Blackjack is a casino banking game. It is the most widely played casino banking game in the world. It uses decks of 52 cards and descends from a global family of casino banking games known as "twenty-one". This family of card games also includes the European games vingt-et-un and pontoon, and the Russian game Ochko. The game is a comparing card game where players compete against the dealer, rather than each other.
Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality.
An evolutionarily stable strategy (ESS) is a strategy that is impermeable when adopted by a population in adaptation to a specific environment, that is to say it cannot be displaced by an alternative strategy which may be novel or initially rare. Introduced by John Maynard Smith and George R. Price in 1972/3, it is an important concept in behavioural ecology, evolutionary psychology, mathematical game theory and economics, with applications in other fields such as anthropology, philosophy and political science.
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of behavioral relations. It is now an umbrella term for the science of rational decision making in humans, animals, and computers.
Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two competing entities, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one's gain is equivalent to player two's loss, with the result that the net improvement in benefit of the game is zero.
The prisoner's dilemma is a game theory thought experiment that involves two rational agents, each of whom can cooperate for mutual benefit or betray their partner ("defect") for individual reward. This dilemma was originally framed by Merrill Flood and Melvin Dresher in 1950 while they worked at the RAND Corporation. Albert W. Tucker later formalized the game by structuring the rewards in terms of prison sentences and named it the "prisoner's dilemma".
In game theory, the Nash equilibrium is the most commonly-used solution concept for non-cooperative games. A Nash equilibrium is a situation where no player could gain by changing their own strategy. The idea of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to his model of competition in an oligopoly.
A solved game is a game whose outcome can be correctly predicted from any position, assuming that both players play perfectly. This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory and/or computer assistance.
In the card game of poker, a bluff is a bet or raise made with a hand which is not thought to be the best hand. To bluff is to make such a bet. The objective of a bluff is to induce a fold by at least one opponent who holds a better hand. The size and frequency of a bluff determines its profitability to the bluffer. By extension, the phrase "calling somebody's bluff" is often used outside the context of poker to describe situations where one person demands that another proves a claim, or proves that they are not being deceptive.
Mastermind or Master Mind is a code-breaking game for two players invented in Israel. It resembles an earlier pencil and paper game called Bulls and Cows that may date back a century.
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a position that the players take turns changing in defined ways or moves to achieve a defined winning condition. Combinatorial game theory has not traditionally studied games of chance or those that use imperfect or incomplete information, favoring games that offer perfect information in which the state of the game and the set of available moves is always known by both players. However, as mathematical techniques advance, the types of game that can be mathematically analyzed expands, thus the boundaries of the field are ever changing. Scholars will generally define what they mean by a "game" at the beginning of a paper, and these definitions often vary as they are specific to the game being analyzed and are not meant to represent the entire scope of the field.
In combinatorial game theory, the strategy-stealing argument is a general argument that shows, for many two-player games, that the second player cannot have a guaranteed winning strategy. The strategy-stealing argument applies to any symmetric game in which an extra move can never be a disadvantage. A key property of a strategy-stealing argument is that it proves that the first player can win the game without actually constructing such a strategy. So, although it might prove the existence of a winning strategy, the proof gives no information about what that strategy is.
Evolutionary game theory (EGT) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith and George R. Price's formalisation of contests, analysed as strategies, and the mathematical criteria that can be used to predict the results of competing strategies.
Backward induction is the process of determining a sequence of optimal choices by reasoning from the endpoint of a problem or situation back to its beginning using individual events or actions. Backward induction involves examining the final point in a series of decisions and identifying the optimal process or action required to arrive at that point. This process continues backward until the best action for every possible point along the sequence is determined. Backward induction was first utilized in 1875 by Arthur Cayley, who discovered the method while attempting to solve the secretary problem.
Determinacy is a subfield of set theory, a branch of mathematics, that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Alternatively and similarly, "determinacy" is the property of a game whereby such a strategy exists. Determinacy was introduced by Gale and Stewart in 1950, under the name "determinateness".
Parrondo's paradox, a paradox in game theory, has been described as: A combination of losing strategies becomes a winning strategy. It is named after its creator, Juan Parrondo, who discovered the paradox in 1996. A more explanatory description is:
God's algorithm is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, but which can also be applied to other combinatorial puzzles and mathematical games. It refers to any algorithm which produces a solution having the fewest possible moves. The allusion to the deity is based on the notion that an omniscient being would know an optimal step from any given configuration.
The mathematics of gambling is a collection of probability applications encountered in games of chance and can get included in game theory. From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, and it is possible to calculate by using the properties of probability on a finite space of possibilities.
In game theory, a simultaneous game or static game is a game where each player chooses their action without knowledge of the actions chosen by other players. Simultaneous games contrast with sequential games, which are played by the players taking turns. In other words, both players normally act at the same time in a simultaneous game. Even if the players do not act at the same time, both players are uninformed of each other's move while making their decisions. Normal form representations are usually used for simultaneous games. Given a continuous game, players will have different information sets if the game is simultaneous than if it is sequential because they have less information to act on at each step in the game. For example, in a two player continuous game that is sequential, the second player can act in response to the action taken by the first player. However, this is not possible in a simultaneous game where both players act at the same time.
Game design is the process of creating and shaping the mechanics, systems and rules of a game. Games can be created for entertainment, education, exercise or experimental purposes. Additionally, elements and principles of game design can be applied to other interactions, in the form of gamification. Game designer and developer Robert Zubek defines game design by breaking it down into its elements, which he says are the following:
