Game of the Month: Rithmomachy

by Dagonell the Juggler

Salaamallah the Corpulent, a Laurel for board games, says "Rithmomachy was invented to keep philosophers off the streets at night." He may be right. The game was invented in the 11th century and played throughout Europe during the Middle Ages, but it was only played by those who considered themselves to be well learned.

Several versions of the rules have survived. Whether the variations are due to the game evolving over time, or extrapolation by the writers of the manuscripts is unknown. What follows is a simplified compilation of the various sets of rules. For a complete set of all the rules, see Salaamallah's book, Medieval Games.

The board is eight squares wide and either fourteen or sixteen squares long. The easiest way to create a Rithmomachy board is to simply place two chess boards edge to edge. The initial board set up is given in the diagram below. The pieces are either squares (S), triangles (T), or circles (C), painted white on one side and black on the other. A captured piece may be turned over and used by the capturing side. Additionally, each piece has a numerical value which comes into play in the later stages of the game.

Each player also has one pyramid (P), a vertical stack of playing pieces. White has a pyramid worth 91 points: (36S, 25S, 16T, 9T, 4C, 1C). Black has a pyramid worth 190 points: (64S, 49S, 36T, 25T, 16C).

361S 225S

121S 49S
190P 120S 64T 56T 30T 36T 66S 28S
100T 90T 81C 49C 25C 9C 12T 16T

9C 7C 5C 3C

2C 4C 6C 8C

9T 6T 4C 16C 36C 64C 72T 81T
15S 45S 25T 20T 42T 49T 91P 153S
25S 81S

169S 289S

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.