Feedback on my Thought Process
https://forumserver.twoplustwo.com/32/be...
The thread in the above link has been like a song in my head that won't go away. Like poker in general, it appears pretty straightforward; but there's a hidden depth underneath. I didn't want to hijack the thread; so I'm posting here and looking for your feedback.
A hand's total equity is (fold equity + hand strength vs V's range). But in practice, I approach each component independently. For example, we're OTT, OOP, HU, and we believe that our hand strength equity vs V's range is 25%. I will only attempt a bluff if I have confidence that my opponent will fold at a higher frequency than the break even percent requires. If not then the next option is to consider whether my opponent will cooperate (by not raising) with a blocking bet of 1/3 PSB, giving me the minimum direct odds to continue. If neither option is feasible then by default the correct action is to check.
As far as the math, @statmanhal provided an equation to arrive at the EV. Frankly the math is beyond me. So I'm wondering if there's a simplified equation that might involve more steps but arrive at the same result.
1 Reply
As shown in the referenced thread, the basic EV equation for a hero bet with fold equity is:
EV = Pr(fold)*Pot +(1-Pr(fold))*(eq*(Pot + 2*Bet)- Bet)
Now if you set EV to 0 so that you are assured to at least break-even, you can solve for any one of the 4 variables given you know or can estimate the others.
For example, with a pure bluff bet, eq = 0, so
EV = fe *Pot +(1-fe)*(-Bet) = fe*(Pot + Bet) – Bet [fe = fold equity = Pr(fold)]
If villain always calls, fe = 0 and EV = - Bet
If villain always folds, fe=1 and EV = Pot
For another example, you assumed the card equity was 25%. Therefore, the equation will tell you that for a bet of B into a pot of P villain must fold with at least this frequency:
fe >= X / (X-P), where X = eq*(P + 2B) -B
So if a pot size bet is made, B=P. Then X = 0.25*(P +2P) – P = -P/4 so for at least break-even
fe >= -P/4 / (-P/4 -P) = P/(5P) = 20%
If you made this calculation and guessed that villain will not fold that often, you then will consider calling a blocking bet of B= P/2 (you had P/3) which assures breakeven
EV = eq*(Pot +2*Bet) -Bet= 0.25*(P + 2*P/2) - P/2 = P/2 – P/2 = 0
I hope the above indicates how you can use the basic EV equation in steps to answer questions like this to help develop a winning strategy through study. The math involves no more than high school algebra and the more you do it, the easier it gets (so they claim).
This is not to say the math is all you need for factors like opponent tendency, stack sizes, tournament standing, etc. are important but the math can give you a first cut look .
