Hexapawn is a deterministic two-player game invented by Martin Gardner. It is played on a rectangular board of variable size, for example on a 3×3 board or on a regular chessboard. On a board of size n×m, each player begins with m pawns, one for each square in the row closest to them. The goal of each player is to either advance a pawn to the opposite end of the board or leave the other player with no legal moves, either by stalemate or by having all of their pieces captured.
Hexapawn on the 3×3 board is a solved game; with perfect play, White will always lose in 3 moves (1.b2 axb2 2.cxb2 c2 3.a2 c1#). Indeed, Gardner specifically constructed it as a game with a small game tree in order to demonstrate how it could be played by a heuristic AI implemented by a mechanical computer based on Donald Michie's Matchbox Educable Noughts and Crosses Engine (MENACE).
A variant of this game is octopawn, which is played on a 4×4 board with 4 pawns on each side. It is a forced win for White.
Only 24 matchboxes are required for a hexapawn version of Matchbox Educable Noughts and Crosses Engine.
As in chess, a pawn may be moved in two different ways: it may be moved one square vertically forward, or it may capture a pawn one square diagonally ahead of it. A pawn may not be moved forward if there is a pawn in the next square. Unlike chess, the first move of a pawn may not advance it by two spaces. A player loses if they have no legal moves or one of the other player's pawns reaches the end of the board.
Whenever a player advances a pawn to the penultimate rank and attacks an opposing pawn, there is a threat to proceed to the final rank by capture. The opponent's only sensible responses, therefore, are to either capture the advanced pawn or advance the threatened one, the latter only being sensible in the case that there is one threatened pawn rather than two. If one restricts 3×N hexapawn with the additional rule that capturing is always compulsory, the result is the game Dawson's chess. The game was invented by Thomas Rayner Dawson in 1935. [1]
Dawson's chess reduces to the impartial game denoted .137 in Conway's notation. This means that it is equivalent to a Nim-like game in which:
The initial position is a single heap of size N. The nim-sequence for this game is
0.1120311033224052233011302110452740 1120311033224455233011302110453748 1120311033224455933011302110453748 1120311033224455933011302110453748 1120311033224455933011302110453748 ...,
where bold entries indicate the values that differ from the eventual periodic behavior of the sequence.
Chess is a board game for two players, each controlling a set of chess pieces, with the objective to checkmate the opponent's king, i.e. threaten it with inescapable capture. It is sometimes called international chess or Western chess to distinguish it from related games such as xiangqi and shogi. The recorded history of chess goes back at least to the emergence of a similar game, chaturanga, in seventh-century India. The rules of chess as they are known today emerged in Europe at the end of the 15th century, with standardization and universal acceptance by the end of the 19th century. Today, chess is one of the world's most popular games, and is played by millions of people worldwide.
Nim is a mathematical game of strategy in which two players take turns removing objects from distinct heaps or piles. On each turn, a player must remove at least one object, and may remove any number of objects provided they all come from the same heap or pile. Depending on the version being played, the goal of the game is either to avoid taking the last object or to take the last object.
Baroque chess is a chess variant invented in 1962 by Robert Abbott. In 1963, at the suggestion of his publisher, he changed the name to Ultima, by which name it is also known. Abbott later considered his invention flawed and suggested amendments to the rules, but these suggestions have been substantially ignored by the gaming community, which continues to play by the 1962 rules. Since the rules for Baroque were first laid down in 1962, some regional variation has arisen, causing the game to diverge from Ultima.
The king is the most important piece in the game of chess. It may move to any adjoining square; it may also perform, in tandem with the rook, a special move called castling. If a player's king is threatened with capture, it is said to be in check, and the player must remove the threat of capture immediately. If this cannot be done, the king is said to be in checkmate, resulting in a loss for that player. A player cannot make any move that places their own king in check. Despite this, the king can become a strong offensive piece in the endgame or, rarely, the middlegame.
A chess piece, or chessman, is a game piece that is placed on a chessboard to play the game of chess. It can be either white or black, and it can be one of six types: king, queen, rook, bishop, knight, or pawn.
The pawn is the most numerous and weakest piece in the game of chess. It may move one square directly forward, it may move two squares directly forward on its first move, and it may capture one square diagonally forward. Each player begins a game with eight pawns, one on each square of their second rank. The white pawns start on a2 through h2; the black pawns start on a7 through h7.
