In game theory, a player's strategy, in a game or a business situation, is a complete plan of action for whatever situation might arise; this fully determines the player's bahaviour. A player's strategy will determine the action the player will take at any stage of the game, for every possible history of play up to that stage. 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. ... Game theory is the branch of mathematics in which games are studied: that is, models describing human behaviour. ... Economics (deriving from the Greek words οίκω [okos], house, and νέμω [nemo], rules hence household management) is the social science that studies the allocation of scarce resources to satisfy unlimited wants. ...

A strategy profile is a set of strategies for each player which fully specifies all actions in a game. A strategy profile must include one and only one strategy for every player.

The mathematically precise description of behaviour is connected to computer programming and algorithms. Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of figures and numbers. Mathematical knowledge is constantly growing, through research and application, but mathematics itself is not usually considered a natural science. ... This article needs to be cleaned up to conform to a higher standard of quality. ... Flowcharts are often used to represent algorithms. ...

Examples of strategies

Tit for Tat

Strategies in game theory are of essential importance, since the prisoners dilemma was shown never to lead to cooperation unless multiperiod strategies are considered. A highly effective strategy is "Tit for Tat". It was found in a programming contest, with several algorithms competing for the highest utility score. 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. ... Will the two prisoners cooperate to minimise total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? The prisoners dilemma is a type of non-zero-sum game. ... Tit for Tat is a highly-effective strategy in game theory for the iterated prisoners dilemma. ...

Roulette

There is a variety of betting strategies and tactics in the Roulette game. The most famous strategy is the doubling strategy: This page is about the game. ...

1. Set 1€
2. If you lose: double your bet
3. Repeat 2. until you have a profit

This was originally called the "Martingale strategy", and was formalized simply to show why it will not create an expected profit. However, it is a common (folk) strategy seen in many casinos (especially by beginning players, sometimes called "system players"). The typical casino prefers the "system player" to other types of player because the casino's risk is very low (they stand to lose only the minimum bet each time the player starts), but their potential reward is extremely high (the entire capital the gambler stakes). However, most "system players" tend to play only for a short time, and so the casino's edge is not compounded as often against the system player as against the usual roulette players (who vary their bet size less). A separate article treats the device for fastening horses bridles or dogs collars called a martingale. ... 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... The Trump Taj Mahal in Atlantic City, New Jersey A casino is a building that accommodates gambling. ... In politics a capital (also called capital city or political capital — although the latter phrase has an alternative meaning based on an alternative meaning of capital) is the principal city or town associated with its government. ... Gambling (or betting) is any behavior involving the risk of money or valuables on the outcome of a game, contest, or other event in which the outcome of that activity is partially or totally dependent upon chance. ... Edge may have one of the following special meanings, in addition to its dictionary definition: wiktionary:edge. ...

Main article: Gambler's fallacy
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The gamblers fallacy is one of many common misunderstandings which arise in everyday reasoning about probabilities, many of which have been studied in a great detail. ...

Hedging

Hegding is a strategy for financial investments, that searches for the lowest risk or optimal risk to performance ratio. Some kind of hedges are uniquely determined from simple parameters. The Black-Scholes equation demonstrates how a continuous stock buy and selling strategy can replicate an option without risk. There are other meanings of the word hedge. ... The Black-Scholes model, often simply called Black-Scholes, is a model of the varying price over time of financial instruments, and in particular stocks. ... In finance, an option is a contract whereby the contract buyer has a right to exercise a feature of the contract (the option) on or before a future date (the exercise date). ...