But if you assume that the opponent knows that they shouldn't pick between 37-64, doesn't that change your odds? The game theory here is similar to another qui

But if you assume that the opponent knows that they shouldn't pick between 37-64, doesn't that change your odds? The game theory here is similar to another quiz "Guess 1/3 of the average". You are really trying to guess how deep the other has thought about the problem, so you can tell which strategy they settled on, and then you adapt your strategy based on that. Of course, it's a loop.