Quick Omaha 8 question.

[slavic]

Let's say you have AA xy with xy being > 8

board is A A 4 suits are unimportant.

there are 24 cards remaining that can bring a low. There are two chances for those cards so the low should hit.

1-[(21/45)*(20/44)] = 78.79%

However if someone stays to draw can't we infer that at least two of their cards are below or equal to 8 and adjust accordingly? It still doesn't make the numbers look all that good.

[Crooked Paul]

First off, unless the board gives someone a straight flush, you have the absolute nuts here, so it's a no-brainer to bet or call any raises. You're making money on this pot even if there is a low hand. =)

But you're asking what's the chance that you scoop based on your high hand if someone else is drawing to the low. All right. Let's assume that there's one other player who has two non-A (obviously), non-4 low cards. He has a chance at the low hand. There are two ways to figure out his chances.

1. Count up his outs and figure out the chance that he'll hit one on the turn plus the chance that he'll miss on the turn and hit on the river:
= outs/45 + (non_outs/45)*(outs/44)

2. Count up his outs, subtract that from the number of unseen cards to get his "blanks," cards that don't help him, and figure out the chances that you'll get two of these cards running:
= (blanks/45)*((blanks-1)/44)

I think the second way is easier. Okay, so how many blanks are there in the 45 remaining cards? Well, K Q J 10 9 don't help him (that's 20), and neither do the remaining three 4s (23), and neither do the three cards each that match his two low cards (29) ... but you said the other two cards in your hand were > 8, so subtract two from that tally (so that we're not counting any blanks more than once) to get a final total of 27 "blanks."

So, with all the information we have available and assuming that your one opponent has two low cards and needs just one more for a low hand, his chances are:

(27/45)*(26/44) = 702/1980 = 35.5%

I think I got all that math right. Anyone want to check me?


Crooked

[MickeyHoldem]

if your opponent holds two low cards (non A,4), we know something about 11 cards in the deck.

You hold AAxy, where x,y are high, the board is AA4, and our opponent has abcd, where a,b are low and c,d are high

so there are 41 unknown cards... 16 of which will give our opponent the low, so...

No Low = 25/41 * 24/40 = .3659

If he holds 3 low, he gains 5 outs,

No Low = 20/41 * 19/40 = .2317

and with 4 low, he loses an out ...

No Low = 21/41 * 20/40 = .25610

[slavic]

In the running blanks calculation, you come up with the chance that the opponent won't make a low right?

So that means the chance of scoop for the hero is 35.5% and the chance of a split is 1 - .355

Or better yet Hero has 1/3 equity and opponent has 2/3 equity in the low side of the pot.

The reason I bring this up is because of a player posting a hand were hero flops quads, he bets and nobody calls. This seems bad but in O8 it's probably a better solution than having someone call with 36KK given that most pots start fairly large to begin with 6 to 8BB and a low would have odds to draw even paying full bets to your half bet.