A noob question, apologies in advance for wasting your time...

[ringwielder]

Wondering if someone can confirm or correct my maths here? Been playing NL for 3 months, doing ok (9BB/100) but still a lot to learn. Never knew poker was such a science til i read some of the threads here! Anyway, my question -

If i hold KK at a full ring table (10 players), the odds of someone else holding AA are -

(220 / 9) : 1, or approx 24.5 : 1.

Thats based on the odds of someone being dealt AA (or any other specific pp) being 220 : 1, dividing by the number of players at the table. I ask because PT tells me i've faced that situation 8 times out of 83 occasions that i've held KK (at Carribean Sun Poker, database of 14,000 hands). Seems a bit harsh to me? Or not enough hands for an accurate read?

Thanks.

Seems weird but you can't come to any big conclusions without more data.

[Benholio]

Well, the odds are actually off a little bit, since you hold 2 non-aces in your hand, so the other players benefit from a slight more ace-rich portion of the deck. Also, each person that doesn't have AA or any A increases the odds for the next person.

However, and probably more importantly, analyzing these kinds of statistics usually isn't very productive. You can't control how often your opponents get dealt AA, and given enough time this rate will normalize. Dwelling on bad beats or bad luck is very counterproductive.

[BZ_Zorro]

10 handed:
Prob(KK vs. AA) = 9*6/C(50,2) - C(9,2)/C(50,4) = 4.39% = 1 in 22.78

There are many excellent answers to your question in the Probability Forum:
Distribution of AA vs KK in a given sample size (see the first reply)

So your AA vs KK stats seem a bit high, exactly what statistical significance I couldn't say.

Good post, BZ. For now he knows that his KK is running bad. There's some peace of mind there, I would imagine. Also will keep him from getting too gunshy with his KK to know this hasn't been the normal frequency with which his kings will run into aces. (hint, hint, OP. [img]/images/graemlins/wink.gif[/img])

[ringwielder]

Thanks BZ, great thread. Never even saw there was a forum just for probabilities, or would have posted there.

[BZ_Zorro]

BTW here's the definitive answer. I have a maths degree so I may as well start using the damn thing - I've avoided it for 860 posts before this one [img]/images/graemlins/smile.gif[/img].

Your situation follows a Binomial Distribution. You can think of it like a normal distribution with a small sample size. In this case you have a certain probability (4.39%) of an event occuring, run over n = 80 trials.

Here is a calculator for the binomial distribution. Your sample size is 83. The probability is 4.39% = 0.0439. i is the number of times it happens = 8. Click on calculate.

Here are the numbers:

Number of times you encounter AA when you hold KK:

O: 2.4%
1: 11.5%
2: 17.2%
3: 21.4%
4: 19.6%
5: 14.2%
6: 8.5%
7: 4.3%
8: 1.87%
worse than 8: 1.06%

So after 83 KKs, 2.94% of people encounter AA 8 times or more. That's 1 in 34.

[ringwielder]

Ok, give me a minute to get my breath back. My head hurts after going through all that! [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img]

It is somewhat reassuring that my statistical average is running high just now though.

[BZ_Zorro]

Yeah it's pretty ugly. I just post in the probability forum when I want an answer, and someone works it out [img]/images/graemlins/grin.gif[/img].

[jtr]

[ QUOTE ]
So after 83 KKs, 2.94% of people encounter AA 8 times or more. That's 1 in 34.

[/ QUOTE ]

Nice work BZ_Zorro -- you saved me the time of cranking up the old stats package to do a binomial calculation.

To the OP, think of it this way: 34 people just like you have been playing and hitting aces against their kings at various rates. You happen to be the guy at the bottom of the luck distribution (someone has to be) and thus you've been motivated to post about how often KK meets AA. The other 33 people are doing a little better with KK and thus didn't post.

This and all other problems can be fixed by playing more hands.