[nimih]

The result holds even if Player 1 knows Player 2's strategy and attempts to foil it, although as you correctly observe, the paper only claims >50%, and Player 1 can minimize that margin by picking the two numbers to be right next to each other (and trying to choose them such that they occur in a low-density area of Player 2's distribution f(t) ).

[cortesoft]

Yeah, as I was working it out in my head, I was realizing that it would approach 50% but never hit it, since no matter the distribution you choose, the higher number will always be greater on average than the smaller (by definition). You can approach an equal average as you choose a larger and larger range, but never hit it.... which I guess is what the paper is proving.

Practically, though, you could get close enough to 50% that it would be immeasurable by sampling.