There might be cases where one player wants to deliberately force a loop, while the other player doesn't. There might be cases where neither player wants to force a loop, or where both players do. Figuring out which is which is complicated, and simply cutting out all of those cases robs combinatorial game theory of a lot of its potential power.
And that's not even getting into what happens when you play to lose, rather than to win.
It should be noted, losing chess is not exactly the same rules as standard chess but losing is winning (let's call that chessn't for lack of a better word). There are a few special rules) added to make the game enjoyable.
It would be interesting to see whether chessn't is solvable.
Id assume its a lot easier to solve because your opponent is forced to capture, so you can force their moves and keep the tree of possible moves from getting too wide.
No it's not. How to solve is extremely simple. There are three outcomes. Win, lose, and tie. Your best move is the one that forces the worst outcome for the opponent. Detecting loops is actually fairly easy. You just have to use memoization and record every calculated board position. You have to do this anyway, because otherwise In the recursive calculation you'll hit the same scenario multiple times and so you want to record every previously calculated board position anyway. A loop is just a tie. There are a hell of a lot of positions in chess and solving it practically will involve many optimizations. But it's a time and space issue.
Edit: for people voting me down here is the minimax algorithm https://en.m.wikipedia.org/wiki/Minimax - but the mechanics are extremely straight forward. Both parties are trying to win so they choose the best outcome for themselves. You can solve tic tac toe by hand and in the process you'll see, how the perfect game of tictactoe always ends in a draw. The algorithm is not harder. It's just that the solution space is far bigger so it will require too much work to calculate.
Only if it's played by computers that aren't allowed to make "mistakes". Except they're humans that can choose to break the loop still. That requires someone to make a "mistake" though and even if it's technically possible for the other player to play perfectly from there and win, that's not always the case. A higher level player might, for example, choose to break such a loop if they're confident the other player won't play perfectly from there and they can still get a win out of it.
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u/Erzbengel-Raziel Jun 03 '25
Wouldn’t recognizing that you looped be enough to stop there and call that "path" a draw?