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Matching Pennies is the name for a simple example game used in game theory. It is played between two players, Player A and Player B. Each player has a penny and must secretly turn the penny to Heads or Tails. The players then reveal their choices simultaneously. If the pennies match (both heads or both tails), Player A receives one dollar from Player B (+1 for A, -1 for B). If the pennies do not match (one heads and one tails), Player B receives one dollar from Player A (-1 for A, +1 for B). This is an example of a zero-sum game, where one player's gain is exactly equal to the other player's loss. Game theory is a branch of applied mathematics that uses models to study interactions with formalised incentive structures (games). It has applications in a variety of fields, including economics, international relations, evolutionary biology, political science, and military strategy. ...
Above: A variety of coins considered to be lower-value, including an Irish 2p piece and many US pennies. ...
Zero-sum describes a situation in which a participants gain (or loss) is exactly balanced by the losses (or gains) of the other participant(s). ...
The game can be written in a payoff matrix like the one below. Each cell of the matrix shows the two players' payoffs, with Player A's payoffs listed first. A payoff matrix or payoff function is a concept in game theory which shows what payoff each player will receive at the outcome of the game. ...
| | Heads | Tails | | Heads | (1, -1) | (-1, 1) | | Tails | (-1, 1) | (1, -1) | This game has no pure strategy Nash equilibrium since there is no pure strategy (heads or tails) that is a best response to a best response. Instead, the Nash equilibrium of this game is in mixed strategies - in theory, each player's best strategy is to be as random as possible with their choice, choosing heads or tails with equal probability. In this way, the opponent has no way of predicting what the player will choose and will therefore have no way of taking advantage of any predictability. In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ...
In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ...
Of course, if one is sufficiently adept at psychology, it may be possible to predict the opponent's move and choose accordingly, in the same manner as expert Rock, Paper, Scissors players. In this way, a positive expected value might be attainable (whereas, with a purely random strategy, the expected value is zero). Rock, Paper, Scissors chart Rock, Paper, Scissors (sometimes with the elements in its name permuted and/or Rock replaced with Stone and/or Paper with Cloth, but also known as Roshambo, Rochambeau, Row-Sham-Bow, Ick-Ack-Ock, Janken, Mora, Morra Cinese, Gawi-Bawi-Bo, JanKenPon, Ca-Chi-Pun, Farkle...
In probability (and especially gambling), the expected value (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects to win per bet if bets with identical odds are...
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