (3200+3600+480+270+180) / 48c3 = 0.447

[EasilyFound]

Thanks. One question though.

The probability of a low draw (two of the three flop cards being low) is greater if you have 3 low cards in your hand as opposed to two? That seems counterintuitive, so I must be missing something.

[MickeyHoldem]

OK... the 8 low ranks are aces,2s,3s,4s,5s,6s,7s,8s... when you have 2 low cards, you have to hit 2 ranks out of the remaining 6 ranks to get your draw...

when you have 3 low cards, it's true that there is one less low card remaining in the deck, but this is more than made up for by the fact that you can choose what cards from your hand play.

As an example: You have 32xx in your hand... a flop of 34K won't help you... but if you had 32Ax in you hand, the same flop gives you a draw!!

[EasilyFound]

Gotcha. So I was missing something. Now I understand. Thanks a bunch. Very helfpful.