1. what is the chance to deal a nut hand in holdem?

example, you get AA, and the board is AA, and there is no str8 flush.

or you get 10Jo, the board is AKQXX, no flush, no pair on the board.


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2. what is the chance to deal a nut hand in omaha?


3. what is the chance to deal a nut hand in 5 card omaha?



4. what is the chance to deal a nut hand in 6 card omaha?


5, the most difficult one -
what is the chance to deal a nut hand in holdem on the flop?

The only kind of nut hand on the flop is str8 flush.
if you get KK, the board is KKX,
someone may get AA, and the last two cards are AA, you still lose.

but you may get the bad beat jackpot.
so the only kinds of nut hands on the flop is str8 flush or 4 of a kind.

Why is #5 the most difficult?

I doubt these are serious questions, or rather I doubt OP expects any serious answers.

However, let me start the ball rolling (David's post brought this thread back to my attention). For virtually every board there is a nut hand. I suppose if there is a royal flush on board, there are no nut hands (or all hands are the nuts). Also, what are we calling the nuts? The absolute nuts or any hand that is guaranteed to win the pot?

For example, if board is Td9d8d7d6d, then the absolute nuts is QdJd. But, clearly, if you hold the Jd you are guaranteed to win the pot. I presume that OP means the second definition (so Jd3c would be considered the nuts). T9 cannot be beaten on a board of TT932 but TT would be the absolute nuts.

Also, I presume that OP means what are the chances that any one player holds the nut hand, regardless of how many people are at the table. Essentially, think about dealing out the board first. Then determine what the nut hand is (or nut hands are). Count them up. Divide by C(47,2). Is that right?

Anyway, if I am bored tomorrow, I may take a crack at question #1 (chance of nut hand in HoldEm with a complete 5-card board).