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GTO play decreases EV

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Posted by 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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