Re: blitzing on third and long and the problem with poker forum advice
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I want an example to the following, or a proof that it does not exist:
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[in a poker like game] a mixed strategy in which some of the elements have different expected value from the others is maximally profitable
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Try slapping yourself really hard and then reading it again.
If it still isn't obvious, observe that exploitive strategies are pure strategies for the simple reason that we never choose not to exploit our opponent when his strategy is exploitable. If he's exploitable, we exploit him 100% of the time or we give up EV.
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Uh... an exploitable mixed strategy often (not always) can only be exploited by another mixed strategy.
I think you misunderstand chen and akerman's argument... they are not arguing mixed strategy is not optimal; they are arguing against most opponents, who are not using a mixed strategy or even half way observant, the optimal strategy is almost always pure. This IS consistent with what Pete and Tower are saying.
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