AA vs. KK

[KJL]

Hi all,
What are the odds that at an 8 person table i get dealt pocket Kings twice an am up against aces both times. This happened the other night, while playing online. I figure I played around 300 hands that night. Also can you include the formula you sed to get this.
Thank you

[MickeyHoldem]

Given that your have KK the odds of a single opponent having AA at an 8 player table would be

= 7*6/1225 - 2*(7c2)/(50c4) = 0.034103343

Given that you only got KK twice during the session the odds that both times a single opponent held AA bould be

= 0.034103343^2 = 0.001163 = ~1 in 860

Now you should get pocket kings once every 221 hands so the chance of getting them exactly twice in 300 hands is

= 300c2 * (1/221)^2 * (1 - 1/221)^298 = 0.237705498

Note: You can use excels binomdist function for this... =binomdist(2, 300, 1/221, FALSE)

so now the odds of all this happening would be

= .2377 * .001163 = 0.000276461 = ~1 in 3617

[PowerHouse]

I was reading ESPN.com i found this on there poker page from Phil Gordon it shows your probability of winning with AA vs. KK. It shows the probability of the hand but it goes onto show what happens if you keep winning with the AA to your probability every time you are up against KK and you have won the previous sequence. I disagree with it after the first hand. It shows KK's gains advantage everytime the AA wins in a game. This is a fallacy because every hand is shuffled and redealt meaning that each hand is an independant trial from the hand before. So by some freek of nature you are dealt back to back KK and someone gets AA, you have still a 18.74% if winning the hand (assuming different suits for your pocket pairs). It would be like saying if you pick the same 5 numbers everytime in the lotto you will win eventually, but that isn't the case you have the same probability every time you buy a ticket because all the balls go back into the machine and are reshuffled.

AA vs. KK
Chance of All In Survival

1 81.26%

2 66.02%

3 53.65%

4 43.59%

5 35.42%

6 28.78%

7 23.39%

8 19.00%

9 15.44%

10 12.55%

11 10.19%

12 8.28%

13 6.73%

14 5.47%

[KJL]

I'm not sure, but what Phil Gordon says seems right. I am not sure of the exact math but if AA is supposed to win 8/10 times and wins 15 times in a row it seems likely that KK would win the next time.

[mosdef]

[ QUOTE ]
if AA is supposed to win 8/10 times and wins 15 times in a row it seems likely that KK would win the next time.

[/ QUOTE ]

please tell me you're joking

[KJL]

you are right, I just re read the post and understand what he meant.

I also read the article that Gordon wrote. I think that his point was that when you face this situation over and over these bad beats become more likely to happen.

[LetYouDown]

I believe what Phil was getting at, was the odds of that you will hold up that many times in a ROW. Each individual run has the same probability in terms of outcome...but eventually KK will win. That probability "chart" seems accurate if that's what he was getting at.