Re: Head Up Theory Question
Assuming that you bet or raise if you have a better hand than opponents average hand, you reraise 8 times. (when the opportunity to reraise time number 9 gets to you, his average hand is 999,998.1 without rounding.)
For pot limit, I would guess you bet the pot when you figure to be ahead of 66% of the hands he could have, since you are always offering him 2:1 (not sure about the first bet, probably still 500K or higher). That gets you to 5 reraises (all raises assumed to be full pot) before you stop if I did the math right.
In pot limit, though, I think you can make your bets more exactly, but I would really have to think about that and there are information considerations to not betting the size of the pot.
Edit - If your initial bet line is 666,667, it is still 5 reraises if I did the math correctly.
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