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Postby excession » Tue Apr 22, 2008 4:04 pm

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Postby Aisthesis » Wed Apr 23, 2008 12:43 am

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Postby DaFish » Wed Apr 23, 2008 4:25 am

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Postby Aisthesis » Wed Apr 23, 2008 11:23 am

It's the other way around, actually. Value bet range is always top half of calling range--and is determined by the call range.

B's call range is determined exclusively by bluff prevention. He has to call enough to prevent A from profitably bluffing at 1.

If A never bluffs, B's call range will be completely different. Suppose A value bets only and keeps the same range of [0,1/18]. Now B has to call 8 for a chance to win 9. B thus needs a win probability of 8/17 to break-even. So, now he only calls on with < (9/17)*(1/18), whatever that is.

That's also the reason why the solution seems counter-intuitive to anyone who has in mind the adage that you need more to call than to bet. That's only the case against players who are rarely bluffing.
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Postby Aisthesis » Wed Apr 23, 2008 9:48 pm

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Postby Aisthesis » Wed Apr 23, 2008 11:37 pm

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Postby excession » Thu Apr 24, 2008 6:29 am

The do it for 0.5, 1, 2, 3 , 4 and 10 (you have already done it for 8).
Will give you a good approximation of the answer.
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Postby Aisthesis » Thu Apr 24, 2008 10:17 am

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Postby Aisthesis » Thu Apr 24, 2008 10:34 am

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Postby Aisthesis » Fri Apr 25, 2008 3:42 am

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Postby Aisthesis » Fri Apr 25, 2008 3:50 am

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Postby excession » Fri Apr 25, 2008 6:57 am

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Postby Aisthesis » Fri Apr 25, 2008 1:53 pm

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