Odds please?

[wilfuljoker]

This is one for the mathmaticians...

At a SNG recently I picked up aces and after a raise and reraise, me and Uberdonk both all in. Bit miffed to see him turn over the other two aces. Just curious to know what the odds are on this? Then he hits a flush knocking me out. Interested to know what the odds are on this happening? I know its not unusual for aces to lose to a flush but what are the combined odds of this happening in the same hand?

[tfeilding]

Aces versus aces are:

220 x (50/2 x 49/1)
which is 269500/1

However - this assumes that you are playing heads up. A 10 handed table means there are 9 people out there who can get the other set of rockets.

As for a flush, this is probability which I was never any good at but roughly for one of the aces to become a flush after a preflop all-in is:

47/11 x 46/10 x 45/9 = 98/1
4.26 4.6 5
There are only three sums there cos the first card on the flop is going to match one of the aces 100% of the time. You then need 3 out of the following four to match the first card out or the next four all need to be the same. This is why my sum above is incorrect. Probability gets too confusing!

So as a guesstimation, for two players to have aces and for one to hit a four card flush is in the region of 26,411,000/1

Therefore it must only happen online, right?

[Dice Man]

Not quite sure what questions you're really asking...

If you're asking, what is the probability that another player has AA given that you have AA, then that is 1/1225 x the number of players at the table.

As for the flush, I just pokerstoved AA vs AA, and they each have a 2.17% chance of winning the pot, and I don't think there is any way for them to win other than by a flush, so my answer is 2.17%.

This is how I calculate the probability of a flush otherwise. Given, as Tom says, that the first card doesn't have any effect on the probability of a flush:

11/47. 10/46. 9/45. 4

3960/ 97290

396/9729

132/ 3243

44/ 1081

=4.07%

Pokerstove (I think) gets the result of 4.34% though, so I don't know where that extra/missing 0.27% is, although I am probably wrong. Maybe that has something to do with the possibility that sometimes when there are 5 of the same suit on the board, it will be a split because they will each play a straight flush? But if anything that should reduce each players chance of winning, not increase it, so I don't know.

Tom, you missed out the x4, because the extra card (the 4th card) can be in any of the places of those 4 cards.

Plus, 11/47 x 10/46 x 9/45 doesn't exactly equal 1/98.

[wilfuljoker]

4.26 4.6 5

Therefore it must only happen online, right?

Actually it was live at the Gala last night after I donked out of Nick's game when my queens had lost to Drago's 46s. The advantage of it being live was that I could actually hit the dealer as opposed to scream abuse at an inanimate screen. Those poker gods are mean. Luckily won the second SNG and ended up ahead for the evening.

[Steve A]

Glad you got the second one Judi - wp!