Tactics versus strategies—the case of chess

Does chess admit of winning or drawing tactics? Which information exactly do we need to include as part of the board position?

This is part three of a series on tactics and strategies in the theory of games.

In previous weeks, we introduced and explored the distinction between tactics and strategies in the theory of games, and we saw how with many games, one can achieve a tactical form of the fundamental theorem of finite games.

This week, I should like to consider this issue specifically in regard to the game of chess. Are we able generally to achieve winning tactics in chess? Or drawing tactics for both players? We have observed on abstract game-theoretic grounds that if we supplement the usual chess board positions with more information from the game tree, making them rich (in the technical sense of rich board positions), then indeed we shall achieve the tactical conclusion of the fundamental theorem—one of the players will have a winning tactic or both players will have drawing tactics. But how much information do we actually need? Perhaps we don't need the full game history, but much less.

Question. How little information will suffice to include in the board positions of chess in order to ensure that one player will have a winning tactic or both will have drawing tactics?

Can we make due with information just about the pieces on the board? Do we need the list of currently legal moves? Or do we actually need to know the full history for the purposes of three-fold repetition? What about en passant? What about castling? What about the fifty move rule?

Which information, exactly, is sufficient to make the conclusion of the fundamental theorem for tactics in place of strategies?

Interlude

Let me give a full answer, which uses rather less information than might naturally have been expected—the winning and drawing tactics do not need to know any information at all concerning three-fold repetition or the fifty-move rule.