Many abstract games and puzzles can be described in terms of players, pieces and moves on a board.
Games have two or more players, human or computer, who compete to reach some defined goal. Puzzles have one player and the goal is to solve the puzzle.
A game board consists of a set of predefined locations, each of which can hold a piece. The locations are arranged in some way for display purposes and may be related by directions and grouped into zones to assist in defining legal moves, but there is nothing special about any particular arrangement. A chess board or a card table or a crossword puzzle are all kinds of game board.
Each piece is owned by a player when it is played to a location. Pieces have a fixed visual appearance, to make them recognisable on display. As a simplifying assumption, a location can hold only one piece of one kind, so groups of pieces on a single location and pieces that are modified to look different are represented as different pieces.
Pieces are provided with legal moves according to a set of rules.Moves are arbitrarily complex, from simply placing a piece on a location on the board, to long sequences of moves and captures that may affect the entire board.
The game proceeds from a starting position through a series of played moves until it ends. The state of the game is represented by a sequence of board states comprising played pieces. These are games of perfect information, with no hidden state.
The game ends when some specific condition is satisfied. A player may win, lose or draw at the end of any turn and before the next player can move.
Both legal moves and ending conditions may have arbitrarily complex rules which depend on the players, pieces and locations. The game may define neutral players, dummy pieces and dummy locations to assist in defining complex moves and ending conditions.