If it’s impossible to win, because your opponent always picks second, then every choice is optimal.
If you pick simultaneously, picking the highest number you can describe is optimal, so that’s another situation where there is no optimal solution for an infinite mind, but for a finite mind, there is an optimal solution.
If it’s impossible to win, because your opponent always picks second, then every choice is optimal.
If you pick simultaneously, picking the highest number you can describe is optimal, so that’s another situation where there is no optimal solution for an infinite mind, but for a finite mind, there is an optimal solution.