Basic Statistics...

Tickner · #1 09-26-2007, 10:16 PM

Any math buffs out there, help me figure this out. I'm too lazy to look up the correct method of solving this.

The probability of a player having AA or KK on any random shuffle is 1/114 (approx - so give or take a few on that). Anyway...

If there are 6 players at a table, all dealt a random hand, what is the probability that ONE of the players has AA or KK? And how do you figure this?

n1nj4.br · #2 09-26-2007, 10:24 PM

6/114

Jay Riall · #3 09-26-2007, 10:28 PM

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6/114

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No, because you have not factored for cards that have been already dealt.

Tickner · #4 09-26-2007, 10:28 PM

thats what I quickly came up with too.... but it doenst seem right to me.

Works out to about 5%, meaning one in every 20 hands a player has AA/KK.

Is that right?

Jay Riall · #5 09-26-2007, 10:29 PM

It won't be far off.

Tickner · #6 09-26-2007, 10:36 PM

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6/114

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No, because you have not factored for cards that have been already dealt.

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What do you mean exactly?

tarheeljks · #7 09-26-2007, 10:37 PM

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6/114

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No, because you have not factored for cards that have been already dealt.

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What do you mean exactly?

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the second person has a smaller # of card combinations available b/c the first person has taken away 2 cards. the same follows for persons 3-6

edit: xpost this in probability and jayshark or someone will have it done pretty quickly. i'm lazy [img]/images/graemlins/smile.gif[/img]

Jamougha · #8 09-26-2007, 10:41 PM

It's very annoying to work out but 5% is probably close. Do a monte carlo sim if you rly wanna know.

Tickner · #9 09-26-2007, 10:45 PM

cool, thx guys

Pokey · #10 09-26-2007, 10:48 PM

Probability that a player is dealt AA: 1 in 221.
Probability that a player is dealt KK: 1 in 221.
Probability that a player is dealt AA or KK: 2 in 221.
Probability that a player is NOT dealt AA or KK: 219 in 221.

Probability that six players are not dealt AA or KK: since these are nearly independent events, we can get a rough estimate by taking 219/221 to the sixth power, which is 94.7%. The odds that one or more players is dealt AA or KK will then be 100% - 94.7% = 5.3%. Since the odds of TWO players being dealt AA or KK is going to be about a factor of 100 smaller than the odds of one player being dealt AA or KK, we can just pretend this is the answer.

So, call it five and a half percent or so. The numbers are rough estimates, and calculating it exactly would improve the accuracy very little while being markedly more of a pain in the butt.