Goofspiel
Encyclopedia
Goofspiel, also known as The Game of Pure Strategy or GOPS, is a card game
for two or more players. It was invented by Merrill Flood
while at Princeton University
.
It is simple to learn and play, but has a large degree of tactical depth. It is popular with game theorists
because, as a game of pure strategy, it is susceptible to analysis.
. Even if this is not the case, a player knows all the cards held by her opponent(s) — this makes it atypical for a card game.
on the number of cards, Ross showed that the optimal strategy for the second (non-randomizing) player is to match the upturned card, i.e. if the upturned card is the Jack, he should play his Jack, etc. In this case, the expected winnings
of player two is 28 points.
Card game
A card game is any game using playing cards as the primary device with which the game is played, be they traditional or game-specific. Countless card games exist, including families of related games...
for two or more players. It was invented by Merrill Flood
Merrill M. Flood
Merrill Meeks Flood was an American mathematician, notable for developing, with Melvin Dresher, the basis of the game theoretical Prisoner's dilemma model of cooperation and conflict while being at RAND in 1950 Merrill Meeks Flood (1908 – 1991) was an American mathematician, notable for...
while at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
.
It is simple to learn and play, but has a large degree of tactical depth. It is popular with game theorists
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
because, as a game of pure strategy, it is susceptible to analysis.
Game play
Goofspiel is played using cards from a standard deck of cards, and is typically a two-player game, although more players are possible. Each suit is ranked A (low), 2, ..., 10, J, Q, K (high).- One suitSuit (cards)In playing cards, a suit is one of several categories into which the cards of a deck are divided. Most often, each card bears one of several symbols showing to which suit it belongs; the suit may alternatively or in addition be indicated by the color printed on the card...
is singled out as "competition suit" (in this explanation, we use the spades suit); each of the remaining suits becomes a hand for one player, with one suit discarded if there are only two players, or taken from additional decks if there are four or more. The spades are shuffled and placed between the players with one card turned up. - Play proceeds in a series of rounds. The players make "closed bids" for the top (face up) spade by selecting a card from their hand (keeping their choice secret from their opponent). Once these cards are selected, they are simultaneously revealed, and the player making the highest bid takes the competition card. Rules for ties in the bidding vary, possibilities including the competition card being discarded, or its value split between the tied players (possibly resulting in fractional scores). Some play that the current spade may "roll over" to the next round, so that two or more cards are competed for at once with a single bid card.
- The cards used for bidding are discarded, and play continues with a new upturned spade card.
- After 13 rounds, there are no remaining cards and the game ends. Typically, players earn points equal to sum of the ranks of cards won (i.e. Ace is worth one point, 2 is two points, etc, Jack being worth 11, Queen 12, and King worth 13 points). Players may agree upon other scoring schemes.
Variant with perfect information
If all spades are arranged face up (in order) from the start of the game, then Goofspiel becomes a game of perfect informationPerfect information
In game theory, perfect information describes the situation when a player has available the same information to determine all of the possible games as would be available at the end of the game....
. Even if this is not the case, a player knows all the cards held by her opponent(s) — this makes it atypical for a card game.
Mathematical analysis
Goofspiel (or variants of it) has been the subject of mathematical study. For example, Sheldon Ross considered the case when one player plays his cards randomly, to determine the best strategy that the other player should use. Using a proof by inductionMathematical induction
Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers...
on the number of cards, Ross showed that the optimal strategy for the second (non-randomizing) player is to match the upturned card, i.e. if the upturned card is the Jack, he should play his Jack, etc. In this case, the expected winnings
Expected value
In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...
of player two is 28 points.
External links
- Goofspiel analysis
- h2g2
- GOPS page at Pagat.comPagat.comPagat.com is a website containing rules to hundreds of card games from all over the world. Maintained by John McLeod, it contains information for traditional, commercial, and newly invented card games from all over the world....