An odds question

The following hand came up and I am not sure I can compute the odds correctly.


After flop I have set of Kings. Opponent has pair of 7s with A kicker. No other draws.


To win he must have either A-A from the 3 remaining Aces, or 7-7 ( both remaining 7s.)


This was a no limit, live game, with 250.00 going in pre-flop and my remaining 300.00 going in on the flop.


I am comming up with around 270 to 1 after flop.

Can this be correct? Sounds un-believable.

You can actually run this on poker probe or "twodimes.poker/net". But I think the math is something like:


Probability of an ace on the turn followed by an ace at the river is: (3/45 unknown cards)*(2/44 unknown cards) which is 0.003.


Probability of a seven on the turn followed by a seven at the river is (2/45)*(1/44) which is 0.001. Adding the two probabilities yields a total probability of 0.004 which is 4 out of 1000. The odds against are 996-to-4 which is about 249-to-1, I think. Your 270-to-1 I think is a tad bit too high.

I make him a 246.5 to 1 dog


But given that you're going back to calculate it, I'd be only mildly shocked to hear that he pulled it

Could you have been cold decked?


Certainly these 250-1 shots happen (otherwise, the prob. would be zero). But if this guy gets $250 in pre-flop with A7 and another $300 on the flop with only a pair of 7's and a K on the board.


Unless you were playing no limit with $100 blinds and you were in fact short-stacked, in which case it makes more sense.

You think exactly right (by calculation and simulation).

But that still leaves out the chance of him getting a fourth king.

How can he get a 4th king if 2 sevens or 2 aces come? The above result is correct.

It is a casino dealt game. Don't beleive any kind of cheating could be involved. It is a 5 and 10 blind game. My 550.00 or so was a relatively small stack.


I was high because I used the calculation of 3 aces from 47 unseen cards, but I now see that for the problem to exist, I have to have pocket Kings, so it is correct to start with 3 aces out of 45 unseen cards, etc.

The odds are 246.5:1, 986 wins for the Kings, 4 wins for the A7.