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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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