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  #1  
Old 07-17-2005, 01:36 PM
LuvDemNutz LuvDemNutz is offline
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Default 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.
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  #2  
Old 07-17-2005, 02:30 PM
MickeyHoldem MickeyHoldem is offline
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Default 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.
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  #3  
Old 07-18-2005, 03:53 PM
LuvDemNutz LuvDemNutz is offline
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Default 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?

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  #4  
Old 07-18-2005, 04:01 PM
LetYouDown LetYouDown is offline
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Default 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  
Old 07-18-2005, 04:03 PM
LuvDemNutz LuvDemNutz is offline
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Default 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?
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  #6  
Old 07-18-2005, 04:13 PM
LetYouDown LetYouDown is offline
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Default 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%
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  #7  
Old 07-18-2005, 05:21 PM
LuvDemNutz LuvDemNutz is offline
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Default 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.
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  #8  
Old 07-18-2005, 06:00 PM
uuDevil uuDevil is offline
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Default 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.
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  #9  
Old 07-19-2005, 06:36 AM
ThinkQuick ThinkQuick is offline
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Default 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
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  #10  
Old 07-20-2005, 03:02 PM
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Default 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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