Is there non-terminating game of chess? I ran into this problem while designing a machine learning model to estimate the probability that a given chess player wins. If we ignore the 50-move-rule and any other repetition clauses, could a chess game diverge?
If both players have infinite knowledge and the goal of continuing the game indefinitely, is this possible? I do not know enough game theory to reach a conclusive answer on this. Could we even use Nash-equilibrium theory to model this?
If we considered the statement "from this point in the game, it is possible to play perfectly to avoid a stalemate" as a draw, would this enable us to view this as a finite game?
The rules of modern chess are designed to terminate any game. Especially the threefold repetition rule, the 50 (75 sometimes ?) moves rule and the draw for insufficient material rule allow this. The rules developed over time. One worldchampion (I have Steinitz in mind) even proved mathematically that with an old rule set there was an infinite game so they formulated a stronger threefold repetition rule.
Therefore ignoring one of the rules definitely allows an infinite game. For an example you can take the perpetual check from the comments.