Question: We know that chess has at least one Nash equilibrium even though we can't solve for it, we can still reach some conclusions. Specifically, if

We know that chess has at least one Nash equilibrium even though we can't solve for it, we can still reach some conclusions. Specifically, if there is a Nash equilibrium in which the first-mover wins, then the first-mover wins in every Nash equilibrium Likewise, if there is an equilibrium in which the second-mover wins, then the second-mover wins in every equilibrium. And if there is an equilibrium that results in a draw, then every equilibrium results in a draw. Can you figure out why?

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