Great post. Just fixing a very small (but important) typo above.
Now my question: What if villain loosens up his calling range not to 100%, as you suggested, but say to 50%? What does that do to the numbers? I'll even increase your win % to 40%, since villain is calling with a much wider range than before.
He folds you win = 3650 * .5 = 1825
He calls you lost = 0 * .2 = 0.00
He calls, you win = 6800 * .2 = 3400
EV(shove) = 5225
EV(fold) = 3250.00
As you said, intuatively, you would think calling with a wider range (but not ATC) would be better, but the math says otherwise. That's awesome.
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