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Why To Never Do Anything 100%
I've been doing some work with pareto equilibriums and I've come to a realization about poker strategies. If our opponent is highly exploitable, say, in a way that would cause us to CORRECTLY perform an action 100% of the time, we will be MORE profitable if we only perform that action 80% of the time.
The 20% of the time when the action is likely close break-even (due to our hand strength, our opponents tendencies, the board, etc) will not produce good enough results to compensate for our need to keep our strategy deceptive.
I am officially withdrawing all of my "I'd XYZ him 100%" strategies and making them "I'd XYZ him 80%."
Saje busts SAGE
Better Than Nash Shoving Equilibriums
The Nash-equilibrium push-fold chart is a good resource for new HU SNG players, because it illustrates the power of going all-in with a wide range of hands. Playing your hands according to the Nash charts guarantee that you won't lose money, but the goal of poker is to win money, not merely avoid losing it. Clearly, against a player who folds 100% of their hands, even at very large stack sizes we could profit by shoving hands that the Nash equilibrium charts would tell us to fold. This proves that there exists maximally exploitative all-in range (called a "best response") that is different from the Nash ranges. To solve for a better solution, I considered a total of three variables: your hand range, your opponents calling range, and your effective stack size.