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it seems like there actually should be a static rule based strategy that would be impossible to beat. Although it wouldn't be optimum against most players.
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Assuming this is true, then to me the interesting part is that as you pursue this strategy, you basically push the game towards a coin flip. I just posted
this over on the sleepy poker theory board. I'm still trying to wrap my head around why this doesn't feel right. Like a brain itch I can't scratch.