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68-427: Losing chess was weakly solved in 2016 by Mark Watkins as a win for White, beginning with 1.e3. The rules are the same as those for standard chess , except for the following special rules: Draws by repetition , agreement , or the fifty-move rule work as in standard chess. Positions when neither player can win are also draws: for example, when the only pieces remaining are bishops of opposite colors . (This

136-584: A chess championship . On the other hand, players in a game may constitute their own audience as they take their turn to play. Often, part of the entertainment for children playing a game is deciding who is part of their audience and who is a player. A toy and a game are not the same. Toys generally allow for unrestricted play whereas games present rules for the player to follow. 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

204-407: A controller or a motion sensitive tool ( console games ). More esoteric devices such as paddle controllers have also been used for input. There are many genres of video game; the first commercial video game, Pong , was a simple simulation of table tennis . As processing power increased, new genres such as adventure and action games were developed that involved a player guiding a character from

272-414: A lawn ; an area of mowed grass (or alternately, on graded soil) generally smaller than a sports field (pitch). Variations of many games that are traditionally played on a sports field are marketed as "lawn games" for home use in a front or back yard. Common lawn games include horseshoes , sholf , croquet , bocce , and lawn bowls . A tabletop game is a game where the elements of play are confined to

340-507: A tarot deck of 78 cards (used in Europe to play a variety of trick-taking games collectively known as Tarot, Tarock or Tarocchi games), or a deck specific to the individual game (such as Set or 1000 Blank White Cards ). Uno and Rook are examples of games that were originally played with a standard deck and have since been commercialized with customized decks. Some collectible card games such as Magic: The Gathering are played with

408-560: A community much larger than the group of players. A city or town may set aside such resources for the organization of sports leagues. Popular sports may have spectators who are entertained just by watching games. A community will often align itself with a local sports team that supposedly represents it (even if the team or most of its players only recently moved in); they often align themselves against their opponents or have traditional rivalries. The concept of fandom began with sports fans. Lawn games are outdoor games that can be played on

476-428: A different game. There are exceptions to this in that some games deliberately involve the changing of their own rules, but even then there are often immutable meta -rules. Rules generally determine the time-keeping system , the rights and responsibilities of the players, scoring techniques, preset boundaries, and each player's goals. The rules of a game may be distinguished from its aims. For most competitive games,

544-472: 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. Ludwig Wittgenstein was probably the first academic philosopher to address the definition of the word game . In his Philosophical Investigations , Wittgenstein argued that

612-429: A game. Muggins , Mexican Train , and Chicken Foot are very popular domino games. Texas 42 is a domino game more similar in its play to a "trick-taking" card game . Variations of traditional dominoes abound: Triominoes are similar in theory but are triangular and thus have three values per tile. Similarly, a game known as Quad-Ominos uses four-sided tiles. Some other games use tiles in place of cards; Rummikub

680-409: A high degree of luck, which can be directed to some extent by the player through more strategic elements of play and through tenets of probability theory . Such games are thus popular as gambling games; the game of craps is perhaps the most famous example, though liar's dice and poker dice were originally conceived of as gambling games. Domino games are similar in many respects to card games, but

748-627: A large area in which to play them, large amounts of strength or stamina, or specialized equipment other than what comes in a box. This class of games includes any game in which the skill element involved relates to manual dexterity or hand-eye coordination, but excludes the class of video games (see below). Games such as jacks , paper football , and Jenga require only very portable or improvised equipment and can be played on any flat level surface, while other examples, such as pinball , billiards , air hockey , foosball , and table hockey require specialized tables or other self-contained modules on which

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816-503: A large number of video games have been created to simulate strategic combat), and the board may be a map on which the players' tokens move. Virtually all board games involve "turn-based" play; one player contemplates and then makes a move, then the next player does the same, and a player can only act on their turn. This is opposed to "real-time" play as is found in some card games, most sports and most video games. Some games, such as chess and Go , are entirely deterministic, relying only on

