2 best hands pre-flop....

[BouncinRound]

So ya... I lost big the other night hard rock'n the KKs vs AAs. This was an extremely tough loss and I would like to be reassured that this will hopefully never happen again, or at least that its more rare than a blue moon. So can anyone tell me the pre-flop odds of 1/8 people having pocket AAs IF you have KKs?

[BouncinRound]

Now that I gave it some thought, 4/50(1st card is A)*4/50(2nd hole card is an A) =.64% chance. Anyone agree?

[BouncinRound]

err 4/50 * 3/49. = .49% chance sound better?

[jae686]

If you plan on playing poker often get used to this. It really isn't that rare. I've been playing seriously for a couple years and I've gotten to showdown with this or the opposite a few dozen times.

[World Jugador]

[ QUOTE ]
So ya... I lost big the other night hard rock'n the KKs vs AAs. This was an extremely tough loss and I would like to be reassured that this will hopefully never happen again, or at least that its more rare than a blue moon. So can anyone tell me the pre-flop odds of 1/8 people having pocket AAs IF you have KKs?

[/ QUOTE ]

There are C(4,2) = 6 ways to make AA. Of the fifty cards that remain, there are C(50,2) = 1225 ways to make a hand. So 1225-6 = 1219 ways to make something besides AA. So with X opponents, the probability of NOT making AA is 1 -1219/1225 * 1218/1224 * 1217/1223 * ... * (1219-X+1)/(1225-X+1), which is equivalent to 1-(P(1219,X)/P(1225,X)) where is the permutation function. With 8 opponents, your probability of running into AA with KK is about 3.9%.

[World Jugador]

[ QUOTE ]

So with X opponents, the probability of NOT making AA is 1 -1219/1225 * 1218/1224 * 1217/1223 * ... * (1219-X+1)/(1225-X+1)


[/ QUOTE ]
Of course there's a typo here. That's the probability of making AA. The probability of NOT making AA is the term without the "1 - " in front. At any rate, the answer of making AA is right (if my math is right) but the solution has the one little typo when I consolidated two steps.

[jay_shark]

I'll give two methods to show this . One is an approximation and the other is an exact solution .

The probability that the player behind you doesn't have aces is 1219/1225 . Take this number to the power 8 and then take the complement of that number . You get 1-(1219/1225)^8=0.038518

Here is the exact solution which uses the inclusion/exclusion formula .

6/1225*8 - 8C2[6/1225*1/48C2] = 0.039062

I've subtracted the times when two players may hold pocket aces as we don't want to over count .

[T50_Omaha8]

Although it's pretty common to run your KK against AA, you've also got an odd 4% chance of running your AA up against someone else's KK. So don't despair OP.

[miw210]

[ QUOTE ]
If you plan on playing poker often get used to this. It really isn't that rare. I've been playing seriously for a couple years and I've gotten to showdown with this or the opposite a few dozen times.

[/ QUOTE ]

[BouncinRound]

ahh well thanks, I think I can live with it only happening 4% of the time.

[Gonso]

[ QUOTE ]
well thanks, I think I can live with it only happening 4% of the time.

[/ QUOTE ]

Yeah, that will be offset by the times you have AA to someone else's KK.