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# AA vs KK

Discussion in 'Chit Chat' started by bigmrfrank, Jan 31, 2010.

1. ### bigmrfrank

I need help from some of you math wizzes. A poker buddy and I were having a debate about how many times statistically AA runs into KK and vise versa. I can do quick at the table type % but I'm looking for an exact figure to settle the debate.

TIA

2. ### FanOfFridays

The odds of KK running into AA depend completely on the number of opponents at the table. If it's a heads up game, the odds are 1 in 48841 hands. At a 6 man table it's 1 in 9768 hands. At a 9 man table it's 1 in 6105 hands.

I sense a potential misunderstanding here. So to make this very clear: Before the cards are dealt in a hand, the chances that you will get KK and then face AA are about 1:5039 on a 10-player table. However, if you already have KK in your hand, then the chance that someone else has AA are 1:21.8.

Some further observations: If people have already folded before you, then the probability falls roughly in proportion (so if 5 people folded, then it would be approx. 1:43.6). Also, suppose that opponents will reraise with JJ+ and AK and nothing else, then if you have KK and get reraised, the probability that you are facing aces is now actually 1:2.67 - 27%.

The take-away is not to get stuck in thinking "the chances of KK and AA facing each other in a hand are 1:5039" and not taking in new information (such as "I've got KK").

http://forumserver.twoplustwo.com/25/probability/how-often-my-kks-up-against-aa-preflop-53353/

3. ### bigmrfrank

Interesting. The was my argument - "it depends". I always used the rough formula that assumes you already have the hand in question which is -

The amount of pocket pairs that beat yours

x

The amount of players in the hand or yet to act

divided by 2

Example -

So I have 99 UTG at a 9 handed table = 5 pairs higher than mine

x

8 players yet to act = 40/2 = 20% chance of a higher pair

or

So I have 99 in CO and it's folded around to me at a 9 handed table = 5 pairs higher than mine

x

3 players yet to act = 15/2 = 7.5% chance of a higher pair.

So with KK UTG there should be a +/- 4% chance of running into AA and if KK in CO there should be a +/- 1.5% chance.

My theory was it depends and his was it's fixed once the cards are in the air. In a way we are both right but in practical application it should depend on if you hold the pair in question. Pokertracker seems to support the "it depends" as well. Over a large sample size and not taking position into account I see my KK running into AA around 3% of the time.

Thx

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