Theory question concerning GTO v suboptimal ranges
Posted by SquishyDoggy
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SquishyDoggy
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High Stakes
Theory question concerning GTO v suboptimal ranges
Very important theory question, let say we are bluffcatching at GTO frequency with our range, then our opponent starts overbluffing, but we don't adjust and continue defending that fixed frequency (since he is using the same bet size), does our opponent lose EV since he is playing suboptimally, if so where is he losing EV from?
So imagine a one street river toy game where one has a polarised range and other has bluffcatchers, the player with bluffcatchers decide to play GTO calling frequency regardless and never adjust to any deviation by the bettor.
The bettor starts overbluffing by adding in way too many bluffs, but his bluffs all remain at 0EV at that sizing (assuming no card removal), because caller is still calling same % v that sizing. So how does this suboptimal play lose EV v a GTO calling range. The bluffcatchers supposedly now gain EV, but we also see less showdowns in the whole river spot and lose the pot more often than we should.
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Then he bluffs too much for the sizing and your call is good a higher % than it would be if he was bluffing GTO, so he loses money.
You're essentially claiming that if our opponent takes a 0EV action more often, they'll lose money. That's ridiculous
Villain deviates from GTO -- > we are no longer indifferent to calling --> Our static calling range picks up EV.
Villain maximises EV by having a ratio of value to bluffs. Your GTO perfect bluffcatching solution demands the smallest possible amount of bluffs in that ratio.
GTO is not about making villain indifferent to any action. Whisper his name, but Doug Polk has a very good layman's explanation of this confusion about indifference in GTO on youtube.
Pretty sure you are both wrong. Call is good a higher % of the time but total EV on the river remains the same until we adjust our strategy.
You can run this game in piosolver or CREV to check results.
Pot = 1
Stacks = 1
Board = 22233
Hero range = KK(6)
Villain range = AA(6), 87o(12)
Equilibrium is villain betting 1 with AA(6), 87o(3) and checking with 87o(9). Hero calls with KK(3) and folds KK(3).
Hero EV = p(check)ev(check) + p(bet)0 = 0.51 + 0 = 0.5
Villain EV = p(check)0 + p(bet)p(call)p(AA)1.5 + p(bet)p(call)p(87o)0 + p(bet)p(fold)1 = 0 + .5.5.666661.5 + 0 + .5.5*1 = 0.5
What if villain starts betting with entire range and hero continues to call 50% and fold 50%?
Hero EV = p(check)ev(check) + p(bet)p(call)(p(AA)-1+ p(87o)2) + p(bet)p(fold)0 = 0 + .5.33333-1 + .5.66666*2 = 0.5
Villain EV = p(call)p(AA)2 + p(call)p(87o)-1 + p(fold)1 = .5.333332 + .5.66666-1 + .51 = 0.5
In equilibrium villain bluffs with a frequency that makes hero's EV = 0 when he faces a bet. All of hero's EV comes from give-ups.
In the scenario where villain bets 100%, the opposite is true. None of our EV comes from give-ups and all of it comes from calling villain's unbalanced bet.
Until we adjust by calling more often, our EV will still be 0.5.
Yeah, you're right. Total EV remains the same, calling EV increases and villains bluff ratio is what makes us indifferent to deviating from equilibrium. If we do not deviate he can bet 100%. I am humbled.
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