You have these backwards. A chess game has a finite number of possible states, and each position is a theoretical win, draw, or loss. (And endgames with up to 7 pieces have been 'solved' via a tablebase, so you instantly know what the right move is). It's bridge which has an infinite number of states, since you have to take into account not just the current state of the cards, but also the potential reasoning that was behind every past bid and play from everyone else at the table.