[Troll_Inc]

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Is this the appropriate place for extensive content discussion? So far, I like it and expect it to spawn some lively discussion.

I did pick up one error on page 48. The unconditional probabilities p(A_has_the_nuts) and p(A_has_a_bluff) in the equation for <B,call> should be replaced by probabilities conditional on the event "A_bets".

p(A_has_the_nuts|A_bets) = 0.2/(0.2+x)

p(A_has_a_bluff|A_bets) = x/(0.2+x)

Notice that these will sum to 1. This change leaves the critical value x*=0.04 unaffected, but game value will now be seen to be a non-linear function of x. The primary conclusions don't depend on linearity and are unaffected.

A similar error occurs on page 56 in the expression for <A,call>.


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I'm trying to use this formula to solve a problem on river bluffing, and I don't get your comment on non-linearity.

It seems that if you convert to a formula where 0.2 is really 1-x. (In the book example, x=80% as a given value of bluffing, so 1-x = 0.2.)

So if you plug 1-x into everywhere you have 0.20 doesn't the denominator sum to 1 (as you state), and therefore revert to the original formula (which doesn't have a fraction)? And further, then isn't it linear?

Or are you saying that the solution is non-linear if player A doesn't bet 100% of the time? Presumably this would be done with the expectation of sometimes being able to check-raise?