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This is almost correct but not quite. Optimal strategy wins against many other strategies and breaks even against others. The ones it breaks even against are not necessarily optimal themselves, they just don't make mistakes vs the optimal one but might be exploitable themselves.

To be more precise: you only need to replicate not mixed (pure) plays of the optimal strategy to not lose against it. Your frequencies for mixed actions can be completely off though.




In theory you are right but when talking specifically about poker, I can't think of any example of imperfect play that isn't exploited (to a certain extent) by optimal play. Yes, playing the opponent would win more, but optimal play makes a (smaller) profit as well. Or would you know an example?


The imperfect play is in the mixing. Imagine you play like optimal but every time you have a mixed action of bluff or check you bluff. You won't be exploited by an optimal strategy but you will be very vulnerable vs someone who bluff catches a lot.




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