Rhythromachy

Alternate spellings: Rithmomachy (Latin rithmomachia, the "battle of numbers").  Also called: The Philosopher's game (Latin Ludus philosophorum, the "philosophers' game").

For this game, the references are listed at the bottom of this page.  It is a fairly long descriptions, as this is the most complex game I have come across.  It is included because it is a purely Renaissance game.  No similar game is in existence today.  Rhythmomachy is played on a chess-style board.  It is a capture game, again like chess, but that is where the similarities end.  The captures are accomplished by numerical association.  One never has to actually come in contact with the captured piece.

A Extremely Brief History:

Current sources I have read place the invention of this game in the 12th century, with references to it in gaming books as late as the 17th century.  The general consensus seems to be that chess replaced it in popularity.  Due to the mathematical progressions involved, the game was probably limited to the more learned people.  One researcher also noted that "It is remarkable in that it is very nearly the only period game for which nothing even remotely similar exists today."  This is the main reason I think this game, in particular, should be one that is played at the Duck.

The Pieces

The playing pieces consist of forty-eight men.  The pieces are colored on one side with one color and on the other side with the opposing color.  Each side also indicates the piece's numeric value.  They are set up this way because one option during the game is to allow captured pieces to switch sides and play for the capturing army.

The pieces come in three different shapes. Each side has eight round, eight triangles, and eight squares. One of the squares is designated the king and has four more pieces stacked pyramid-fashion on top of it; one more square, two triangles, and a round. Therefore, there are twenty-eight numbers in each army plus the sum of the king pyramid.

The Board

The playing surface is the common checkerboard pattern of a chess table eight columns wide but sixteen rows deep. In fact, two chessboards can be placed together to create a Rhythmomachy table.  The starting arrangement is as follows:

Movement of the Men

Each shape has different movements it can perform.  However, there is a restriction on pieces that move multiple squares.  No piece can jump over any other man.  This is very important to keep in mind on the L-shaped moves.

Circles can only move one space diagonally.

Triangles have two options.  They can move two spaces horizontally or vertically but not diagonally, and they may not leap over any other man.

They can also "fly". "Flying" refers to moving like a knight in chess.  There is a lot of disagreement in the literature as to the purpose and frequency of this move.  The limits are sometimes as severe as allowing the King only one such move in a game to avoid capture.  For the purposes of the Guilde of St. Ives, we will base the practice of "flying" on the source quote, ". . . with theyr flying draughte they can take no man, but if needed by helpe to besiege a man."  One cannot use the "flying" move to capture a man or to form the Triumphs, which will be explained later.  The move itself has to be performed as moving two spaces straight and then one to the side.  One cannot move one to the side and two forward to avoid jumping over a man.  Also, a capture cannot be made with the "flying" move.

Squares move just like triangles, but they move three squares rather than two.  They can also "fly", with the same restrictions on jumping and capture.

Kings are intriguing pieces.  They are five pieces of different shapes stacked in a pyramid.  Because of this, they are granted the ability to perform the movements of all the pieces it contains.  The King also has one special move of its own.  It may move three spaces diagonally as well.  A King may lose levels of his pyramid during play, as the levels can be captured separately.  When the King loses a shape, it then loses the ability to move like that piece.  If the King's circle is captured, for example, it can no longer move one space diagonally.

Capture

There are several different capture situations that can take place.  Most rely on a mathematical formula; one is simply by entrapping an enemy piece so it has no legal move.  There are two ways a capture can occur.  When you move your piece into position to create a capture situation, the opponent's piece is removed, turned over, and placed in the last rank of your side of the board, becoming a new soldier in your army.  There is no need to move your piece to the opponent's square. The other way a capture occurs is if an opponent inadvertently moves into a capture situation.  In this case, you must actually move one of your pieces to your opponent's square, removing his piece for the capture and making it part of your army as before.

The capture situations are as follows:

Capture by Oblivion is surrounding an enemy with four of one's own pieces so that no legal moves are possible, such as occupying the four corners around a circle piece. None of the four attacking pieces may be in the position of being captured by the surrounded man.  This is important, as there is no rule against stepping into a capture situation from a source other than the surrounded may.  You still make the capture by oblivion.  For example, you may not use the triangle 9 to surround the circle 9, as the circle can capture the triangle.  If the circle was a 5, however, the triangle 9 may surround it even if the move places the 9 in jeopardy with other capture situations.

