#1
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Question for stats gurus - odds of KK vs. AA
After 73,000 hands of No Limit on Party Poker and skins I have been dealt KK 345 times.
Of those 345 times I have come up against AA 11 times. These 11 times are hands that have gone to showdown - they obviously do not include times where I folded before the river. So the true number is probably 13-15. My question is statistically is this the amount of times, on average I should expect to come up against AA when dealt KK. (About 1 in 23-28 times). If not, can anyone estimate the odds of coming up against AA say, 13 out of 345 times I am dealt KK? Also, is my sample too small or biased in any way? Thanks. |
#2
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Re: Question for stats gurus - odds of KK vs. AA
You don't mention whether you play 10-handed or 6-handed so I'll give you both answers....
10-handed you should expect to see AA about .043925315 of the time. Given the 345 times you've been dealt KK the following table gives the probabilty for times you will see AA..... 7 0.008728493 8 0.016942951 9 0.029147379 10 0.044994751 11 0.062955987 12 0.080505457 13 0.094743465 14 0.103224402 15 0.104650709 16 0.099165178 17 0.088171704 18 0.073816532 19 0.058367468 20 0.043710072 21 0.031079115 22 0.021028778 23 0.013567874 24 0.008363335 For 6-handed play you will see AA about 0.024446374 of the time, and here is the appropriate table with the probabilities... 2 0.007293231 3 0.020895664 4 0.044769845 5 0.076512656 6 0.10864863 7 0.131852759 8 0.139598015 9 0.130987528 10 0.110289085 11 0.084168185 12 0.058705189 13 0.037682585 14 0.022393091 15 0.012382664 16 0.006399873 You're numbers fall very much inline. |
#3
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Re: Question for stats gurus - odds of KK vs. AA
I play 10-handed.
OK - let me ask this. Any given time that I am dealt KK what are the odds that one of my 9 opponents is holding AA? Wouldn't it be something like ((6 divided by (the number of possible 2 card combinations)) times 9? |
#4
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Re: Question for stats gurus - odds of KK vs. AA
That should give you a rough idea. You run into issues where A-A is held by more than one opponent...but it will give you a very close approximation.
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#5
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Re: Question for stats gurus - odds of KK vs. AA
[ QUOTE ]
That should give you a rough idea. You run into issues where A-A is held by more than one opponent...but it will give you a very close approximation. [/ QUOTE ] OK great - any idea what the number of possible two card combinations is? |
#6
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Re: Question for stats gurus - odds of KK vs. AA
C(50,2) = 1225
Link to BruceZ's post on inclusion/exclusion: http://archiveserver.twoplustwo.com/...;o=&fpart= Excerpt from that post (which oddly enough answers your exact question): This is the simplest non-trivial poker example. If you hold KK before the flop, what is the probability that at least one of your 9 opponents holds AA? Note that at most 2 opponents can have AA. The probability that any particular player holds AA is 6/C(50,2). So the first term in inclusion-exclusion is simply 9*6/C(50,2). That is the sum of the 9 probabilities of each player having AA. This alone is very close to the exact answer, but it double counts the times that 2 players hold AA. For the second term, we take the probability of 2 particular players having aces, 1/C(50,4), and multiply by the number of ways to pick the two players, which is C(9,2). So the final answer is: P(KK vs. AA) = 9*6/C(50,2) - C(9,2)/C(50,4) or about 4.39% |
#7
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Re: Question for stats gurus - odds of KK vs. AA
Thanks -
4% - so 25:1. So being dealt KK 345 times I would expect to see AA, 345/25 = 14 times. |
#8
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Re: Question for stats gurus - odds of KK vs. AA
[ QUOTE ]
Thanks - 4% - so 25:1. So being dealt KK 345 times I would expect to see AA, 345/25 = 14 times. [/ QUOTE ] 25:1 is 1/26, not 1/25 .0439 is ~1/22.78 345/22.78=15.1 The value of 15 is in agreement with the value in the table provided by MickeyHoldem earlier in this thread. |
#9
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Re: Question for stats gurus - odds of KK vs. AA
[ QUOTE ]
Thanks - 4% - so 25:1. So being dealt KK 345 times I would expect to see AA, 345/25 = 14 times. [/ QUOTE ] Ok but do understand that there is a probability distribution, as given earlier in the thread. and yah, 1/26 |
#10
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Re: Question for stats gurus - odds of KK vs. AA
6 handed and 10 handed play should have equal probability of hitting aces. your delt 2 random cards each time and it is in isolated incident. get back to me on this
thanks chris larmore larmorec@msu.edu |
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