Rithmomachy

Alternate Names

The name Rithmomachy is derived from the Latin "Rithmomachia" which, in turn is derived from the Greek rithmos (number) and mache (battle). Other derivations include Arithmomachia, Rythmomachy, and Rhythmomachy. The name "The Philosophers' Game" refers to "Philosopher" as used in the medieval sense of the word as an equivalent to what we would now call scientists or mathematicians.

No. of Players

Two

Equipment

The Rithmomachy board is a 8x16 checkered square grid, equivalent to two conjoined chessboards. Is the checkering relevant?

Most varieties of the game require each piece to bear its number on both sides, but in the opposite color on the reverse.

History

Medieveal writers attributed the invention of the game to Pythagoras, but no mention of it has ever been found in Greek literature. It's first written evidence dates back to around 1030.

The first written evidence of Rithmomachia dates back 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 the respected 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.

Objective

There are eight possible ways to win, five lesser victories and three greater victories. The first lesser victory, called De Corpore: capture the number of pieces which the players have agreed to beforehand. The second lesser victory, De Bonis: capture enough pieces whose value meets or exceeds a numerical total which the players have agreed to beforehand. The third lesser victory, De Lite: capture pieces with a set number of digits which the players have agreed to beforehand. For example, if the players agree to the digits 1, 2, & 3, White may win by capturing 12T & 3C, or 120S & 36T, or 225S & 361S, etc. The fourth lesser victory, De Honore: capture enough pieces to meet or exceed both a total number of pieces and a sum of their values which the players have agreed to beforehand. The fifth lesser victory, Honore Liteque: the sum of the digits of the captured pieces must meet or exceed a numerical total which the players have agreed to beforehand.

The greater victories, or triumphs, require lining up at least three pieces in a arithmetical progression (e.g. 2C, 3C, & 4C), a geometrical progression (e.g. 4C, 8C, & 16C) or a harmonic progression, either late period (a/b = b/c) or early period (a/b = c/d). A triumph cannot occur until the opponent's entire pyramid has been captured. It doesn't matter if the opponent manages to re-capture any of the component pieces, because those re-captured men are now played as separate pieces and may not be re-assembled back into the pyramid. The Great Triumph: three pieces lined up to form one of the progressions. The Greater Triumph: four pieces lined up to form two of the progressions simultaneously. The Greatest Triumph: four pieces lined up on the opponent's side of the board to form all three progressions simultaneously.

Play

With White moving first, alternate turns entail the movement of a single friendly counter, orthogonally or diagonally.

Players alternate turns moving one piece per turn. White goes first. Circle pieces move exactly one square in any direction, horizontally, vertically or diagonally. Triangle pieces move exactly two squares horizontally, vertically or diagonally. Square pieces move exactly three squares horizontally, vertically or diagonally. Pyramids move the same way as their bottom-most piece moves. Pieces may not jump over other pieces, either their own or their opponents. The path must be clear for the entire length of their move. They may not shorten their move, but must move the entire distance they are allowed. Pieces may not turn in mid-move but must continue in the direction they started.

There are four methods of capturing your opponent's pieces: assault, ambush, sally and siege. In assault, a piece may capture and replace any piece of equal value occupying a square it can reach by a legal move. In ambush, any higher numbered piece adjacent to lower numbered enemy pieces whose sum or product were equal to it could be captured. For example, 45S could be captured by either 30T, 12T, & 3C (sum) or 5C & 9C (product). In sally, a piece of value n which was x squares away from an enemy piece of value (x * n) captured and replaced it. The distance must include both of the occupied squares. For example, 8C can capture 16T by being adjacent to it (8 * 2 = 16). In siege, a piece can be captured if it is surrounded on all sides by enemy pieces which are not in danger of being captured themselves. A captured piece may be placed on the capturing side's own back row as one of their own pieces in place of a move.

Pyramids attack and capture as either their total value or the value of their bases. Pyramids may be captured by their total value, the value of their bases, one layer at a time, or the sum of several layers at a time.

There are eight possible ways to win, five lesser victories and three greater victories. The first lesser victory, called De Corpore: capture the number of pieces which the players have agreed to beforehand. The second lesser victory, De Bonis: capture enough pieces whose value meets or exceeds a numerical total which the players have agreed to beforehand. The third lesser victory, De Lite: capture pieces with a set number of digits which the players have agreed to beforehand. For example, if the players agree to the digits 1, 2, & 3, White may win by capturing 12T & 3C, or 120S & 36T, or 225S & 361S, etc. The fourth lesser victory, De Honore: capture enough pieces to meet or exceed both a total number of pieces and a sum of their values which the players have agreed to beforehand. The fifth lesser victory, Honore Liteque: the sum of the digits of the captured pieces must meet or exceed a numerical total which the players have agreed to beforehand.

The greater victories, or triumphs, require lining up at least three pieces in a arithmetical progression (e.g. 2C, 3C, & 4C), a geometrical progression (e.g. 4C, 8C, & 16C) or a harmonic progression, either late period (a/b = b/c) or early period (a/b = c/d). A triumph cannot occur until the opponent's entire pyramid has been captured. It doesn't matter if the opponent manages to re-capture any of the component pieces, because those re-captured men are now played as separate pieces and may not be re-assembled back into the pyramid. The Great Triumph: three pieces lined up to form one of the progressions. The Greater Triumph: four pieces lined up to form two of the progressions simultaneously. The Greatest Triumph: four pieces lined up on the opponent's side of the board to form all three progressions simultaneously.

Strategy

Variations

Sources

1. Parlett, David. The Oxford History of Board Games. Oxford: Oxford UP, 1999.

2. Botermans, Jack. The Book of Games: Strategy, Tactics & History. Sterling Publishing Co., Inc., 2008. ISBN 978-1-4027-4221-7