Re: Approximate general solution
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Might take another stab at this one with the lowball version in the meantime. Doesn't the simplicity really depend on whether you end up with more "1-x"s or just plain "x"s in the indifference equations?
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Yes, that is the reason.
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Actually, that's another topic that I think would be very much worth exploring sometime, as my "grain of salt" translation is obviously pretty vague. I will have to admit that I really like applying the [0,1] game more to pre-flop issues simply because the range of holdings is completely open prior to betting--hence at least allowing the assumption of completely even hand distributions. Once you get to the river, or even the flop, the distribution of possible hands makes for some major complications, as I see it.
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Well, what you say about unequal distributions on later streets is absolutely true. What you might look at are games like the [0,1] vs [0,1]^2 game, where player B has hand X with probability density function X^2. This actually resembles (to some arbitrary extent such that it makes sense to Bill and I) one-card vs two-card draw situations in lowball. I think this game has pretty strong insights about playing in the blind against a field raiser.
Another game you might look at, which I think I'm going to explore in our book, is the straight-flush vs nut flush vs aces hand on the flop in holdem (ie, flop of 9h 6h 3c and the hands are Ah2h, 8h7h, and AcAd). Try to figure out collusive strategies for the various pairs of hands--it's interesting.
Jerrod
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