Probability

[Dorado71]

Hi, I wonder if anyone can tell me the draw odds for this occurrence.

On 6th street you hold two pair, but you know that your lone opponent holds two higher pair.
For simplicity lets say that straight and flush draws are not relevant here. Let's also assume that your 4 outs giving you a full house are all alive, and so is your opponents 4 live cards that would make him a Full house.

Therefore you loose when neither of you improve.
You loose when you both improve.
You loose when your opponent improves.
And you win only when only you improve.

I wonder if anyone can tell me what the odds would be to win is this situation.

Many thanks.

[cgrohman]

This is a very simple version. The only time you win is when you improve and he does not improve.

Lets assume a standard eight handed game that gets head up on 3rd. You know all 6 of your cards, the 4 upcards of your opponent, and the 6 upcards of people who folded on third. That means there are 36 cards left. You need 4 out of those 36, so your chances of hitting are 1/9.

Likewise, you need your opponent to miss. He will miss his 4 full-house outs, 8/9 times (I got lazy and didnt subtract the extra card off).

So you will win (1/9)*(8/9) of the time or 8/81 . . . so approximately 10 percent. Pot better be laying your good odds.

[Dorado71]

Thank you!
Sometimes the pot does offer you 1 to 9 or more in low limit games, thats why I wanted to know how high pot odds I needed to make the call profitable.