Maximally exploitive strategy question

[SeanC]

[ QUOTE ]
[ QUOTE ]
How does that math work on the flip side--the person with the decent hand determining the optimal calling percentage?

[/ QUOTE ]
It works the same way. Take the example from the OP. Let y equal the frequency with which player B calls. Again there will be an indifference threshold. If player B calls less than this player A should bluff everytime; if player B calls more than this player A should never bluff.

EV(bluffing) = 3(1-y) + (-1)*y
EV(not bluffing) = 0

Set them equal and solve. y = 0.75.

If B will call less than 75% of the time A should bluff everytime; if he calls more than 75% of the time A should never bluff; if he calls exactly 75% of the time it doesn't matter if a bluffs or not.

This result is consistant with common sense pot odds way of thinking about it, which may make a little more sense. Player A needs to risk 1 bet in order to steal 3 bets. If he can steal the 3 bets 1 of 4 times he'll break even. Player B must catch him 3 out of 4 times (3/4 = 0.75) .

[/ QUOTE ]

Simple enough, thanks!