Phutball (short for Philosopher's Football) is a two-player abstract strategy board game described in Elwyn Berlekamp, John Horton Conway, and Richard K. Guy's Winning Ways for your Mathematical Plays . [1]
Phutball (short for Philosopher's Football) is a two-player abstract strategy board game described in Elwyn Berlekamp, John Horton Conway, and Richard K. Guy's Winning Ways for your Mathematical Plays . [1]
Phutball is played on the intersections of a 19×15 grid using one white stone and as many black stones as needed. [1] In this article the two players are named Ohs (O) and Eks (X). The board is labeled A through P (omitting I) from left to right and 1 to 19 from bottom to top from Ohs' perspective. Rows 0 and 20 represent "off the board" beyond rows 1 and 19 respectively.
As specialized phutball boards are hard to come by, the game is usually played on a 19×19 Go board, with a white stone representing the football and black stones representing the men.
The objective is to score goals by using the men (the black stones) to move the football (the white stone) onto or over the opponent's goal line (rows 1 or 19). Ohs tries to move the football to rows 19 or 20 and Eks to rows 1 or 0. At the start of the game the football is placed on the central point, [1] unless one player gives the other a handicap, in which case the ball starts nearer one player's goal.
Players alternate making moves. A move is either to add a man to any vacant point on the board or to move the ball. There is no difference between men played by Ohs and those played by Eks. [1]
The football is moved by a series of jumps over adjacent men. Each jump is to the first vacant point in a straight line horizontally, vertically, or diagonally over one or more men. The jumped men are then removed from the board (before any subsequent jump occurs). This process repeats for as long as there remain men available to be jumped and the player desires. Jumping is optional: there is no requirement to jump. In contrast to checkers, multiple men in a row are jumped and removed as a group. [1]
The diagram on the right illustrates a single move consisting of a series of jumps.
If the football ends the move on or over the opponent's goal line then a goal has been scored. If the football passes through a goal line, but ends up elsewhere due to further jumps, the game continues.
The game is sufficiently complex that checking whether there is a win in one (on an m×n board) is NP-complete. [2] From the starting position, it is not known whether any player has a winning strategy or both players have a drawing strategy, but there exist other configurations from which both players have drawing strategies. [3]
Given an arbitrary board position, with initially a white stone placed in the center, determining whether the current player has a winning strategy is PSPACE-hard. [4]
Gomoku, also called Five in a Row, is an abstract strategy board game. It is traditionally played with Go pieces on a Go board. It is played using a 15×15 board while in the past a 19×19 board was standard. Because pieces are typically not moved or removed from the board, gomoku may also be played as a paper-and-pencil game. The game is known in several countries under different names.
Hex is a two player abstract strategy board game in which players attempt to connect opposite sides of a rhombus-shaped board made of hexagonal cells. Hex was invented by mathematician and poet Piet Hein in 1942 and later rediscovered and popularized by John Nash.
Nine men's morris is a strategy board game for two players dating at least to the Roman Empire. The game is also known as nine-man morris, mill, mills, the mill game, merels, merrills, merelles, marelles, morelles, and ninepenny marl in English. In North America, the game has also been called cowboy checkers, and its board is sometimes printed on the back of checkerboards. Nine men's morris is a solved game, that is, a game whose optimal strategy has been calculated. It has been shown that with perfect play from both players, the game results in a draw.
Alquerque is a strategy board game that is thought to have originated in the Middle East. It is considered to be the parent of draughts and Fanorona.
Checkers, also known as draughts, is a group of strategy board games for two players which involve diagonal moves of uniform game pieces and mandatory captures by jumping over opponent pieces. Checkers is developed from alquerque. The term "checkers" derives from the checkered board which the game is played on, whereas "draughts" derives from the verb "to draw" or "to move".
Havannah is a two-player abstract strategy board game invented by Christian Freeling. It belongs to the family of games commonly called connection games; its relatives include Hex and TwixT. Havannah has "a sophisticated and varied strategy" and is best played on a base-10 hexagonal board, 10 hex cells to a side.
