Rithmomachy, 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".

Object of the game is to win by any of:

• capturing 15 of the (more than half) of the opposing pieces
• capturing pieces whose value sums to 1315 or more White, or 984 or more Black (3/4 of the sum of the total opponent values)
• forming a glorious victory on the opponent's side of the board, with one of your own pieces as one end
  • all three pieces (A,B,C) are on the opponent's side of the board
  • they form an unobstructed evenly spaced horizontal or vertical line or a triangle
  • the values of the pieces form an arithmetic (B-A) = (C-B), geometric (A*C) = (B*B), or harmonic ((A+C)*B) = (A*C*2) progression

Moves:

Players alternate turns, starting with Black. Movement is only possible to an empty square. Horizontal and vertical moves are blocked by intervening pieces. Moves with a diagonal component can't be blocked - they're like chess knights moves.

• Rounds move one step diagonally
• Triangles move 2 steps horizontally, or a knight's move
• Squares move 3 steps horizontally or vertically, or a longer knights move
• Pyramids move in any of the ways permitted by any of the pieces they still contain.

Capturing:

Capturing depends on the geometric or numeric relationship between the captured and capturing pieces. Capturing never involves moving into the square occupied by the captured piece. Capturing pieces stay where they are. If by luck or design multiple captures are possible after a single move, they all occur. Pyramids can capture or be captured using either their total value, or the value of any component.

• Capture by Siege:
  A piece is captured by siege if it is surrounded by enemies or the edge of the board on all 4 orthogonal or all four diagonal directions.
   
  
• Capture by Equality:
  A piece or stack is captured by equality if the attacking piece (or stack) has the same value, and if the attacking piece could move to the position of the attacked piece if it were vacant. Note that very few of the black and white pieces have the same value.
   
  
• Capture by Eruption:
  A piece or stack is captured by eruption if the value of the smaller, multiplied by the distance between the pieces, is equal to the value of the greater. Captures by eruption do no depend on the natural movement of the pieces. The starting and ending locations are both counted, so the minimum distance between pieces is 2.
   
  
• Capture by Ambush:
  A piece is captured by ambush if two pieces, which could move to the enemy to be captured, have a sum, difference, product, or quotient equal to the captured piece value.

See Also:
1. http://en.wikipedia.org/wiki/Rithmomachy
2. http://www.boardspace.net/rithmomachy/english/rules.html