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Originally Posted by venice10
This to me seems to be an important point. In order for the villain to get to the river with just a bluff catcher, it implies that the game is being played for thin value. GTO just reduces the value to zero.
im not quite sure what you mean by "being played for thin value," but this game doesn't imply anything about thin value. the structure of the river game is actually the opposite - our value bets are assumed to win 100% of the time when called. you can extend the game to include earlier streets, and the villain will still be calling on earlier streets in order to prevent us from being able to bluff too much (his call % will be lower on earlier streets bc of the fact there are more streets to play, though). if you change the % of the time we win when called on the river to model thin value bets, you will just see that we can bluff less often.
an important point about the game is that the value of the game to the betting player is
not 0, even when both players are playing gto, since when the bettor bets he expects to capture the whole pot, on average. if the bettor never has to x/f (ie he doesn't have "too many" bluffs), then the value of the game to him is the amount in the pot. nothing about gto guarantees that any player will be able to break even or that one player cannot profit, and this game is structured such that the bettor will profit. i think people have brought up the argument that if one player's gto strategy has negative ev (ie the best he can do is minimize his losses), then he can just choose not to play the game. this is sort of circular though, since that is just adding a rule/assumption to the game that players can choose not to play, and therefore break even. you could just as easily add a stipulation that someone has a gun to the player's head and is forcing him to play. games dont necessarily have to model real life to have informative value.
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CMV's point on knowing the villain's range brings up another question. On-line, one can record and tabulate thousands to millions of hands to come up with precise range. Realistically, can a live player generate a near approximation of this same precise range? If so, how would they do it?
even with a database you can't "know" the villains range. this is simply a challenge in applying game theory to poker, and to playing poker generally.