CHECKERS VS RITHMOMACHY

Draughts (/drɑːfts, dræfts/; British English) or checkers (American English) 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. Draughts developed from alquerque. The name 'draughts' derives from the verb to draw or to move, wheras 'checkers' derives from the checkered board which the game is played on. The most popular forms are English draughts, also called American checkers, played on an 8×8 checkerboard; Russian draughts, also played on an 8×8, and international draughts, played on a 10×10 board. There are many other variants played on 8×8 boards. Canadian checkers and Singaporean/Malaysian checkers (also locally known as dum) are played on a 12×12 board. English draughts was weakly solved in 2007 by a team of Canadian computer scientists led by Jonathan Schaeffer. From the standard starting position, both players can guarantee a draw with perfect play. Draughts is played by two opponents, on opposite sides of the gameboard. One player has the dark pieces; the other has the light pieces. Players alternate turns. A player may not move an opponent's piece. A move consists of moving a piece diagonally to an adjacent unoccupied square. If the adjacent square contains an opponent's piece, and the square immediately beyond it is vacant, the piece may be captured (and removed from the game) by jumping over it. Only the dark squares of the checkered board are used. A piece may move only diagonally into an unoccupied square. When presented, capturing is mandatory in most official rules, although some rule variations make capturing optional. In almost all variants, the player without pieces remaining, or who cannot move due to being blocked, loses the game.

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Rithmomachy (or Rithmomachia, also Arithmomachia, Rythmomachy, Rhythmomachy, or several other variants; sometimes known as The Philosophers' Game) is a highly complex, early European mathematical board game. The earliest known description of it dates from the eleventh century. A literal translation of the name is "The Battle of the Numbers". The game is much like chess, except most methods of capture depend on the numbers inscribed on each piece. It has been argued that between the twelfth and sixteenth centuries, "rithmomachia served as a practical exemplar for teaching the contemplative values of Boethian mathematical philosophy, which emphasized the natural harmony and perfection of number and proportion. The game, Moyer argues, was used both as a mnemonic drill for the study of Boethian number theory and, more importantly, as a vehicle for moral education, by reminding players of the mathematical harmony of creation." Very little, if anything, is known about the origin of the game. Medieval writers attributed it to Pythagoras, but no trace of it has been discovered in Greek literature, and the earliest mention of it is from the time of Hermannus Contractus (1013–1054). The name, which appears in a variety of forms, points to a Greek origin, the more so because Greek was little known at the time when the game first appeared in literature. Based upon the Greek theory of numbers, and having a Greek name, it is still speculated by some that the game originated in Greek civilization, perhaps in the later schools of Byzantium or Alexandria. The first written evidence of Rithmomachia dates to around 1030, when a monk named Asilo created a game that illustrated the number theory of Boëthius' De institutione arithmetica, for the students of monastery schools. The rules of the game were improved shortly thereafter by another monk, Hermannus Contractus from Reichenau, and in the school of Liège. In the following centuries, Rithmomachia spread quickly through schools and monasteries in the southern parts of Germany and France. It was used mainly as a teaching aid, but gradually intellectuals started to play it for pleasure. In the 13th century Rithmomachia came to England, where famous mathematician Thomas Bradwardine wrote a text about it. Even Roger Bacon recommended Rithmomachia to his students, while Sir Thomas More let the inhabitants of the fictitious Utopia play it for recreation. The game was well enough known as to justify printed treatises in Latin, French, Italian, and German, in the sixteenth century, and to have public advertisements of the sale of the board and pieces under the shadow of the old Sorbonne.

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