Below are the rules as copied from the wikipedia page (linked above) about the game but be sure to also see the information by the SCA laurel who wrote "Medieval Games" here: http://www-cs.canisius.edu/~salley/SCA/ ... machy.html

The rules below describe the most common version of the game, played through much of the Middle Ages and Renaissance. There was also a variant propounded by Fulke in the 16th century, with significantly different (and somewhat more consistent) capture rules.[2]

**Pieces**

There are four types of pieces, which are Rounds, Triangles, Squares, and Pyramids.

**Rounds**: Rounds move one square in any of the four diagonals.**Triangles**: Triangles can move exactly two squares vertically or horizontally, but not diagonally.**Squares**: Squares can move exactly three squares vertically or horizontally, but not diagonally.**Pyramids**: Pyramids are not actually one piece, but more than one piece put together. The White Pyramid is made of a "36" Square, a "25" Square, a "16" Triangle, a "9" Triangle, a "4" Round, and a "1" Round, which totals up to the Pyramid's value of 91. The Black Pyramid is made up of a "64" Square, a "49" Square, a "36" Triangle, a "25" Triangle, and a "16" Round, which adds up to the Pyramid's value of 190. These irregular values make it hard for them to be captured by most of the capturing methods listed below, except for**Siege**. Pyramids can move like a Round, a Triangle, or a Square, as long as they still contain the respective piece, which makes them very valuable.

**Capturing**

There were a variety of capture methods. Pieces do not land on another piece to capture it, but instead remain in their square and remove the other. If a piece is captured, it changes sides.[3]

**Meeting**: If a piece could capture another piece with the same value by landing on it, the piece stays in its location and the opponent's piece is taken from the board.**Assault**: If a piece with a small value, multiplied by the number of vacant spaces between it and another larger piece is equal to the larger piece, the larger piece is captured.**Ambuscade**: If two pieces' sum is equal to an enemy piece that is placed between the two (i.e. the enemy piece is within a move of both attacking pieces), the enemy piece is captured and removed from the board.-
**Siege**: If a piece is surrounded on all four sides, it is removed.

**Victory**

There were also a variety of victory conditions for determining when a game would end and who the winner was. There were common victories, and proper victories, which were recommended for more skilled players. Proper victories required placing pieces in linear arrangements in the opponent's side of the board, with the numbers formed by the arrangement following various types of numerical progression. The types of progression required — arithmetic, geometric and harmonic — suggest a connection with the mathematical work of Boëthius.

**Common Victories**:**De Corpore**(Latin: "by body"): If a player captures a certain number of pieces set by both players, he wins the game.**De Bonis**("by goods"): If a player captures enough pieces to add up to or exceed a certain value that is set by both players, he wins the game.**De Lite**("by lawsuit"): If a player captures enough pieces to add up to or exceed a certain value that is set by both players, and the number of digits in his captured pieces' values are less than a number set by both players, he wins the game.**De Honore**("by honour"): If a player captures enough pieces to add up to or exceed a certain value that is set by both players, and the number of pieces he captured are less than a certain number set by both players, he wins the game.**De Honore Liteque**("by honour and lawsuit"): If a player captures enough pieces to add up to or exceed a certain value that is set by both players, the number of digits in his captured pieces' values are less than a number set by both players, and the number of pieces he captured are less than a certain number set by both players, he wins the game.

**Proper Victories**:**Victoria Magna**("great victory"): This occurs when three pieces that are arranged are in an arithmetic progression.**Victoria Major**("greater victory"): This occurs when four pieces that are arranged have three pieces that are in a certain progression, and another three pieces that are in another type of progression.**Victoria Excellentissima**("most excellent victory"): This occurs when four pieces that are arranged have all three types of mathematical progressions in three different groups.