# Spoof Game - Rules

## Introduction

Spoof is a strategy game, typically played as a gambling game, often in bars and pubs where the loser buys the other participants a round of drinks. The exact origin of the game is unknown, but one scholarly paper addressed it, and more general n-coin games, in 1959. It is an example of a zero-sum game. The version with three coins is sometimes known under the name Three Coin.

## Gameplay

Spoof is played by any number of players in a series of rounds. In each round the objective is to guess the aggregate number of coins held in concealment by all the players, with each player being allowed to conceal up to three coins in their hand. At the beginning of every round each player conceals a quantity of coins, or no coins at all, in their closed fist, extended into the circle of play. The initial player calls what they think is the total number of coins in play. Play proceeds clockwise around the circle until each player has ventured a call regarding the total number of coins, and no player can call the same total as any other player. The call of "Spoof!" is sometimes used to mean "zero". After all players have made their calls, they open their fists and display their coins for the group to count the total. The player who has correctly guessed the total number of coins withdraws from the game and the remainder of the group proceeds to the next round. If no player guesses the total correctly, the entire group continues play in the next round. The starting player for each subsequent round is the next remaining player, clockwise from the starter of the previous round. Play continues until all players have been eliminated except for one.

## Heads Up stage

When there are only two players left, they must play until one of them reach the goal wins previous established.

• **Bullet:** One of the players just needs to win one game.

• **Blitz: ** One of the players needs to win two games.

• **Classical: ** One of the players needs to win three games.

## Mathematical analysis

This first guesser has the initial advantage in that all possible sums are available for his guess, but also lacks insight into what the others might be holding, as indicated by their subsequent guesses. Some variants also have the 'no bum shouts' or impossible call rule whereby a player cannot call more than the total number of coins possible taking into account what they have in their hand (e.g. if there are 5 players and they hold 1 coin, the maximum number to call would be 13). The generalized (n-coin) two player version of this game was the subject of a paper in 1959. It was shown that for every n ≥ 1 this game is a "fair game", i.e. each player has a mixed strategy that guarantees their expected payout is at most zero to his or her opponent.

## No Bum Shout

This means that each call that is made must be hypothetically possible given only your knowledge of what you hold in your hand and the number of other players in that round of the game. Consider, as an example, two players competing in a round, one of whom holds two coins. Given that the other player could conceivably have as many as three coins, or as few as zero, this player can make any call between two and five inclusive. A shout of either six, one or spoof would be a 'bum shout'. The penalty for making a bum shout is be to endure being called an idiot, and to have to play the round again.