Fox games are a category of asymmetric board games for two players, where one player is the fox and tries to eat the geese / sheep, and the opposing player directs the geese/sheep and attempts to trap the fox, or reach a destination on the board. In another variant, Fox and Hounds, the fox merely tries to evade the hounds. There are several versions known:
The Game of the Amazons is a two-player abstract strategy game invented in 1988 by Walter Zamkauskas of Argentina. The game is played by moving pieces and blocking the opponents from squares, and the last player able to move is the winner. It is a member of the territorial game family, a distant relative of Go and chess.
English draughts or checkers, also called straight checkers or simply draughts, is a form of the strategy board game checkers. It is played on an 8×8 checkerboard with 12 pieces per side. The pieces move and capture diagonally forward, until they reach the opposite end of the board, when they are crowned and can thereafter move and capture both backward and forward.
Hasami shogi is a variant of shogi. The game has two main variants, and all Hasami variants, unlike other shogi variants, use only one type of piece, and the winning objective is not checkmate. One main variant involves capturing all but one of the opponent's men; the other involves building an unbroken vertical or horizontal chain of five-in-a-row.
Gess is an abstract strategy board game for two players, involving a grid board and mutating pieces. The name was chosen as a conflation of "chess" and "Go". It is pronounced with a hard "g" as in "Go", and is thus homophonous with "guess".
Clobber is an abstract strategy game invented in 2001 by combinatorial game theorists Michael H. Albert, J.P. Grossman and Richard Nowakowski. It has subsequently been studied by Elwyn Berlekamp and Erik Demaine among others. Since 2005, it has been one of the events in the Computer Olympiad.
Turkish draughts (Armenian: շաշկի)(Arabic: دامە)(Kurmanji: دامە) is a variant of draughts (checkers) played in Turkey, Greece, Egypt, Kuwait, Lebanon, Syria, Jordan and several other locations around the Mediterranean Sea and Middle East.
Kōnane is a two-player strategy board game from Hawaii. It was invented by the ancient Hawaiian Polynesians. The game is played on a rectangular board. It begins with black and white counters filling the board in an alternating pattern. Players then hop over one another's pieces, capturing them similar to checkers. The first player unable to capture is the loser; their opponent is the winner.
Dameo is an abstract strategy board game for two players invented by Christian Freeling in 2000. It is a variant of the game draughts and is played on an 8×8 checkered gameboard.
Brazilian draughts is a variant of the strategy board game draughts. Brazilian Checkers follows the same rules and conventions as International draughts, the only differences are the smaller gameboard, and fewer checkers per player.
This glossary of board games explains commonly used terms in board games, in alphabetical order. For a list of board games, see List of board games; for terms specific to chess, see Glossary of chess; for terms specific to chess problems, see Glossary of chess problems.
Poddavki, also known as Giveaway checkers, Suicide checkers, Anti-checkers or Losing draughts is a draughts (checkers) game based on the rules of Russian draughts, with the variation that a player wins if they have no legal moves on their turn, either by giving up all their pieces or having them all blocked. As in most varieties of draughts, capturing is mandatory. The game is played in Russia and some parts of the former Soviet Union.
Bashni, also known as column draughts, multi-level checkers, and rarer Chinese checkers, is a variation of draughts, known in Russia since the 19th century. The game is played according to the basic rules of Russian draughts, with the main difference being that draughts being jumped over are not removed from the playing field but are instead placed under the jumping piece . The resulting towers move across the board as one piece, obeying the status of the upper draught. When a tower is jumped over, only the upper draught is removed from it. If, as a result of the combat, the top draught changes colour, ownership of the tower passes on to the opposing player. Based on Bashni, but according to the basic rules of English draughts, world chess champion Emanuel Lasker developed the draughts game "Laska" and, in 1911, published its description. Lasker described towers that can only be "double-layered": i.e. there can be no alternation of colors. He also showed that during the game the number of game pieces either remains constant or decreases. Column draughts are a subject of interest for the mathematical Sciences: combinatorics, theory of paired zero-sum games, etc.