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
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/
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