Goofspiel
| Players | 2+ |
|---|---|
| Setup time | Short |
| Playing time | Short |
| Random chance | Low |
| Skill(s) required | Tactics, psychology |
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 in the 1930s, and Alex Randolph describes a similar game as having been popular with the 5th Indian Army during the Second World War.
The game is simple to learn and play, but has some degree of strategic depth. It is commonly used as an example of multi-stage simultaneous move game in game theory and artificial intelligence.
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).
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 induction on the number of cards, Ross showed that the optimal strategy for the 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 final score is 59½ - 31½, for a 28-point win.
The game as defined by Ross, where payoffs are point differences, was solved using linear and dynamic programming in 2012.
Any pure strategy in this game has a simple counter-strategy where the opponent bids one rank higher, or as low as possible against the King bid. As an example, consider the strategy of matching the upturned card value mentioned in the previous section. The final score will be 78 - 13 with the King being the only lost prize.
In general, making a very low bid can be advantageous if the player has correctly guessed that the opponent is making a high bid; despite losing a (presumably high-scoring) prize, the player gains an advantage in bidding power that can last for multiple turns. In the variant in which tie bids cause prizes to accumulate, the player with a bidding advantage might make bids that are more likely to tie, knowing that he can then use his uncontested high-bid card to win the accumulated group.
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