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You're writing something that is at best accidentally misleading and at worst confidentially incorrect.

What is your formal definition of "optimal strategy"? A Nash equilibrium is considered optimal in the sense that it's a state where no one can gain an advantage by deviating from the equilibrium.

Sure, if your opponents don't play the Nash equilibrium, there is room to exploit that deviation and potentially gain more than what you would get from playing the Nash equilibrium. However, you also make yourself exploitable in return, so I don't think you're presenting the whole picture here.



Poker players typically optimize for making the most money in expectation per hand. Either way, I'm certain that the exploits I've described for players that bluff too much or call too much are correct so I'm not too worried about being slightly off. Poker strategy is about heuristics.


For practical poker, I'd formally define "optimal strategy" as the strategy that maximizes profit per time (or per game) for a set of opponents, including also the actions needed to "explore" and discover any bias before exploiting it.

Assuming at least one of opponents is not playing Nash equilibrium (which is a very solid assumption), playing the Nash equilibrium becomes suboptimal as it doesn't exploit the exploitable as much.




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