Solved game

A solved game is a game whose outcome (win, lose, or draw) can be correctly predicted from any position, given that both players play perfectly. Games which have not been solved are said to be "unsolved". Games for which only some positions have been solved are said to be "partially solved". This article focuses on two-player games that have been solved.

Overview

A two-player game can be "solved" on several levels:

Despite the name, many game theorists believe that "ultra-weak" are the deepest, most interesting and valuable proofs. "Ultra-weak" proofs require a scholar to reason about the abstract properties of the game, and show how these properties lead to certain outcomes if perfect play is realized.

By contrast, "strong" proofs often proceed by brute force—using a computer to exhaustively search a game tree to figure out what would happen if perfect play were realized. The resulting proof gives an optimal strategy for every possible position on the board. However, these proofs aren't as helpful in understanding deeper reasons why some games are solvable as a draw, and other, seemingly very similar games are solvable as a win.

Game theory

Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science, biology and poker. Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by the 1944 book Theory of Games and Economic Behavior, co-written with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.

Call of Duty

Call of Duty is a first-person shooter video game franchise. The series began on Microsoft Windows, and later expanded to consoles and handhelds. Several spin-off games have been released. The earlier games in the series are set primarily in World War II, including Call of Duty, Call of Duty 2, and Call of Duty 3. Beginning with Call of Duty 4: Modern Warfare, which is set in modern times, the series has shifted focus away from World War II. Modern Warfare, released November 2007, was followed by World at War and Modern Warfare 2. Black Ops, released November 2010, takes place in the Cold War, while Modern Warfare 3, released November 2011, takes place in a near-future setting. Black Ops II, released November 2012, takes place mainly in the year 2025. Call of Duty: Ghosts was released in November 2013. In May 2014, Advanced Warfare was announced. On April 9, 2015, Treyarch announced Black Ops III.

The Call of Duty games are published and owned by Activision. While Infinity Ward is still a developer, Treyarch and Sledgehammer Games also develop several of the titles with the release of the studios' games alternating with each other. Some games have been developed by Gray Matter Interactive, Nokia, Exakt Entertainment, Spark Unlimited, Amaze Entertainment, n-Space, Aspyr, Rebellion Developments, Ideaworks Game Studio, and nStigate Games. The games use a variety of engines, including the id Tech 3, the Treyarch NGL, and the IW engine.

Dark Souls

Dark Souls (ダークソウル, Dāku Sōru) is an action role-playing video game developed by FromSoftware. It was released for PlayStation 3 and Xbox 360, and published by Namco Bandai Games internationally. A spiritual successor to FromSoftware's Demon's Souls and the second installment of the Souls series, Dark Souls began development under the working title of Project Dark. The game was released in Japan on September 22, 2011, and in North America, Australia, and Europe the following month. On August 24, 2012, the "Prepare to Die" edition of Dark Souls was released for PC, featuring additional content previously unavailable to PlayStation 3 and Xbox 360 users. On October 23, 2012, the additional content from the PC version was released as downloadable content for consoles under the title Artorias of the Abyss.Dark Souls takes place in the fictional kingdom of Lordran. Players assume the role of a cursed undead character who has been chosen to make a pilgrimage out of the Undead Asylum to discover the fate of the Undead.

Game

A game is structured form of play, usually undertaken for enjoyment and sometimes used as an educational tool. Games are distinct from work, which is usually carried out for remuneration, and from art, which is more often an expression of aesthetic or ideological elements. However, the distinction is not clear-cut, and many games are also considered to be work (such as professional players of spectator sports or games) or art (such as jigsaw puzzles or games involving an artistic layout such as Mahjong, solitaire, or some video games).

Key components of games are goals, rules, challenge, and interaction. Games generally involve mental or physical stimulation, and often both. Many games help develop practical skills, serve as a form of exercise, or otherwise perform an educational, simulational, or psychological role.

Attested as early as 2600 BC, games are a universal part of human experience and present in all cultures. The Royal Game of Ur, Senet, and Mancala are some of the oldest known games.