Theoretically, is brute force an unbeatable strategy in chess?

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Assume you brute forced chess and now know all paths to all outcomes. Do you automatically have an unbeatable strategy? What would the strategy be? And what if both players know the whole tree?

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Yes, assuming that you are playing the right colour. That's because chess is a game of perfect information and there are only finitely many legal board positions, and there is a finite bound on the length of games since a game is drawn if a position is repeated thrice (See Zermelos theorem). See here for estimates on the number of positions and games.

Given that chess is a finite game, there are only three possible outcomes:

  1. White has a winning strategy.
  2. Black has a winning strategy.
  3. The game is always drawn.

For 1. and 2. it doesn't matter whether the opponent knows the perfect strategy. The player playing the perfect strategy and having the winning colour always wins. If outcome 3. should be true, then a draw is guaranteed if both players play perfectly.

As for the strategy: just use the complete game tree that you have computed using brute force, following the paths that lead to winning (or drawn, in the case of 3.) leaves.