Math question

[klondike]

How are the odds calculated for KK vs QQ heads up before the flop? Say your in a NL tourney & hold KK and someone goes all-in with QQ how much of favorite are the kings ?

Thanks

[gaming_mouse]

These odds are usually calculated by enumerating over all possible board cards and counting the number of times each hand wins. This is usually done with a computer program. You can download a free one here:

www.pokerstove.com

gm

[Yads]

Generally for pairs, the high pair is about a 4:1 favorite.

[klondike]

Thanks for the replys.
Yads can you give a short explanantion of thr math for this.
I would think the odds were much higher.

[gaming_mouse]

[ QUOTE ]
Thanks for the replys.
Yads can you give a short explanantion of thr math for this.
I would think the odds were much higher.

[/ QUOTE ]

Take QQ vs KK, for example. Roughly, you can say that QQ will win when the board contains at a Q but not a K, or both queens.

How many boards contain a Q? There are 48 cards left, with 2 Q and 2 K left. Each Q can be matched with (44 choose 4) cards. So there 389160 boards which contain exactly 1 Q and no K. An additional (46 choose 2) - 44 = 991 boards contain both QQ and at most 1 K. There are a total of 48 choose 5 = 1712304 possible boards, so the odds of the queens winning are:

(389160+991)/1712304=.2278

In odds form this is 1:3.4

Remember that this was an approximation. It doesn't account for straights, flushes, or full houses. The actual answer is 18%, not 23%. Again, the "math" for the exact calculation is just a matter of enumerating all possibilities, and this is usually done with a computer program. But the above calculations should give you a general feel for what's going on.

gm

[fnord_too]

I calculated all the probabilities for hand versus hand iteratively once (that is, I took all the starting hands to isomorphism and ran them against every possible two card hand with every possible board), but I get anal at times. Using a monte carlo is quick, easy, and will give you a very good approximation. (There are some free and open source packages out there for doing hand analysis; I wrote my own, it is a relatively simple problem if you are into software development.)

[klondike]

Ok now I have a better understanding I thought it was a little more complicated than just the qq has 2 outs. 4:1 is a good approximation for the math challenged like myself

Thanks again