GTO play decreases EV
Posted by TuttiFrutti
Posted by TuttiFrutti posted in Gen. Poker
GTO play decreases EV
Given the definition of Equilibrium that no player can unilaterally change their strategy to increase their EV, how come that a suboptimal betting frequency will increase the EV of the bettor?
Let's assume the pot is 100 and Villain's range is 2 combos of AA and 2 combos of QQ and we have KK only. He value bets pot size with a GTO range, meaning he bets both combos of AA and 1 QQ combo. We call 50% (GTO frequency). In this case, the EV for both Hero and Villain is 0 (Both will win half of the pot). However, if Villain decides to bet all his combos, our 50% calling frequency will result in a -0.25 EV.
Villain EV when villain bets all combos:
1/2100 + 1/2(1/2200 - 1/2100) = 125
Villain EV when villain bets GTO frequency:
1/2100 + 1/2(2/3200 - 1/3100) = 100
So where does Hero get back the EV lost in this spot? Am I missing something?
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