odds of KK running up vs. AA in the same hand?
 

Just a quick stat. question...a detailed explaination of how someone reasons this out would be super.

We know from common knowledge that you'll get AA only 1-210 times at a table. The same goes for KK, of course.

What are the odds on say, a 9 or 10 handed table, of a player like us getting KK and end up playing against AA on the same hand. This is preflop of course, and in NL, probably the kind of hand where ALL the chips go in the middle of the pot...LOL

I've just felt it's been happening a lot lately to me. Statistically, it's within reason to happen every few games, esp. in a tourney. Just curious how many times I'll see it when I get KK.

rb

Re: odds of KK running up vs. AA in the same hand?
 

First off, you will get once for every 221 hands(220-1), not 210, but that's mincing. Secondly, I think you're under the impression that KK is so rare, the chances of getting AA against you are even more remote. This is not the case. Chances are slightly over 204-1,( i will illustrate later) I think you may be operating under the assumption similar to the fact that 220-1 x 204-1=44,880-1, therefore it will only happen once every 44880 hands, which is correct, leaving you in 12th sigma hell. However, this is only part of the equation; you already have KK; thus taking 220 to 1 out of the equation, and leaving 204-1 as your only odds to factor. However still, there's more to that. It goes like this;

Chance of getting any card= 4 in 52(1 in 13) or .076923
Chance of getting a second card of same rank= 3/51 or .0588235
.076923 X .0588235=.0045248, or approximately 1 in every 221 hands, therefore 220-1. Easy enough, right. lets continue,(math is fun!);

Chance of getting an ace with KK out=4/50 or .08
Chance of getting second ace with KK out=3/49 or .0612244
.08 X .0612244=.0048979 or barely less than once every 205 hands, therefore 204-1

Ok so the chances of getting KK vs.AA is that 220-1 X 204-1, right? Right. But you already have KK, so you wanted to know the chance AA would be dealt out against you in this situation. That's our trusty old 204-1, as we have seen. So you take the business end of cowboys missing their bullets(as I like to refer to this phenomenon), once every 205 times you get it right? Right.

Headsup.

What, you don't play much headsup? Ok then, we need to factor in the nember of total opponents dealt in, usually 9. Easy enough; 205/9=22.77 (I'm sure there's some variance in here, but i'm fairly sure i'm really close) . Therefore, you will be in your very own version of the 7th circle of hell once every 24 hands in which you hold KK. Yippee! Don't worry, you'll suck out on him about 18% of the time, snapping him off and salvage a split another .5% of the time.

Also, the chances of AA vs. KK in any given 10 person hand? Well, it's tempting to say once every 4488 hands(44881/10), but that would be wrong. Chances are 22-1 times 20.4-1, meaning 448.8-1. So for about every 12 hours or so you play, it'll happen once,(although you may not see it, predicated upon board cards and betting).
I'm pretty sure of there figures, although I did do them myself and could very well be wrong,(but I doubt it.)