Omaha hi/lo hand odds

[onadraw]

What are the odds that a player would get both A-5 straight flush for low and Royal for high? Say player is holding KQ23 all spades and the board is AJT45 all spades.

[Tom1975]

There are C(48,5)=1712304 possible boards, only one of which meets your criteria, so 1 in 1712304 is the answer.

[Silent A]

This not quite right. In your hand you need 2 broadways and 2 wheels all of the same suit, but you can't have the A since that has to be on the board for this to happen.

C(4,2)*C(4,2)*4 suits = 6*6*4 = 144 starting hands that can have this happen.

The total number of starting hands is C(52,4) = 270725

For each starting hand there is only one board that can give the double. The odds of this is, as Tom said, 1 in 1712304.

So for this to happen to you 3 things have to happen:

1) you must be dealt such a hand. odds = 144 in 270725
2) the board must come with all the 5 cards you need
3) you must see the river. Given (1) and (2), odds = almost 1 (since your hand is at least somewhat playable and you're going to like the flop no matter what)

total odds = (144/270725)(1/1712304) = 1 in 3,219,190,975