The rules of chess govern the play of the game of chess. Chess is a two-player abstract strategy board game. Each player controls sixteen pieces of six types on a chessboard. Each type of piece moves in a distinct way. The object of the game is to checkmate the opponent's king; checkmate occurs when a king is threatened with capture and has no escape. A game can end in various ways besides checkmate: a player can resign, and there are several ways a game can end in a draw.
This glossary of chess explains commonly used terms in chess, in alphabetical order. Some of these terms have their own pages, like fork and pin. For a list of unorthodox chess pieces, see Fairy chess piece; for a list of terms specific to chess problems, see Glossary of chess problems; for a list of named opening lines, see List of chess openings; for a list of chess-related games, see List of chess variants; for a list of terms general to board games, see Glossary of board games.
In chess, en passant describes the capture by a pawn of an enemy pawn on the same rank and an adjacent file that has just made an initial two-square advance. The capturing pawn moves to the square that the enemy pawn passed over, as if the enemy pawn had advanced only one square. The rule ensures that a pawn cannot use its two-square move to safely skip past an enemy pawn.
Tamerlane chess is a medieval chess variant. Like modern chess, it is derived from shatranj. It was developed in Central Asia during the reign of Emperor Timur, and its invention is also attributed to him. Because Tamerlane chess is a larger variant of chaturanga, it is also called Shatranj Al-Kabir, as opposed to Shatranj as-saghir. Although the game is similar to modern chess, it is distinctive in that there are varieties of pawn, each of which promotes in its own way.
Kriegspiel is a chess variant invented by Henry Michael Temple in 1899 and based upon the original Kriegsspiel developed by Georg von Reiswitz in 1812. In this game, each player can see their own pieces but not those of their opponent. For this reason, it is necessary to have a third person act as an umpire, with full information about the progress of the game. Players attempt to move on their turns, and the umpire declares their attempts 'legal' or 'illegal'. If the move is illegal, the player tries again; if it is legal, that move stands. Each player is given information about checks and captures. They may also ask the umpire if there are any legal captures with a pawn. Since the position of the opponent's pieces is unknown, Kriegspiel is a game of imperfect information.
Yari shogi is a modern variant of shogi ; however, it is not Japanese. It was invented in 1981 by Christian Freeling of the Netherlands. This game accentuates shogi’s intrinsically forward range of direction by giving most of the pieces the ability to move any number of free squares orthogonally forward like a shogi lance. The opposite is true of promoted pieces which can move backward with the same power.
The touch-move rule in chess specifies that a player, having the move, who deliberately touches a piece on the board must move or capture that piece if it is legal to do so. If it is the player's piece that was touched, it must be moved if the piece has a legal move. If the opponent's piece was touched, it must be captured if it can be captured with a legal move. If the touched piece cannot be legally moved or captured, there is no penalty. This is a rule of chess that is enforced in all formal over-the-board competitions.
Minichess is a family of chess variants played with regular chess pieces and standard rules, but on a smaller board. The motivation for these variants is to make the game simpler and shorter than standard chess. The first chess-like game implemented on a computer was the 6×6 chess variant Los Alamos chess. The low memory capacity of early computers meant that a reduced board size and a smaller number of pieces were required for the game to be implementable on a computer.
The octal games are a class of two-player games that involve removing tokens from heaps of tokens. They have been studied in combinatorial game theory as a generalization of Nim, Kayles, and similar games.
The following outline is provided as an overview of and topical guide to chess:
Wildebeest chess is a chess variant created by R. Wayne Schmittberger in 1987. The Wildebeest board is 11×10 squares. Besides the standard chess pieces, each side has two camels and one "wildebeest" - a piece which may move as either a camel or a knight.
Dragonfly is a chess variant invented by Christian Freeling in 1983. There are no queens, and a captured bishop, knight, or rook becomes the property of the capturer, who may play it as their own on a turn to any open square. The board is 7×7 squares, or alternatively a 61-cell hexagon with two additional pawns per side.
The Matchbox Educable Noughts and Crosses Engine was a mechanical computer made from 304 matchboxes designed and built by artificial intelligence researcher Donald Michie in 1961. It was designed to play human opponents in games of noughts and crosses (tic-tac-toe) by returning a move for any given state of play and to refine its strategy through reinforcement learning.