Analysing An All In Preflop Play

[NMcNasty]

I made some super rough calculations for just pairs that show its 99, although 88 is right behind and if a complicated factor that I didn't calculate was calculated I think 88 and possibly 77 might be correct.

One person has a hand better than 99 (all the other pairs) 15/663 of the time which is .023%. So the probability that no one has a better hand than 99 with 9 players left at a table is (.977)^9 = .81. So 99 takes the blinds 81% of the time and is a huge dog 19% of the time. Coincidentally when 99 is a huge dog there's a 19% chance it will win. I just got this number by casually fooling around with the cardplayer calculator and using QQ sharing one suit as the average dominating hand. You get 23 when you win (your opponents matching stack plus the blinds) and you lose your 20 when you lose. So the EV when up against a pair is roughly .19(23)+.81(-20) = -11.83. So we then plug that in to get our final EV .81(3)+.19(-11.83) = .18.
With 88 our chance that we are beat preflop rises from a 19% to a 22% chance.
So its the EV is .78(3)+.22(-11.83) = -.2626

There are two factors I did not calculate though. One is that you don't always win 23 when you win because sometimes your caller is in the blinds, so you'll only win 22 or 21. This factor would lower your EVs a little. The huge factor I'm not calculating though is when there's a second or third caller. When you get called by JJ and then QQ, your chance to win is only reduced by a few percentage points although the money in the pot is almost doubled. I think that factor would be enough to put 88 in the +EV range and possibly even 77.

Again these numbers are all super rough estimates with all sorts of rounding errors and I also completely ignored the possibility of split pots.