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Old 05-26-2005, 03:38 PM
A_PLUS A_PLUS is offline
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Join Date: Aug 2004
Posts: 44
Default Mathematical Hand Analysis (the EV of pushing 99 from MP)

Ok, I posted earlier about doing a more complete mathematical analysis of a questionable play. I did a quick and dirty version of the analysis. First, I ignored the fact that there would be more than one caller. This will lead to an inflated EV number in my analysis (although not to dramatic, b/c the addition of another hand, even if it is AA-KK, does not eliminate the equity of 99, instead almost halfing the EV of a showdown). Also, I ignored other options (opportunity cost, sorry I'm an Econ grad student).

ANALYSIS

Situation: 110 players remain, 40 places pay. I have 3200 TCs, average is 4400. Blinds 100/200. I am sitting in MP with 5 players yet to act behind me (including the blinds).
Everyone is comfortably stacked, ranging from 2600-5500. Play has been fairly tight, but not overly so.

Calculations
Two possible outcomes, I get called, or I win the blinds
I give my opponents the calling range of AA-77, AK-AJ


% of time called =
Total number of hand combinations remaining after removing 99 = c(50,2)=1225

The number of hand combinations that my opponents will call with = (7*6)[PP other than 99] + (16*3)[AK-AJ] + 1[99] = 91

This next part is not exact, and may very well be dead wrong

1225 total hand possibilities, 5 random hands = c(1225,5)=
22 trillion and change

1134 total hand possibilities that will not call (1225-91), 5 random hands = c(1134,5) = 15 trillion and change

So c(1134,5) / c(1225,5) = .6794

67.94% chance of stealing the blinds

So....

Steal the Blinds 300
% of time 0.679359427
subtotal 203.8078281

Showdown pot 6550
equity vs range 0.463
EV of showdown -167.35
% of time 0.320640573
subtotal -53.65919987

TOTAL EV 150.1486283

Now assuming that CEV = $EV, does anyone see a problem with my calculations? I am a little worried about how I handled the % of times that I will steal the blinds. For instance, someone will fold A7, but that will affect the number of Aces available for hands like AK that will call.
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