odds question

[rybones]

I posted this in the prob. forum, but they did not seem to get the question. The answer I got was 220: 1. but that was not what I asked. could you look at the questions below and help?

Does anyone know where to find or have the odds of someone/anyone having A,A at a table of 10 during a given hand?

I also have the same question for A,Ks and A,Ko. and would like to know how those odds change as the table gets smaller?

In addition, what are the odds of two or more players having pp 10 handed. Again, how does this change as the number of players goes down?

Any thoughts on where to find this info would be great.

Any info on how to do the math would be fun to look at, but for me it would be like seeing the opera: looks and sounds great, but I don't get it.

Thanks,

Ryan

[se2schul]

I'll answer the AA question.
Basically, you disregard the fact that there are 10 people at a table and work out the probabiliy that dealing 2 random cards to someone gives them AA.

(Probability that a random player is dealt 2 aces) = (number of ways they can get two aces) / (number of ways they get any 2 cards)

= 4C2 / 52C2

= 6/1326

= .4 % chance that someone is dealt 2 aces (4 times in a thousand)

(note: 4C2 means 4 "Choose" 2, where "choosing" is defined as nCm = [n*(n-1)*(n-2)*...*(n-m+1)]/[m*(m-1)*(m-2)*...*2*1]

Now, each person at the table has equal probability of being dealt AA. So, at a 10 person table, the probability that someone is dealt AA = 10 * .004 = .04 = 4%

So, on average, at a 10 person table, there will be someone holding AA about 4 times every hundred deals.

Note: if you are playing at a 10 person table, you likely want to know what is the probability of one of the nine remaining people holding AA pre flop given that you either have an A or don't.
Also Note: As the hand progresses with the flop, you have more information and this probability changes. For example, if the flop comes down 2-4-9, that will increase the probability that someone is holding AA, but it the flop comes down A-2-A, that probability decreases.

All your questions can be answered in a similar way to this. Some of them are more complex, but they can be solved analytically. For more complex problems of this nature, I think it would be easier to write a simulator and solve by simulation.

Hope this helps.
If it's not what you meant, let me know and I'll try again.

Steve