It's quite an unusual saying and I had to look it up. "It's a wash" means that the thing is hopeless - you are wasting your time if you are trying to decide who the better player is
My guess is that it comes from "It's a washout". Two football teams turn up and hope to play a game, but the field is completely waterlogged - it's washed out - so the thing is hopeless, undecide
dave_anon I disagree with Cambridge as to why that is
Cambridge is not alone in its definition:
Informal An activity, action, or enterprise that yields neither marked gain nor marked loss: "[The company] doesn't do badly. That is, it's a wash"(Harper's).