884-477: A loss. If there are multiple options with the same outcome, perfect play is sometimes considered the fastest method leading to a good result, or the slowest method leading to a bad result. Perfect play can be generalized to non- perfect information games, as the strategy that would guarantee the highest minimal expected outcome regardless of the strategy of the opponent. As an example, the perfect strategy for rock paper scissors would be to randomly choose each of

952-443: A move in a given position, a game is not considered to be solved weakly or strongly unless the algorithm can be run by existing hardware in a reasonable time. Many algorithms rely on a huge pre-generated database and are effectively nothing more. As a simple example of a strong solution, the game of tic-tac-toe is easily solvable as a draw for both players with perfect play (a result manually determinable). Games like nim also admit

1020-408: A new type of equilibrium strategy not found in traditional games. The entanglement of player's choices can have the effect of a contract by preventing players from profiting from what is known as betrayal . Games can take a variety of forms, from competitive sports to board games and video games. Many sports require special equipment and dedicated playing fields, leading to the involvement of

1088-410: A non-final position as identical to the position that is one move away and best valued for the player whose move it is. Thus a transition between positions can never result in a better evaluation for the moving player, and a perfect move in a position would be a transition between positions that are equally evaluated. As an example, a perfect player in a drawn position would always get a draw or win, never

1156-444: A pawn on a board, play money , or an intangible item such as a point scored. Games such as hide-and-seek or tag do not use any obvious tool; rather, their interactivity is defined by the environment. Games with the same or similar rules may have different gameplay if the environment is altered. For example, hide-and-seek in a school building differs from the same game in a park; an auto race can be radically different depending on

1224-635: A piece of information that one player knows, and the object is to coerce others into guessing that piece of information without actually divulging it in text or spoken word. Charades is probably the most well-known game of this type, and has spawned numerous commercial variants that involve differing rules on the type of communication to be given, such as Catch Phrase , Taboo , Pictionary , and similar. The genre also includes many game shows such as Win, Lose or Draw , Password and $ 25,000 Pyramid . Video games are computer- or microprocessor -controlled games. Computers can create virtual spaces for

1292-465: A play, to make all open endpoints sum to a given number or multiple, or simply to play all dominoes from one's hand onto the board. Sets vary in the number of possible dots on one end, and thus of the number of combinations and pieces; the most common set historically is double-six , though in more recent times "extended" sets such as double-nine have been introduced to increase the number of dominoes available, which allows larger hands and more players in

1360-416: A player toward winning. For instance, an intermediate aim in football is to score goals, because scoring goals will increase one's likelihood of winning the game, but is not alone sufficient to win the game. An aim identifies a sufficient condition for successful action, whereas the rule identifies a necessary condition for permissible action. For example, the aim of chess is to checkmate, but although it

1428-513: A rigorous analysis using combinatorial game theory . Whether a game is solved is not necessarily the same as whether it remains interesting for humans to play. Even a strongly solved game can still be interesting if its solution is too complex to be memorized; conversely, a weakly solved game may lose its attraction if the winning strategy is simple enough to remember (e.g., Maharajah and the Sepoys ). An ultra-weak solution (e.g., Chomp or Hex on

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1496-405: 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

1564-424: A small area and require little physical exertion, usually simply placing, picking up and moving game pieces. Most of these games are played at a table around which the players are seated and on which the game's elements are located. However, many games falling into this category, particularly party games , are more free-form in their play and can involve physical activity such as mime. Still, these games do not require

1632-413: A small selection of cards that have been collected or purchased individually from large available sets. Some board games include a deck of cards as a gameplay element, normally for randomization or to keep track of game progress. Conversely, some card games such as Cribbage use a board with movers, normally to keep score. The differentiation between the two genres in such cases depends on which element of

1700-457: A sufficiently large board) generally does not affect playability. In game theory , perfect play is the behavior or strategy of a player that leads to the best possible outcome for that player regardless of the response by the opponent. Perfect play for a game is known when the game is solved. Based on the rules of a game, every possible final position can be evaluated (as a win, loss or draw). By backward reasoning , one can recursively evaluate

