07-29-2022 , 02:03 AM
Hi,

Trying to work out the odds on something here but my probability math is a bit rusty.

In 4 card omaha what are the odds of getting specifically three 2's in your hand?

And in 5 card omaha what would be the odds of getting three 2's with two of them being spades and clubs?

Would this just be a 4/52 x 3/52 x 2/51 for the first? I know for hold em that is how we would calculate it but I've no clue how to account for the other cards in 4 and 5 card Omaha.

Any help would be much appreciated.
07-29-2022 , 07:52 AM
This is known as a hypergeometric distribution.

Quote:
Would this just be a 4/52 x 3/52 x 2/51 for the first?
It would be approximately 4 times that since you basically get 4C3 attempts. This estimate is only too high by 4/(52C4).

The chance of exactly 3 deuces (and not all 4) is: 4*48 / 52C4 ≈ 1 in 1410

Quote:
And in 5 card omaha what would be the odds of getting three 2's with two of them being spades and clubs?
There are two choices of suit for the third deuce, and 48C2 choices of non-deuces, so it's 2(48C2)/(52C5) ≈ 1 in 1152
07-29-2022 , 02:22 PM
Thank you so much!

m