If 32 moves by each player occur without any captures or pawn advances the player who moved last wins. Checkmate wins. A bare king loses. This could be applied to any form of chess, with appropriate adjustments for different board sizes.
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The first to give check can win the game by ending it with two bare kings.
So for example: if white would be the first to give check to black, the game goes on and both players could try to win by normal means. But white could ALSO try to reach a two bare kings position and that way white would win.