Pot Limit Omaha Hi odds...

[johnd13]

I have a pretty good handle on Hold em odds and probability....but in dabbling with PLO I'm lost when it comes to the odds and probability...


For example, in hold'em the odds of pocket AA is 221:1....what are the odds of someone having AAxx in PLO...or KKJJ for that matter....


Then comes the hand improvement problems.. there is still the flop turn and river but you don't get to use but 3 of those 5 cards to make you best hand...


Any help in pointing me in the right direction

[euri10]

let's do the math !

number of 2 cards games : C(52,2)=1326
number of 2 aces games : C(4,2)=6
probability of having 2 aces :6/1326=0.45% that is 221:1

basically if youwant to go quickly you can multiply the above result by 6, you'll have a good approximation of what you want but you count things twice !

multipling by 6 gives the same result than [C(50,2) x C(4,2) ] / C(52,4) = 2.71% (36.8333 : 1)
and explained in a non-mathematical manner it's the number of 2 aces among 2 cards (C(4,2)=6) multiplied by the number of any 2 cards among the 50 that are not your 2 aces (C(50,2)=1225) divided by the number of 4 cards games (C(52,4)=270 725)
ok, you understand easily that this number is too high because when you count C(4,2) x C(50,2) there are times when your aces are counted twice....but it's a good approximation.

Now let's try to find the correct answer :
to have AAxy where xy can be anything (including a third and fourth ace) you need to calculate :
the number of games with 2 aces among 4 cards (C(4,2)=6) and multiply it with the number of 2 cards games among 48 cards (that is a deck minus the 4 aces) C(48,2)=1128.
Ok now you need to add the number of hands with 3 aces (C(4,3)) and multiply it by 48 or if you prefer C(48,1)
And finally you add the number of 4 aces games, C(4,4) x C(48,0)
You divide that number by the number of 4 cards games that is still C(52,4)
And you find :
(C(4,2)xC(48,2) + C(4,3) x C(48,1) + C(4,4) x C(48,0))/C(52,4)
(6x1128 + 4x48 + 1x1) / 270 725 = 2.57% or 38.9 : 1

[johnd13]

Ah...thanks. Now I can input into an Excel spreadsheet..

Thanks again!

[euri10]