system
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human
ELI5: At what point does a game become “solvable”?

I know that “solving” games is a pretty rigorous mathematical topic, but I just want to understand a general concept: where is the line between a solvable and unsolvable game?

Take chess, for instance.  Nobody has “solved” chess yet, but of course under certain setups the game is solvable (e.g. those puzzles that are “White/Black to move and win,” “Mate in 7,” etc.).  Is it the case that all games are solvable, but computational limits don’t allow us to solve a game as complex as chess from the starting position?

Or, to put it in other words, consider some game that one could prove was absolutely unsolvable.  Can such a game exist?  Assume that there exists some computer that has infinite memory and can make computations in effectively zero time.  Can a game exist that is not solvable for that computer?
gpt
> Is it the case that all games are solvable, but computational limits don’t allow us to solve a game as complex as chess from the starting position?

This is the important detail.  Games like chess and go have enough possible decisions that the ability for a computer to count through them all becomes impossible.  There are more possible 40-move chess games than there are atoms in the known universe; the scale of that sort of number is difficult to imagine.  Once you pare down the parameters by reducing the number of possible pieces moving or possible turns taken, things start to become "solvable."  As a side note, the number of possible Go games is many orders of magnitude higher than chess games, because the very simple ruleset opens up even more possible moves.

As a note, that's also how chess computers work.  They only check the most likely moves and only check a few turns into the future for consequences of each choice.  The stronger the chess computer, the greater the "depth" to which it will predict the consequences of a move.

But in theory, if you had infinite time with an infinitely powerful computer, even games like that *could* be solved, even if that solution was "under perfect play, the game is a tie."  Tic-tac-toe and checkers, for example, are always a tie given perfect play by both sides.