PLO Probabilities?

[Shandrax]

I was wondering if there is any publication out where one can look up Omaha odds. If not, maybe someone can help out by posting them here.

What are the chances to have a pair pre-flop?
What are the chances to have A-A-x-x pre-flop?
What are the chances to have 2 pair pre-flop?
What are the chances to hit a set on the flop if you started with 1 pair?

[AaronBrown]

These are not hard to compute.

There are C(52,4) = 270,725 Omaha starting hands.

There are 13 different pairs, each of which you can get 6 ways, and can be paired with 48 different third cards (so as not to get three of a kind) and 44 different fourth cards (so as not to get two pair or three of a kind). You have to divide this by two, because the last two cards are indistinguishable. 13*6*48*44/2 = 82,368. Divide by 270,725 to get 0.30425 or 30.425%.

AAxx is 1/13th of this, or 2.340%.

There are 13*12/2 = 78 ways to select the ranks of two pair, and 6 ways to select each. 78*6*6 = 2,808. Divide by 270,725 to get 0.01037 or 1.037%.

Hitting a set on the flop is almost the same as in hold'em. The only difference is you are drawing from 48 unseen cards instead of 50. There are C(48,3) = 17,296 possible flops. 46 of them give you quads. 2,070 of them give you a set, but not quads. So 2,116 of them give you at least a set, the chance of that is 12.234%.

[binions]

[ QUOTE ]
These are not hard to compute.

There are C(52,4) = 270,725 Omaha starting hands.

There are 13 different pairs, each of which you can get 6 ways, and can be paired with 48 different third cards (so as not to get three of a kind) and 44 different fourth cards (so as not to get two pair or three of a kind). You have to divide this by two, because the last two cards are indistinguishable. 13*6*48*44/2 = 82,368. Divide by 270,725 to get 0.30425 or 30.425%.

AAxx is 1/13th of this, or 2.340%.

There are 13*12/2 = 78 ways to select the ranks of two pair, and 6 ways to select each. 78*6*6 = 2,808. Divide by 270,725 to get 0.01037 or 1.037%.

Hitting a set on the flop is almost the same as in hold'em. The only difference is you are drawing from 48 unseen cards instead of 50. There are C(48,3) = 17,296 possible flops. 46 of them give you quads. 2,070 of them give you a set, but not quads. So 2,116 of them give you at least a set, the chance of that is 12.234%.

[/ QUOTE ]

Thanks

So roughly speaking, at a 10 handed table, there are 3 pocket pairs out on average?

Meaning that on every flop of three different ranks at a full table, it is about 7:3 that someone has a set?

[Shandrax]

[ QUOTE ]
These are not hard to compute.

There are C(52,4) = 270,725 Omaha starting hands.

There are 13 different pairs, each of which you can get 6 ways, and can be paired with 48 different third cards (so as not to get three of a kind) and 44 different fourth cards (so as not to get two pair or three of a kind). You have to divide this by two, because the last two cards are indistinguishable. 13*6*48*44/2 = 82,368. Divide by 270,725 to get 0.30425 or 30.425%.

AAxx is 1/13th of this, or 2.340%.

There are 13*12/2 = 78 ways to select the ranks of two pair, and 6 ways to select each. 78*6*6 = 2,808. Divide by 270,725 to get 0.01037 or 1.037%.

Hitting a set on the flop is almost the same as in hold'em. The only difference is you are drawing from 48 unseen cards instead of 50. There are C(48,3) = 17,296 possible flops. 46 of them give you quads. 2,070 of them give you a set, but not quads. So 2,116 of them give you at least a set, the chance of that is 12.234%.

[/ QUOTE ]

Excellent! Thanks a ton!