Calculating redraws

[PoBoy321]

So I was playing in a game with a bunch of middle aged men and a good friend of mine who's a great poker player a little while ago when he got into a situation where he held J9 [img]/images/graemlins/diamond.gif[/img] on a T [img]/images/graemlins/diamond.gif[/img]8x 3 [img]/images/graemlins/diamond.gif[/img] board, giving him the OES+FD, he pushed and was called by Q [img]/images/graemlins/diamond.gif[/img]Qx. We were talking about it and he told me that he was a slight favorite, I told him that he was a slight dog, because if he hit a Q on the turn, the other guy could river a full house, if he hit a diamond on the turn, the villain could river a higher flush, and my friend couldn't make a straight flush.

I ran the situation in pokerstove and I was right, but I'm just curious about how you would calculate something like that.

[AaronBrown]

There are 990 possible hands (45 unknown cards, so 45*44/2 = 990).

If a 7 shows up on either card, he wins. 4 7's times 41 non-7's = 164, plus 6 different ways to get a pair of 7's = 170.

If a Q shows up, he wins unless the other card is Q, 10, 8 or 3. We've already counted the Q 7 combinations, so it's 2 Q's times 30 good companions. That's 60, so we're up to 230.

Two Jacks or two nines can each come up three ways, that gives us 236.

If one diamond shows up he wins, with two diamonds he loses. There are 8 diamonds out and 37 non-diamonds. One of the diamonds is a 7, three of the non-diamonds are 7's and two are Queens, so we get 7*32 = 224 hands. That gets us up to 460. But we have to subtract two Queens times four cards that make the Queens lose, to get 452.

So 452/990.

[AKQJ10]

[ QUOTE ]

If a 7 shows up on either card, he wins.

[/ QUOTE ]

I only read this far but I think it's in error. If a 7 [img]/images/graemlins/diamond.gif[/img] and another diamond fall on the turn and river, Hero loses.

At any rate, I'd just go do it at http://www.twodimes.net except I'm in a hurry.

[AaronBrown]

You're right. However, I redid it and it turned out I subtracted out that case in the flush section. So my words were wrong but I think my number is still right.

However, it's obviously easy to make a mistake doing this stuff.

[AKQJ10]

[ QUOTE ]
You're right. However, I redid it and it turned out I subtracted out that case in the flush section. So my words were wrong but I think my number is still right.


[/ QUOTE ]

OK, scanning it I thought that might be the case, but I wasn't able to do the mental heavy lifting at that point. And I just got done with a Foxwoods all-nighter so I can't really do it now, either. [img]/images/graemlins/smile.gif[/img]