#1
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A question about AA v. KK for the prob. forum
Can someone please give me the math behind this probability listed below. I'm certain I've heard this correctly somewhere, but I have multiple people telling me no way. I will post what I think I've heard in white below.
Thanks for any help. In a 10 handed game, if you look down at KK, what is the probability that someone is holding AA? What I could swear I've heard before: <font color="white"> 1 in 44 </font> |
#2
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Re: A question about AA v. KK for the prob. forum
Your UTG and look down at KK's, the probability that one or more of your nine remaining opponents has aces are as follows.
First term =6/(50c2)*9 = .04408 Second term = (6*3/(50c2)/(48c2))*(9c2) = .00047 First term - second term = .043613 or 1 in 22.93 times This is how often one or more of your opponents will have aces. This was solved using inclusion/exclusion. If you do a search on BruceZ and use the above words he has an excellent description on how to use this technique. Cobra |
#3
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Re: A question about AA v. KK for the prob. forum
Thanks Cobra.
Could you explain the 'first term' and 'second term' thing? I'll also look up the BruceZ info. Could you also explain what/where the numbers in your equation are/come from? Also, does the equation change if I am not specifically UTG, but just saying "regardless of position, what are the odds any other of the 9 have an AA? |
#4
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Re: A question about AA v. KK for the prob. forum
No need for further explanation. I've found all I need.
Now, to make some big monies from some suckers with my newfound info I got from the internets. Yayz. |
#5
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Re: A question about AA v. KK for the prob. forum
[ QUOTE ]
Your UTG and look down at KK's, the probability that one or more of your nine remaining opponents has aces are as follows. First term =6/(50c2)*9 = .04408 Second term = (6*3/(50c2)/(48c2))*(9c2) = .00047 First term - second term = .043613 or 1 in 22.93 times [/ QUOTE ] The second term should be C(9,2)*6*1/C(50,2)/C(48,2). There are 6 ways for the first player to have AA, and 1 way for the second. This gives 4.39% or 1 in 22.8. |
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