Re: Improved raising strategy for A in #4
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Interesting in your answer, however, is that it would seem that there are lots of co-optimal bluff-raising strategies for A. Hence, neither 1/12 nor 2/9 is any kind of "magic number" for when A would want to bluff-raise. Does that mean that 1/12 is just the minimum amount of bluffing to force B down to 2/3 for the limp-call?
If so, I guess it also means that if A starts bluffing more, B could make even more profit by reducing his calling criteria after the limp.
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No; 1/12 is the only co-optimal bluff-raising amount for A. Any other bluff-raising amount can be exploited by B. Now, it turns out in this game, that if B plays his optimal strategy, then A can raise-bluff with all kinds of hands and make the same EV, because he's indifferent to checking and raise-bluffing with most hands. But this is not optimal, because B can in turn exploit it.
Think about Roshambo (rock-paper-scissors). We know that if A plays [1/3,1/3,1/3], then all strategies for B have the same EV. But they are not optimal.
Jerrod
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