Re: No difference based on the assumtion...
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If you looked at the assumption made in my previous post
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If A's strategy is:
[0,x] : raise(bluff)
[x,y] : fold
[y,z] : call
[z,1] : raise
And B's strategy is:
[0,a] : fold if raised
[a,1] : call if raised,
where 0<x<y<a<z<1
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you see that it doesn't matter which hands in [0,y] will be bluffed with,
since z>y anyway!
But if you don't assume A would have thought of that, this would not even
necesserily be B's (co-)optimal strategy I think.
Next Time.
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Actually, it would. The only requirement that a strategy pair be optimal is that neither player can unilaterally increase his equity by changing strategy. So your solution is in fact optimal.
What's also true is that all strategies where B bluffs the right number of hands in the range below calling are all co-optimal.
The fact that a strategy <A> is dominated doesn't preclude it from being optimal; it simply means that there exists another strategy <A'> which performs better than or equal to <A> against all counterstrategies. The strategy where you bluff [0,z] does worse against some suboptimal strategies from A (like where he calls with some bad hands) and is dominated by the strategy where B raise-bluffs his best folding hands rather than his worst.
Jerrod
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