Is there something magical about having 2 opponents?

[Jordan Olsommer]

Hi all - I was just mucking around with the ever-so-useful Gocee chart of race probabilities for certain hands versus x number of random hands, to see what kind of equity edge the hands have.

Calculating the edge is simple, of course - e.g. AA has according to the chart an 85.3% probability of holding up over one random hand, and the average hand in a two-handed game has a 50% probability of winning, therefore AA has an equity edge of 35.3%, since it figures to win 35.3% more than its fair share of pots. Right so far?

If so, then a curious thing arises when you look at the data. Here are the preflop equity edges for AA-TT against 1, 2, and 3 opponents.

AA (1) 35.3%, (2) 40.07%, (3) 38.9%
KK (1) 32.4%, (2) 35.57%, (3) 33.2%
QQ (1) 29.9%, (2) 31.57%, (3) 28.5%
JJ (1) 27.5%, (2) 27.87%, (3) 24.2%
TT (1) 25.1%, (2) 24.37%, (3) 20.2%

For AA-JJ, the preflop equity edge actually goes up when you add a second opponent, but then back down when you add a third! (it goes further down with more opponents for 3+ opponents or for TT or lower). Why is this?? What's so special about having two opponents as opposed to one that makes the edge increase?

[Disclaimer: if you find some glaring incredibly boneheaded basic math mistake in my calculations, please point it out quickly before my window of opportunity to delete this post and save face erodes. Thanks [img]/images/graemlins/smile.gif[/img]]