Capture by Equality is where two pieces are of equal value, such as the two 9's mentioned above. When the triangle 9 moves into a position two spaces away from the circle 9, this creates a capture situation of equality.  There aren't many pieces that are duplicated on both sides.

Capture by Addition begins the more complex mathematical capture situations.  This requires that one moves two pieces into position to capture the same enemy piece.  The two pieces must add up to the number on the opponent's piece.  For example, if the round 3 and round 5 are both one space diagonally from the round 8, the 8 is then captured.  Further, if square 45 is one space diagonally from circle 9 and two spaces horizontally from triangle 36, a capture situation exists on 45.  The other mathematical capture situations are similar.

Capture by Multiplication is where the two attacking pieces multiply to equal the opponent piece, such as 9 time 5 to capture 45.

Capture by Subtraction is where the two attacking pieces subtract to equal the opponent piece, such as 9 minus 6 to capture 3.

Capture by Division is where the two attacking pieces divide, without remainder, to equal the opponent piece, such as 45 divided by 9 to capture 5.

There are also three optional captures that are used if both players agree.  Sources investigated to this point do not indicate which of the numbers is to be the opponents.  I would suggest using the highest number being the captured piece.  However, that could also be optional based on what the players agree to.  Become familiar with the proportional captures, as they are all part of the Triumphs described later.

Capture by Arithmetical Proportion is where the three pieces are separated by the same values. Such a combination would be 3, 7, and 11 (7-3=4; 11-7=4).

Capture by Geometrical Proportion gets a little difficult.  Here, the lowest number is multiplied by the highest. From this product, the square root is calculated. This square root is the middle number, such as the combination of 4, 20, 100. The product of 4*100=400. The square root of 400 is 20.

Capture by Musical Proportion is the most complex.  The difference between the lowest and highest numbers must equal the sum of the differences between the lowest and middle numbers and the middle and highest numbers.  In the combination 9, 15, 45, the difference between 9 and 45 is 36.  Further calculating we find 15-9=6 and 45-15=30. As the last step, the sum of these two differences is 36, equaling the first calculation.

Triumph

The Triumph is the end phase of the game.  The goal is to assemble a Triumph inside your enemy's territory.  Prior to the Triumph phase, the King of the opposing side must be completely captured.  The capturing player then announces which of the three Triumphs will be attempted and which pieces will be used.  These pieces become protected and cannot be captured by the opponent.  For this protection, they forfeit their ability to "fly".

The Great Triumph is creating one row; either horizontally, vertically, or diagonally; of three pieces which demonstrate any one of the three proportions; Arithmetical, Geometrical, or Musical.

The Greater Triumph requires using four pieces to create two of the proportions. They may either be arranged in a line or in the corners of a 3 x 3 grid.

The Greatest Triumph requires using four pieces to create all three proportions at the same time. Again, a square arrangement is acceptable.

The sources reviewed to this point don't detail what happens if the opponent is able to block creation of the Triumph.

Other Versions:

This is only one version of the game as it existed through the centuries.  Some other version options that might be considered for learning and time constraints include use of other forms of victory.

Victory of Bodies is achieved by capturing a preset number of your opponent's men.  Victory of Goods is achieved by capturing a preset total of numeric values from your opponent.  Victory of Quarrel is achieved by capturing a preset total with the addition of the number of numeric digits involved. C apturing the pieces 2, 8, 25, 225 would be seven digits.  Victory of Honor is achieved by capturing a preset number of piece and a preset total numeric value.  Victory of Honor and Quarrel combines all the other victories.  Winning requires obtaining a numeric total with a number of pieces having a number of digits.

References:

1. http://www.inmet.com/~justin/game-recon-rhyth1.html

2. "a transcription of a 1563 translation by William Fulke of de Boissiere's 1554/56 description of Rhythmomachy"

3. "A History of Board-Games Other Than Chess"
H. J. R. Murray
Hacker Art Books, Inc., New York 1978

Period Sources Listed In The References: