Give two players cards, "Check" and "Checkmate".
Both players choose a card. Players then in turns reveal their card, and if Check, make another choice. The player first revealing Checkmate wins if their opponent's currently-chosen card is also a Checkmate.
But then this just gives the win to the first person to open their card, since in that round they had both selected Checkmate. Or, you have an incentive to rush to open your card when you know you've selected Checkmate, as you want to be the first one to open.