I've been running simulations of two strong agents playing Chess which always ended in a draw. Followed by this simulations, can we state that two-player perfect-information games like Go and Chess will always end in a tie when both players play optimally?
Accurding to Zermelo's theorem, in finite two-person 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.
No - there need not always be a tie in the general case. Even in games of perfect complete information there may still be a bias towards one player. For example the game of nim cannot end in a tie, and depending on the starting position gives an advantage to either the first or second player - e.g.
Size of heaps | Result with A | B | perfect play ---------------------------------- 1 | 1 | First player wins 2 | 2 | Second player wins
For the specific games you mentioned (go and chess) then it is not known what the result is with perfect play. For more details see the corresponding Wikipedia articles:
You are missing a couple of important factors in your question that make it impossible to answer as it stands. Mainly that a game with perfect information available to both players doesn't mean that it is not balanced in one players favor.
While it may be true that there are games out there where it is balanced between both players it is also true that there games where it is not the case it can be balanced in favor of either player (such as the second player is more likely to win which is why they go second).
A secondary point is that there are games where a tie or draw is not possible and if it gets to a point where nothing more can be done a player is declared the victor by default.