Gaming mouse: Honestly I'm just trying to understand why the numbers don't match up. I'm going to reference some numbers from the following two sites:
http://www.jazbo.com/poker/huholdem.html (heads up)
http://1-169pockethands.hitstrade.us/ (hand vs 10 players)
AA heads up: 0.8520371
AA on 10 player table 31%
If your formula holds then 0.8520371^9 = .256 should be the amount that AA wins 10 handed. However if the #s on the site above are accurate, AA actually wins 31%.
0.8520371^9 is only an estimate because it doesn't take into account the intererelationship of the various players' hands, as was pointed out by Scorpion Man, and the example posted by Stork, where a 50% heads up hand ended up winning 45% 3 way due to how the cards matched up.
22 heads up: 0.5033402 ^9 = .00207
22 vs 10 handed table: 11.86%
No I think clearly that multiplying the heads up win percentages simply doesn't accurately approximate how a particular hand will perform against multiple opponents.
My goal is to come up with a simple, quick approximation for multiple players when I know what my win % is heads up vs a single opponent's likely starting cards.