1768-409: A third person perspective through a series of obstacles. This "real-time" element cannot be easily reproduced by a board game, which is generally limited to "turn-based" strategy; this advantage allows video games to simulate situations such as combat more realistically. Additionally, the playing of a video game does not require the same physical skill, strength or danger as a real-world representation of

1836-461: A true game played for entertainment or a competitive activity describable in principle by mathematical game theory. John Nash proved that games with several players have a stable solution provided that coalitions between players are disallowed. Nash won the Nobel prize for economics for this important result which extended von Neumann's theory of zero-sum games. Nash's stable solution is known as

1904-415: A virtual environment is provided in which the player may be free to do whatever they like within the confines of a particular game's universe. Sometimes, there is a lack of goals or opposition, which has stirred some debate on whether these should be considered "games" or "toys". (Crawford specifically mentions Will Wright 's SimCity as an example of a toy.) Online games have been part of culture from

1972-416: A wide variety of game types. Some video games simulate conventional game objects like cards or dice, while others can simulate environs either grounded in reality or fantastical in design, each with its own set of rules or goals. A computer or video game uses one or more input devices , typically a button / joystick combination (on arcade games ); a keyboard , mouse or trackball ( computer games ); or

2040-458: A worldwide popularity of ball games such as rugby , basketball , soccer (football) , cricket , tennis , and volleyball . Other tools are more idiosyncratic to a certain region. Many countries in Europe, for instance, have unique standard decks of playing cards . Other games such as chess may be traced primarily through the development and evolution of its game pieces. Many game tools are tokens, meant to represent other things. A token may be

2108-514: Is a variant of the Rummy card game family that uses tiles numbered in ascending rank among four colors, very similar in makeup to a 2-deck "pack" of Anglo-American playing cards . Mahjong is another game very similar to Rummy that uses a set of tiles with card-like values and art. Lastly, some games use graphical tiles to form a board layout, on which other elements of the game are played. Settlers of Catan and Carcassonne are examples. In each,

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2176-443: Is based on the idea of a crossword puzzle , and tic-tac-toe sets with a boxed grid and pieces are available commercially). These games vary widely, from games centering on a design being drawn such as Pictionary and "connect-the-dots" games like sprouts , to letter and word games such as Boggle and Scattergories , to solitaire and logic puzzle games such as Sudoku and crossword puzzles . A guessing game has as its core

2244-403: Is expected that players will try to checkmate each other, it is not a rule of chess that a player must checkmate the other player whenever possible. Similarly, it is not a rule of football that a player must score a goal on a penalty; while it is expected the player will try, it is not required. While meeting the aims often requires a certain degree of skill and (in some cases) luck, following

2312-426: Is one popular example, where players must succeed in each of four skills: artistry, live performance, trivia, and language. Card games use a deck of cards as their central tool. These cards may be a standard Anglo-American (52-card) deck of playing cards (such as for bridge , poker , Rummy , etc.), a regional deck using 32, 36 or 40 cards and different suit signs (such as for the popular German game skat ),

2380-479: Is similar to the dead position rule in standard chess.) The origin of the game is unknown, but believed to significantly predate an early version, named take me , played in the 1870s. Because of the popularity of losing chess, several variations have spawned. The most widely played (main variant) is described in Popular Chess Variants by D. B. Pritchard . Losing chess began to gain popularity in

2448-412: 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. A two-player game can be solved on several levels: Despite their name, many game theorists believe that "ultra-weak" proofs are the deepest, most interesting and valuable. "Ultra-weak" proofs require

2516-478: The Nash equilibrium . If cooperation between players is allowed, then the game becomes more complex; many concepts have been developed to analyze such games. While these have had some partial success in the fields of economics, politics and conflict , no good general theory has yet been developed. In quantum game theory , it has been found that the introduction of quantum information into multiplayer games allows

