[Jazza]

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This is different from your original question

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it is?

in any case it is true that if at least one player randomizes his strategy, 50/50, then the EV has to be 0.

but yeah i'm interested in when they try to outwit each other, for instance, if your opponent did the same thing 1000 times in a row, you would probably consider a strategy that is not randomly picking 0 and 1