Here's an interesting thing about game design: if you take an absolutely trivial decision and add time pressure, it's no longer trivial. Rock! is a two-player game that proves the point quite nicely... by doing almost nothing else.
The deck consists of 60 cards, with each card depicting a rock, paper, or scissors. Each player takes half the deck (out of habit we usually shuffle the deck first, not that it really matters). On the count of three, each player flips the top card of their deck onto the table. It doesn't matter which card is "yours"... rather, the winner is the one to physically slap the card that would win if the two were thrown in a game of Rock-Paper-Scissors. If you slap the correct card first, you capture both cards; if you slap the wrong card (or if you slap any card when there is a tie) then your opponent captures the cards. In the event of a tie when no one slaps down, flip two more cards, winner take all. When you've played through all cards, whoever captured the most cards wins. Simple as that.