2584-399: The track or street course, even with the same cars. Games are often characterized by their tools and rules. While rules are subject to variations and changes , enough change in the rules usually results in a "new" game. For instance, baseball can be played with "real" baseballs or with wiffleballs . However, if the players decide to play with only three bases, they are arguably playing

2652-542: The ultimate aim is winning: in this sense, checkmate is the aim of chess. Common win conditions are being first to amass a certain quota of points or tokens (as in Settlers of Catan ), having the greatest number of tokens at the end of the game (as in Monopoly ), or some relationship of one's game tokens to those of one's opponent (as in chess's checkmate ). There may also be intermediate aims, which are tasks that move

2720-706: The "board" is made up of a series of tiles; in Settlers of Catan the starting layout is random but static, while in Carcassonne the game is played by "building" the board tile-by-tile. Hive , an abstract strategy game using tiles as moving pieces, has mechanical and strategic elements similar to chess , although it has no board; the pieces themselves both form the layout and can move within it. Pencil and paper games require little or no specialized equipment other than writing materials, though some such games have been commercialized as board games ( Scrabble , for instance,

2788-438: The "complexity and beauty" of losing chess is found in its endgame . He noted that, in contrast to regular chess, losing chess endgames with just two pieces require considerable skill to play correctly, whereas three- or four-piece endgames can exceed human capacity to solve precisely. For example, the following endgames may turn out to be quite complicated: 2 Knights vs Rook , 3 Kings vs King , or Bishop+Knight+King vs King . In

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2856-463: The 20th century, which was facilitated by some publications about this variant in the UK, Germany, and Italy. Losing chess gained a new surge in popularity at the turn of the 20th and 21st centuries as an online game, thanks to the implementation of this variant on FICS in 1996, which greatly contributed to the popularization of losing chess. International tournaments were held in 1998 and 2001. As of 2022,

2924-619: The IAF hosts annual international tournaments in Amsterdam, the Netherlands. The internet chess server Lichess facilitates play of the game, referring to it as "antichess"; after regular chess it is the most popular variant on the site in terms of numbers of games played. Since 2018 the site has hosted an annual "Lichess World Championship" for the variant. Chess.com also added this variant to their server, calling it "giveaway." Because of

2992-502: The best strategic move based on the roll of two dice . Trivia games have a great deal of randomness based on the questions a person gets. German-style board games are notable for often having rather less of a luck factor than many board games. Board game groups include race games , roll-and-move games, abstract strategy games , word games , and wargames , as well as trivia and other elements. Some board games fall into multiple groups or incorporate elements of other genres: Cranium

3060-481: The board. However, these proofs are not 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. Given the rules of any two-person game with a finite number of positions, one can always trivially construct a minimax algorithm that would exhaustively traverse the game tree. However, since for many non-trivial games such an algorithm would require an infeasible amount of time to generate

3128-467: The dice has a profound impact on the outcome of the game, however dice games are differentiated in that the dice do not determine the success or failure of some other element of the game; they instead are the central indicator of the person's standing in the game. Popular dice games include Yahtzee , Farkle , Bunco , liar's dice / Perudo , and poker dice . As dice are, by their very nature, designed to produce random numbers , these games usually involve

3196-440: The elements of games, such as play , rules, and competition, all fail to adequately define what games are. From this, Wittgenstein concluded that people apply the term game to a range of disparate human activities that bear to one another only what one might call family resemblances . As the following game definitions show, this conclusion was not a final one and today many philosophers, like Thomas Hurka , think that Wittgenstein

3264-405: The fewer number of pieces remaining; if both have the same number, it is a draw (the piece types are irrelevant). "Joint" FICS/International rules resolves stalemate as a draw unless it is a victory for the same player under both rulesets. The stalemate in the diagram is a win for White under "International" rules, a win for Black under FICS rules, and a draw under "joint" rules. Pritchard discusses

