Game Theory Resolution

[mykey1961]

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x = 0.625, a = 0.4375


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Ok it took a while but the lightbulb finally flickered.

As far as the BB knows, the SB may or may not play optimal, therefore the BB plays an optimal strategy "x" which locks in a win rate >= 5/64BB per hand.

SB also doesn't know if the BB is playing optimal, so SB plays an optimal strategy "a" which locks in a loss rate <= 5/64BB per hand.

Seems to me that if SB determines that the BB is also playing optimal, then SB should open up the range, and look for the BB trying to exploit the new range. Once that happens, SB should tighen up the range to exploit the BB.. and the race is on.