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Goofspiel - also called GOPS¹ - is a two- or three-player card game played with a standard 52-card deck. Game theorists love it, and rejoice in the fact that it is zero-sum - that is, purely strategic.

To play, first divide the deck into four piles, one for each suit (hearts, diamonds, spades, clubs). One of the piles goes to the centre of the playing surface, and the remaining ones become the players' hands. If there are only two players, just discard one suit.

Next, flip over the top card of the central pile onto the playing surface. Each person places one card on the table, face down. Once everyone has played their cards, each should reveal which card they played. The person with the highest card wins the round. In case of ties, the winner is the person who played his card first. The winner of the round collects the face-up card from the pile, and places it in what's called the trophy stack (really just a fancy name for 'extra pile'). The played cards are set aside (face up), and cannot be re-used. Flip over another card to start the new round. And so on until somebody wins.

But how does one go about doing that?

In a two-player game, the first person with 46 points wins. In the three-player variant, the winner needs 31 points. The points come from the trophy stack, wherein each card is worth a certain number of points. Face value determines points for all cards but the ace (1), the jack (11), the queen (12) and the king (13). This makes the total value of a suit 91 points.

There are many variations to goofspiel, as seemingly small changes to the rules can alter the game play completely. For example, in most versions, the used cards that have been set aside are placed face up. A common variation to the rules is placing these cards face down instead. This enters into the game a need for good memory, but disrupts the purely strategic element that mathematicians love so much.

Mastering Goofspiel

While simple to play, goofspiel is incredibly complex to master completely. In order to succeed, you must know your opponent(s) well. To understand the dilemma of the game, consider this situation. The pile card is the queen - a valuable prize - and your opponent has picked a card. Should you go ahead and pick your king? You will most likely win the queen, but later when the king is flipped from the pile, it's not as likely that you'll win it. In addition, if your opponent has picked the ace, you'll still win the queen, but at a much higher relative cost. But choosing a lower card would make you less likely to win the queen. These sort of mental gymnastics make mathematicians smile².