Overview

Rithmomachia (also spelled Rithmomachy), meaning “The Battle of the Numbers,” is an early European mathematical strategy board game dating to the 11th century. Sometimes called the “Philosopher’s Game,” it combines chess-like tactical movement with medieval Boethian number theory. Each piece bears a numerical value, and captures are made through mathematical relationships rather than simple displacement. The game was widely played in medieval European universities.

Components

• 1 board: 8 squares wide by 16 squares long (resembling two chessboards placed end to end)
• White/Even pieces (one player): 8 circles, 8 triangles, 7 squares, 1 pyramid
• Black/Odd pieces (one player): 8 circles, 8 triangles, 7 squares, 1 pyramid
• Each piece is inscribed with a specific number value
• Each pyramid is a stack of pieces whose values sum to the pyramid’s total

Setup

1. Place the board lengthwise between the two players.
2. Each player arranges their pieces on their half of the board (the 8 rows closest to them) according to the traditional starting positions.
3. White (Even) pieces are placed on one side, Black (Odd) pieces on the other.
4. Pyramids are assembled from their component pieces and placed in their designated starting squares.

Turn Structure

Players alternate turns. On each turn, a player either:

1. Moves one piece according to its movement rules, OR
2. Captures an opponent’s piece using one of the mathematical capture methods.

Actions

Movement by Piece Type:

• Circles: Move 1 space diagonally.
• Triangles: Leap exactly 2 spaces in any direction (like a limited knight move), jumping over intervening pieces.
• Squares: Leap exactly 3 spaces in any direction, jumping over intervening pieces.
• Pyramids: May move as any of their component piece types (circle, triangle, or square).

Capture Methods (no displacement – you do not land on the captured piece):

• Encounter (Assault): Your piece could move to the opponent’s square on a subsequent turn, and your piece’s value equals the opponent’s value.
• Siege (Blockade): An opponent’s piece is surrounded on all sides so it cannot move; it is captured regardless of values.
• Ambush (Eruption): Your piece’s value multiplied by the number of spaces between it and the target equals the target’s value.
• Deceit (Equality): Two or more of your pieces whose values sum to the target’s value threaten the target from positions where they could reach it.

Scoring / Victory Conditions

There are multiple levels of victory, increasing in difficulty:

1. De Corpore (Victory of Bodies): Capture a set number of opponent’s pieces (commonly the pyramid).
2. De Bonis (Victory of Goods): Capture pieces whose total value meets or exceeds a target sum.
3. De Lite (Victory of Proportion): Arrange 3 or 4 of your surviving pieces in a line or square formation on the opponent’s half of the board such that their values form an arithmetic, geometric, or harmonic progression.
4. Victoria Magna (Great Victory): Achieve all three conditions simultaneously.

Special Rules & Edge Cases

• Pieces are never displaced by landing on them; all captures are at range through mathematical relationships.
• The pyramid is the most powerful piece, as it can move in multiple ways and its high composite value makes it difficult to capture.
• If a player’s pyramid is captured, they are significantly disadvantaged but not eliminated.
• The mathematical nature of the game means memorizing piece values and their relationships is essential.
• Historical rule sets vary; the most common modern version follows the reconstruction by scholars based on medieval manuscripts.

Player Reference

Piece Type	Movement	Quantity per Side
Circle	1 diagonal	8
Triangle	Leap 2 spaces	8
Square	Leap 3 spaces	7
Pyramid	As any component	1

Capture types: Encounter (equal value, in range), Siege (surrounded), Ambush (value x distance = target), Deceit (sum of pieces = target).

Victory levels: Bodies > Goods > Proportion > Great Victory.