A game is generally a structured form of active play, often undertaken for fun or entertainment, and at times used as an instructional tool. Games are quite different from work, which generally is performed for remuneration; work is normally carried out for a personal satisfaction, with little regard to gaining any other reward. But games are often sought because of the release of some kind of tension or stress. Most people find it difficult to leave their work behind, but with the release of a game all that tension vanishes, leaving the player more relaxed. This relaxation, in turn, has positive health benefits.
Games are played according to certain game theory principles, the first of which states that each player will make a single move, known as a’stroke’. Each player will be aware of only that single thing that affects the game; this includes not only the placement of his pieces, but also their colour and strength. Movement is an action that brings about change, whether this change brings about a benefit or a harm to any one of the players. Therefore, it is not surprising if the same piece could end up in two different positions, one good and one bad, because each player has only just learned that single information. Game theory therefore states that a player will, upon receiving a single stroke, consider all the moves that would have been possible from the previous position, both good and bad, and make the best possible move. The same principle applies to the game’s outcome.
Game theory also suggests that, in order to have a beneficial outcome, a player must consider all the aspects of the scenario, both to create and manipulate the probability of that outcome, but also to ensure that this probability is not reduced by other factors. It therefore follows that a player will not take a chance if there is no likelihood of obtaining a beneficial outcome. That is why in many games a player is required to wait patiently, sometimes for years, for the game to reach a conclusion that is satisfactory to him.
The game of chess is unique among all the games we play because it captures human nature and plays out a constant struggle between players for superiority. Although victory is unlikely and defeat is not impossible, most players consider the game as a form of competition. If there is an outcome that appears to favor one player, other players are more than willing to cooperate and give that player free moves, even if this means accepting a loss of opportunity. This cooperative tendency is what accounts for the emergence of the phenomenon of professional gaming, where the outcome of a game can be predicted by the participants. However, the question remains as to how a player, using quantifiable measures such as angles, strength, timing and tactics, can influence the outcome of a game.
There are many theories on game design and analysis. Many of these stem from disciplines such as psychology, cognitive science, computer science and mathematics. One of the most influential is the so-called “gamification” theory. The goal of gamification is to provide a controlled environment that simulates natural selection and evolution and thereby enables evolutionary forces to effect a change in behavior through natural selection. Gamification has been used in many applications ranging from education and business to health care and the military.
In a non-cooperative game such as a prisoner’s dilemma, the players each choose a state that they believe will result in a favorable outcome, with corresponding strategies for choosing those states. The objective of the game theory is to seek information by analyzing all these probabilities. One approach is to combine statistical analysis with knowledge of the probabilities of the outcomes, leading to a mathematical formulation of the equilibrium. The prisoner’s dilemma game theory can also be applied in a mathematical setting called the counting games, in which players take turns generating a sequence of numbers that is the basis for computing a Fibonacci number, hence the name. Thus, the prisoner’s dilemma is a valuable application of many of the tools and techniques in mathematics, particularly in the areas of probability and statistics.