3332-543: The following variants of the game in The Encyclopedia of Chess Variants . Variant 2 Rules are the same as the main rules, except: Variant 3 Rules are the same as the main rules, except: Variant 4 Rules are the same as variant 3, except: Bibliography Solved game#Weak solution A solved game is a game whose outcome (win, lose or draw ) can be correctly predicted from any position, assuming that both players play perfectly. This concept

3400-412: The forced capture rule, losing chess games often involve long sequences of forced captures by one player. This means that a minor mistake can doom a game. Such mistakes can be made from the very first move—it is currently known that a Black win can be forced after 13 of White's 20 legal opening moves. Some of these openings took months of computer time to solve: they vary greatly in difficulty. In

3468-814: The form of endgame tablebases ), which will allow it to play perfectly after some point in the game. Computer chess programs are well known for doing this. Game A game is a structured type of play , usually undertaken for entertainment or fun , and sometimes used as an educational tool. 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 ). Games are sometimes played purely for enjoyment, sometimes for achievement or reward as well. They can be played alone, in teams, or online; by amateurs or by professionals. The players may have an audience of non-players, such as when people are entertained by watching

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3536-419: The game is foremost in its play; a board game using cards for random actions can usually use some other method of randomization, while Cribbage can just as easily be scored on paper. These elements as used are simply the traditional and easiest methods to achieve their purpose. Dice games use a number of dice as their central element. Board games often use dice for a randomization element, and thus each roll of

3604-409: The game is played. The advent of home video game systems largely replaced some of these, such as table hockey, however air hockey, billiards, pinball and foosball remain popular fixtures in private and public game rooms. These games and others, as they require reflexes and coordination, are generally performed more poorly by intoxicated persons but are unlikely to result in injury because of this; as such

3672-464: The game, and can provide either very realistic, exaggerated or impossible physics, allowing for elements of a fantastical nature, games involving physical violence, or simulations of sports. Lastly, a computer can, with varying degrees of success, simulate one or more human opponents in traditional table games such as chess , leading to simulations of such games that can be played by a single player. In more open-ended video games, such as sandbox games ,

3740-408: The games are popular as drinking games . In addition, dedicated drinking games such as quarters and beer pong also involve physical coordination and are popular for similar reasons. Board games use as a central tool a board on which the players' status, resources, and progress are tracked using physical tokens. Many also involve dice or cards. Most games that simulate war are board games (though

3808-436: The generic device is instead a set of tiles called dominoes , which traditionally each have two ends, each with a given number of dots, or "pips", and each combination of two possible end values as it appears on a tile is unique in the set. The games played with dominoes largely center around playing a domino from the player's "hand" onto the matching end of another domino, and the overall object could be to always be able to make

3876-410: The lack of any formidable opposition. Many games described as "single-player" may be termed actually puzzles or recreations . A multiplayer game is a game of several players who may be independent opponents or teams. Games with many independent players are difficult to analyze formally using game theory as the players may form and switch coalitions . The term "game" in this context may mean either

3944-406: The latter case, in particular, a win may require more than 60 moves, which means that it is sometimes unattainable due to the fifty-move rule . Implementations of the main variant can vary in regard to stalemate. "International" rules are as described above, with the stalemated player winning even if that player still has pieces on the board. FICS rules resolve stalemate as a win for the player with

4012-444: The options with equal (1/3) probability. The disadvantage in this example is that this strategy will never exploit non-optimal strategies of the opponent, so the expected outcome of this strategy versus any strategy will always be equal to the minimal expected outcome. Although the optimal strategy of a game may not (yet) be known, a game-playing computer might still benefit from solutions of the game from certain endgame positions (in

4080-440: The outcome. Many other games involving a high degree of luck do not allow direct attacks between opponents; the random event simply determines a gain or loss in the standing of the current player within the game, which is independent of any other player; the "game" then is actually a "race" by definitions such as Crawford's. Most other board games combine strategy and luck factors; the game of backgammon requires players to decide

