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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.
Trivially solvable. Either player can force the game into a draw. [citation needed] Three musketeers Strongly solved by Johannes Laire in 2009, and weakly solved by Ali Elabridi in 2017. [20] It is a win for the blue pieces (Cardinal Richelieu's men, or, the enemy). [21] Tic-tac-toe Trivially strongly solvable because of the small game tree. [22]
Futile game. In game theory, a futile game is a game that permits a draw or a tie when optimal moves are made by both players. [ 1][ 2] An example of this type of game is the classical form of Tic-tac-toe, [ 3] though not all variants are futile games. The term does not apply to intransitive games, such as iterated prisoner's dilemma or rock ...
Treblecross. Treblecross is a degenerate tic-tac toe variant. [1] The game is an octal game, [2] [3] played on a one-dimensional board and both players play using the same piece (an X or a black chip [4] ). [5] [1] [3] Each player on their turn plays a piece in an unoccupied space. The game is won if a player on their turn makes a line of three ...
Strong positional game (also called Maker-Maker game) The first player to claim all of the elements of a winning set wins. If the game ends with all elements of the board claimed, but no player has claimed all elements of a winning set, it is a draw. An example is classic tic-tac-toe. Maker-Breaker game The two players are called Maker and Breaker.
It is played by two players, called First and Second, who alternately take previously-untaken positions. In a strong positional game, the winner is the first player who holds all the elements of a winning-set. If all positions are taken and no player wins, then it is a draw. Classic Tic-tac-toe is an example of a strong positional game.
Peter Marshall, the cheery actor, singer and nightclub comedian who became one of America's best-known game show hosts on the long-running program "The Hollywood Squares" from 1966 to 1981, died ...
In game theory, an extensive-form game is a specification of a game allowing (as the name suggests) for the explicit representation of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, the (possibly imperfect) information each player has about the other player's moves when they make a decision, and their payoffs for all possible ...
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