In two-player games with perfect information, if both players play optimally, will the game always end in a draw?
Accurding to Zermelo's theorem, in finite two-player games of perfect information in which the players move alternately and no affect of chance, one of those three possibilities is true:


First player can always win.
Second player can always win.
Both players can force a draw.


For example, Tic-Tac-Toe is known to have a strategy by both players that will force a draw.  In 4-in-a-row it is known that the first player has a winning strategy.  Chess haven't been solved yet, I think that the conjecture is that a draw can be forced.


A list of solved games: https://en.wikipedia.org/wiki/Solved_game
The field of this question is called Combinatorial game theory (CGT)
see: Solving Chess