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View Full Version : odds of KK running up vs. AA in the same hand?

whiskeytown
02-04-2003, 04:11 PM
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

Daliman
02-04-2003, 11:06 PM
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.