Rithmomachy Variations

The flow of the game

As I interpret the classical rules, a game would be a long slog, since captured pieces return to the battle, simple exchanges have little net effect.   After a protracted battle to achieve an advantage of numbers, the victor would march forward and form a glorious victory as a sort of flourish.  Imagine two philosopher-monks playing one game over the course of several days.  


Initial Setup

Some sources place the initial armies in the back rows, or in a phalanx in the center of the board.
 alternate starting position
 alt setup 2


Simple Movements

Some sources have all pieces moving in any direction, but blocked by intervening pieces.


 linear round
 linear triangle
 linear square
 alternate pyramid movement


.

Capture by Siege

A common description of capture by siege is that a piece is captured if all of its 'ordinary movements' are blocked by adversaries.  The "orthogonal" directions are considered ordinary, and the "knight's" type moves are considered irregular.  So capture by siege could occur for triangles and squares blocked at a distance of 2 or 3.   If rounds move only diagonally, I suppose they could be besieged by blocking all 4 diagonals. 
alternate siege capture Black 121 captured by siege, all of it's orthogonal movements are  blocked.



Capture by Ambush

Some sources describe capture by Ambush as similar to the custodial capture of Hnefatafl, where the two attacking pieces are adjacent to the captured.

alternate capture by ambush or alt ambush
Some sources do not include all 4 of the arithmetic operations.

Pyramids

Numerous special rules for pyramids occur in various sources.  Among them:

  • A special move 3 steps diagonally, only available while the original pyramid stack is intact.
  • Capturing using the pyramid's total value is only available while the original stack is intact.
  • Capturing the entire pyramid in any attack that captures any component.
  • Optionally offering other pieces as captives instead of capturing pyramid components.
  • Capture of the entire pyramid as a game-ending condition.
  • Requiring capture of the entire pyramid as a precondition to a glorious victory.

Prisoners

The classic rules definitely require the captured pieces to be returned to the back row of the board, in service of the capturing army.  In some variations it is immediate and automatic, in others it is in place of a move.  In any case, the returned pieces are far from the action and have to be moved forward to engage or participate in victories.

Glorious Victories

The standard location of the line defining glorious victories is ambiguous, but probably the usual location is the enemy's original front line.

In most descriptions, glorious victories require the pyramid to be completely captured first.

The pieces participating in the glorious victory probably are intended to be only pieces under your control;  your own pieces or enemy pieces you have captured and returned to service.

Greater Victories

Standard rules also include "greater victories" and "greatest victories" which use four pieces and incorporate two or three types of the ordinary victories.

These superior victories almost always include the ordinary victories as a sub pattern, so in my interpretation they're about style, or bragging rights.