TPE Theory: Board Texture Analysis Using PioSolver with Andrew Brokos (Part 4)
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3for3
Fantastic stuff. Given that I have basically faced zero oversized bets in the past year, does that change how I should be responding to standard sized bets since my opponents range will be different?
Foucault
Great question, gets right to the heart of what equilibrium means. When you put multiple bet sizes into a solver, the responses that it shows you to a particular bet size are valid *regardless of what the opponent’s actual range is*. In other words, if it turns out that your opponent doesn’t overbet or overbets a very different range than what he would at equilibrium, he will not have a higher EV than the equilibrium strategy would against you. That’s what equilibrium means – he can’t increase his EV by unilaterally changing his strategy (though he can certainly decrease it). Now, it might be possible for you to do even better than what the equilibrium would produce by crafting an exploitive strategy, but what I want to emphasize is that it isn’t necessary. You aren’t getting exploited simply because you use an equilibrium calling/raising strategy and it turns out that he’s doing something way off equilibrium.
Foucault
I should expand on this. Let’s suppose that you ran a Pio sim and gave Villain two betting options: 75% or 150% pot. Pio will tell you how to respond to both bets, and it will tell you your EV is $X assuming that you and V both play its suggest strategies. If you were to respond with the Pio strategy to a 75% pot bet, but it turns out that your Villain’s range is way different from what Pio thinks it should be, your overall EV will not be lower than $X. Your response to his 75% pot bet will be suboptimal, but you’ll make up for it elsewhere, mostly in that you won’t lose EV that you would be losing if he were to make optimal use of his overbetting option. In other words, the fact that you’re going to respond suboptimally to his 75% pot bet isn’t enough to make it worthwhile for him to pursue his janky strategy over Pio’s.
That said, it will certainly be possible for you to do better than $X in EV against his janky strategy. A first approximation of how to do that would just be to run another sim without giving him the overbet option. That will produce a new strategy for you and a different EV of $Y. $Y should be greater than or equal to $X, probably greater. You can use the node locking feature to further refine your strategy in light of how you think V will actually play.
Hope that helps!
3for3
That’s what I was looking for. I would prefer the $Y option 🙂