> ...between the current position and winning. (Because chess is entirely deterministic, that distance always exists. We are (currently) unable to measure it in most cases, but we can be sure it does exist.)

Can we?

Just because it's deterministic doesn't mean it always leads to a win - there may be strategies that always lead to a draw, we may just not know about them. Tic-tac-toe is deterministic and we know it always leads to a draw if played correctly - we know about it because it's a much simpler game (much smaller tree of possibilities).