Consider the following situation.

In a 9 handed game of pot limit Omaha, you are on the button with a very sexy-looking JT89. UTG limps, folded to MP1 who limps, folded to you. You raise pot and both blinds call as do the limpers.

5 players

The flop comes AKQ giving you the current nut hand.

Everyone checks to you, and you bet the pot. Everyone except MP1 folds. He raises pot.

In my opinion there are several questions we need to ask here in order to make the best decision.

1) What is the probability that MP1 holds JTxx?
2) What is the probability that MP1 holds JTxx with a club redraw?
3) What is the probability that MP1 holds JTxx with two pair or a set?
4) What is the probability that MP1 holds a set and a flush draw (making him about a 2 to 1 favourite)?
5) What is the probability that MP1 holds any of these combinations?
and finally
6) What is the probability that MP1 holds none of these?

Please give your answer in percentage format.

These answers would depend heavily on a couple of unstated factors:
- which hands MP1 would limp with (instead of raising or folding)
- which hands MP1 would check-raise the flop with (instead of folding or check/calling or leading).

We could work out the probabilities for your six cases as they stand after the flop is dealt but before the flop betting occurs, along with the assumption that MP1 limps 100% preflop.

OK just disregard the betting. It was just for show. The criteria is simply "A player with four random cards"

Here are my answers, I have saved the working in case anyone gets a different answer!

Also, I wasn't quite clear on meanings for 5 and 6, assume in (5) "any of these" means any of 2,3,4; and in (6) "none of these" means JTxx with none of 2,3,4.

1) 4.96%
2) about 1.3%
3) 0.24%
4) about 0.02%
5) about 1.5%
6) about 3.5%

My figures for the flush draw are an approximation, I will re-post if I think of a non-tedious way to work it out exactly

I can't see how that is correct. The first thing I noticed is that the answer to question 6 is surely 100-AQ(1+2+3+4+5)=____%.

AQ=Answer to Question

The second thing that strikes me is that those percentages seem far too low.

See the bit in my post where I commented that it wasn't clear what you meant in 5 and 6 and made an assumption. If you would like to clarify what you meant then please do (I don't see how you would get the formula you just posted either, cases 2,3,4 overlap with case 1 etc.)

It is extremely unlikely that two people will both flop the same straight

I ran a simulation, answers are accurate to about 1 part in 1000 (10M trials):

1) 4.96%
2) 1.58%
3) 0.217%
4) 0.011%