4148-453: The player does". This is often referred to as gameplay . Major key elements identified in this context are tools and rules that define the overall context of game. Games are often classified by the components required to play them (e.g. miniatures , a ball , cards , a board and pieces , or a computer ). In places where the use of leather is well-established, the ball has been a popular game piece throughout recorded history, resulting in

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4216-1332: The rules of a game merely requires knowledge of the rules and some careful attempt to follow them; it rarely (if ever) requires luck or demanding skills. A game's tools and rules will result in its requiring skill, strategy, luck , or a combination thereof, and are classified accordingly. Games of skill include games of physical skill, such as wrestling , tug of war , hopscotch , target shooting , and games of mental skill such as checkers and chess . Games of strategy include checkers, chess, Go , arimaa , and tic-tac-toe , and often require special equipment to play them. Games of chance include gambling games ( blackjack , Mahjong , roulette , etc.), as well as snakes and ladders and rock, paper, scissors ; most require equipment such as cards or dice . However, most games contain two or all three of these elements. For example, American football and baseball involve both physical skill and strategy while tiddlywinks , poker , and Monopoly combine strategy and chance. Many card and board games combine all three; most trick-taking games involve mental skill, strategy, and an element of chance, as do many strategic board games such as Risk , Settlers of Catan , and Carcassonne . Most games require multiple players. However, single-player games are unique in respect to

4284-556: The strategy element for their interest. Such games are usually described as having " perfect information "; the only unknown is the exact thought processes of one's opponent, not the outcome of any unknown event inherent in the game (such as a card draw or die roll). Children's games, on the other hand, tend to be very luck-based, with games such as Candy Land and Chutes and Ladders having virtually no decisions to be made. By some definitions, such as that by Greg Costikyan , they are not games since there are no decisions to make which affect

4352-622: The table below, green marks winning first moves for White; red marks losing first moves; and yellow marks moves that are not yet solved. This main variant of losing chess was weakly solved in October 2016; White is able to force a win beginning with 1.e3. This solution is valid for both FICS and "International" rules on stalemate. Some lines are trivial (1...d6, 1...d5, 1...Na6, and 1...g6 lose in less than 20 moves), others are quite simple (1...Nf6, 1...h6, 1...e5, 1...f5, 1...h5, 1...f6, 1...a6, 1...a5 lose in less than 30 moves, subject to knowledge of

4420-429: The theory), and some are quite complicated (1...Nh6, 1...Nc6, 1...c6, the win in which may require about 60 moves). The most difficult are the following five openings (in order of increasing difficulty): 1.e3 g5 (Wild Boar Defence), 1.e3 e6 (Modern Defence), 1.e3 b5 (Classical Defence), 1.e3 c5 (Polish Defence), and 1.e3 b6 (Liardet Defence). David Pritchard , the author of The Encyclopedia of Chess Variants , wrote that

4488-408: The type of challenges a player faces. Unlike a game with multiple players competing with or against each other to reach the game's goal, a one-player game is a battle solely against an element of the environment (an artificial opponent), against one's own skills, against time, or against chance. Playing with a yo-yo or playing tennis against a wall is not generally recognized as playing a game due to

4556-485: The very earliest days of networked and time-shared computers. Early commercial systems such as Plato were at least as widely famous for their games as for their strictly educational value. In 1958, Tennis for Two dominated Visitor's Day and drew attention to the oscilloscope at the Brookhaven National Laboratory ; during the 1980s, Xerox PARC was known mainly for Maze War , which

4624-753: Was wrong and that Bernard Suits' definition is a good answer to the problem. French sociologist Roger Caillois , in his book Les jeux et les hommes (Games and Men) (1961), defined a game as an activity that must have the following characteristics: Game designer Chris Crawford defined the term in the context of computers. Using a series of dichotomies : Crawford's definition may thus be rendered as: an interactive, goal-oriented activity made for money, with active agents to play against, in which players (including active agents) can interfere with each other. Other definitions, however, as well as history, show that entertainment and games are not necessarily undertaken for monetary gain. Games can be characterized by "what

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