[murbard2]

The reason maximizing EV isn't the answer is that you care about having a larger number than your opponent, not about having the largest number possible.

Imagine we play a die game where whoever rolls the largest number wins. Which die would you rather play with?

1-1-1-1-1-10^250 or 2-2-2-2-2-2

The first die has an EV of about 1.67e249, the second die an EV of 2. Yet, the second die will win 5 out of 6 games against the other one.

To solve the problem, you must find the Nash equilibrium of the game. That is, you must find a strategy which the opponent cannot exploit, no matter what he does.