Goofspiel
Created | Updated Jan 28, 2002
What is Goofspiel?
Goofspiel (also called gops) is a card game played with a standard 52 card deck. Game theorists rejoice in the zero-sum (pure strategy) nature of the game. It can be played by two or three people.
Basic Goofspiel
Setup
Divide the deck into suites (hearts, diamonds, spades, clubs). One of the suites is the pile. If you are playing the two player form of goofspiel, set one suite aside. The remaining piles are the players' hands.
Play
Flip over the top card of the pile onto the playing surface. Each player then places one card on the table, face down. Once all players have played their cards, each player flips over his or her card. The player who played the highest card (special note, the ace is the lowest card, and it's value is one) wins the round. In case of ties, the winner is the player who both tied and played his or her card first. The winner of the round collects the face up card from the pile, and places it in his trophy pile. The played cards are set aside, and can not be reused. Flip over another card to start the new round. Continue this process until someone wins the game (see below).
Scoring
The cards are assigned a point value as follows: one point for the ace, 11 for the jack, 12 for the queen, 13 for the king, and face values for all other cards. This makes the total value of a suite 91 points.
Winning
In a two player game, the first player with 46 points worth or more cards in his or her trophy stack wins. In the three player variant, the first player with 31 points worth or more cards wins.
Advanced Goofspiel
While simple to play, goofspiel is incredibly complex to master completely. In order to suceed, you must know your opponent(s) well. To understand the delima of the game, take this situation as an example: The pile card is the queen (a valuable prize). Your opponent picks a card. On one hand, you could pick your king. You would most likely win the queen. However, later, when the king is flipped from the pile, it is not as likely that you will win it. If your opponent picked the ace, you would still win the queen, but at a much higher relative cost. However, if you choose a lower card, you are not as likely to win the queen.
Variations
There are many variations to goofspiel. Seemingly small changes to the rules can alter the gameplay completely. For example, in most versions, the used cards are set aside are placed face up. A common variation to the rules is that the cards set aside are to be placed face down. This introducing the need for a good memory into the game (however, this disrupts the pure strategy nature of the game that mathematicians love).
References
Dror, "Simple Proof for Goofspiel", Advances in Applied Probability, 21 (1989), pps. 711-712.
Epstein, Theory of Gambling and Statistical Logic, (1977), p. 331.
Luce and Raiffa, Games and Decisions, (1957), pps. 44-47, 52.
Owen, Game Theory, 2nd Ed., (1982), pps. 3,4.
Ross, "Goofspiel - The Game of Pure Strategy", Journal of Applied Probability, 8 (1971), pps. 621-25
