You don't need to consider every state individually to solve a game. For example if you have a game on a 100x100 board and the only goal is to move your piece to the other side you can know you have found the optimal solution if you can do it in 99 moves (assuming that you move 1 per turn).

In the chess scenario if you can prove that there is a set of moves where you win no matter what the other colour does then you have solved the game. You don't need to consider every possible game, just the games reachable within this set of moves.

Solving chess would be proving that "From starting position black can win every time" (or the same for white). You don't need to prove how to win from every possible board state.

I agree, and kind of included this in the "so, unless you had some way of dramatically compressing or simplifying this search space..." disclaimer.

Having said this, the nature of many chess endgames suggests that such a proof is not really possible, or at least would not be "simple". As an example, tempo / opposition flips games from draws to wins, etc.

My money is on perfect play drawing every time.

It would be interesting to take bets on the solution :)

But you won't find a set of moves. You have to find a tree of moves, which is substantially larger.

This is true. It is still a massive problem space but my point is that you don't need to consider every possible game or state.

Not to prove it always-winning; you only have to go down every possible branch for the other player for that (i.e. √ of the number of states you'd otherwise need). To find it, though? Well, unless you hit lucky, you're going to be considering pretty much every possible game or state, except where you can find shortcuts.

It is a bit more than that as it is unlikely that the always win sequence would be a fixed list of moves. You would need to show that for you each move the other player makes you have a reaction that also wins.

You don't need to care about possible games, but game states, what's the best result and the move to achieve it in each. Another user computed an upper bound at 8.7E+45 positions: https://github.com/lechmazur/ChessCounter . I pointed out that our planet has about 1E+50 atoms. And we can further compress the database by perhaps two orders of magnitude if we don't store symmetric positions or positions close to mate. A Kardashev 2 civilization could play perfect chess.

> A Kardashev 2 civilization could play perfect chess.

Assuming they would want to waste part of a planet's worth of computing resources to play perfect chess. In any case, it's far beyond anything we can compute.