hi guys, I don't know if this thread is still active, I hope so. Reading this amazing book I got stuck at one point in chapter 7.3.2 (p248), where it deals with the River bet-or-check decision for the SB.
No problems at all concerning the symmetric distribution (i.e. when EQSB(hv)=hv), but when it goes to the asymmetric distribution all appears very clear but in applying those concepts I find meaningless solutions. Precisely, I am referring to the part where the author says that the
relative strenght of the ranges changes a lot the frequencies. So I ask myself why, if it's the relative strenght what matters, in the formula (7.3) appears EQSB(hv) as a relevant variable while hv doesn't appear at all. From this (surely wrong) point of view something strange is going on there, and the situations gets even stranger when I try to find the cutoff calling hand (hc) from that same equation (7.3), procedure appearently suggested from the author itself in the next page ("The weakest value-betting hand in a spot is something many players seem to have good intuition about. Once we know this, we can immediately find Villain's calling cutoff through Equation 7.3."). What happens trying to solve the equation (7.3) for the variable hc, is that the result (given by a calculator, no human mistakes involved
) is hc = 2(EQSB(hv)) - 1 ; and after experiencing the joy of seeing a very simple solution, i realized it was perhaps too much simple (!), lacking at least two obvious important variables : P (the pot size) and B (the Bet size). How can Villain's calling frequency be indipendent of the Bet and Pot size ? Clearly something was wrong in this previous reasoning.
Something else that further makes me believe I didn't get at all that passage is that for what I understood hc should be to solution of
two indifference equations ; that's to say hc has to make both Hero's best bluffing hand (hb) and Hero's worst value hand (hv) indifferent between checking and betting, and so I expected a system of equations to be used to find hc, but if do there's no warranty I get consistend results from the individual equations.
In short, and to anyone so kind to try to help me I really apologize for the lenght of this post, I'm not able to find Villain's calling frequency (1-hc) and neither Hero's GTO valuebetting frequency (1-hv) when Hero is IP.
Let me know how did you get right that passage