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    Finite Game

    Some notable finite games

    checkers | nim | tic-tac-toe

    Illustrations

    Illustrations Nim

    Illustrations Tic-tac-toe

    Statements

    Two players start on opposite sides of an 8 × 8 board, each with twelve pieces of a fixed color on the starting side. Initially, all pieces may move and capture only in a forward diagonal direction (as viewed by the player making the move), but if a piece is "crowned" by reaching the other side of the board, it may then move forward or backward. An opponent's piece may be captured by jumping over it, and the game is won by capturing all the opponent's pieces or by leaving the opponent with no legal moves.

    Given one or more piles ("nim-heaps"), players alternate by taking all or some of the counters in a single heap. The player taking the last counter or stack of counters is the winner.

    Two players alternately place pieces (typically X's for the first player and O's for the second) on a 3 × 3 board. The first player to get three matching symbols in a row (vertically, horizontally, or diagonally) is the winner. If all squares are occupied but neither player has three symbols in a row, the game is a tie.

    Common classes

    finite | perfect information | sequential | two-player

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