The game of checkers was recently "solved." In principle, can chess be solved?

Question

I know there may be practical considerations that make its solution impossible to discover, but is there something inherent in chess that makes it unsolvable?

Answer 1

I knew a guy that could checkmate you in as little as 3 or 4 moves every time. As long as you went first that is.

Answer 2

Yes, chess is solvable. The proof depends on a few things: First, the 50-move rule means that a game cannot go on arbitrarily long. It can go on a loooong time, but not forever. Thus chess is a finite game. Now, it can be shown (I can't and won't explain it here but you can look it up if you're good with math) that every finite game has a Nash Equilibrium; that is, a combination of strategies for each player such that neither player has any incentive to vary from the strategy he has chosen. In chess, this would mean that each player is making the best possible move at each moment.

Now, the Nash equilibrium defines best play for both sides, but what if one player makes a mistake? What should his opponent do? Well, the players are still playing a finite game, so tehre should still exist an optimal strategy for each player.

Finding these strategies is of course practically impossible; the numebr of possible moves is so great that even the most powerful computers would need eons to solve chess. But some progress is being made, starting from the end of the game. Computers have been able to solve all the possible positions with 5  (sometimes 6) or fewer pieces on the board. So if you can force the game into one of those positions, you know the theoretical result. in theory, you could extend this back all the way to the opening position, but it becomes way harder to do the more pieces are on the board, and the file sizes of the optimal moves for each position get really really big.

So, chess can be solved in theory, but not in practice, at least not without significant advances in computing technology.

Answer 3

no because there are nearly an "infinite" number of moves in chess

Answer 4

Sure. Chess has a finite number of different board settings, and a finite number of moves from each, so it would be theoretically possible to come up with the best move from any given position. Chess is complex enough that I suspect there is no absolute always winning strategy, every move has countermoves, but you can always choose the move that leaves you in the best position.

In reality the sheer # of moves and positions makes chess pretty intractable in terms of an actual solution.