Even that isn't strong enough. The game is determinstic. If chess were _solved_ we'd know a strategy to allow one of the players (likely white) to always win,

Even that isn't strong enough. The game is determinstic. If chess were _solved_ we'd know a strategy to allow one of the players (likely white) to always win, or for either of them to always force a draw. (and we'd know which of these strategies were possible for chess). Consider, say there is a first move white could choose such that no matter what moves black makes, white will win. Then the first would be true. Instead consider, that there is no such move, and any first move has choices where either could win-- if some of those are ones which would force a black win, then the first is again true but for black. Otherwise, a draw can always be forced. These are the only possible outcomes for a solved game of chess.