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Post Reply. I had played Rithmomachia for two years but players are hard to find. Anybody ever played The Philosopher's Game: Rithmomachia? Anicius Manlius Severinus Boethias died A. It is believed Rithmomachia was developed during this period of scholasticism before the advent of the secular universities to teach Boethian mathematics to Catholic monks and Catholic priests.

## Rhythmomachia: The Philosopher's Game

Anyways, Rithmo is still a good game to learn math as you play. Well, your post got me interested enough to buy Anne Moyer's book. Now I just have to learn the rules, make a board, and teach someone else to play so I have an opponent. The figure in the tower which was lost is removed and the duplicate takes its place in the tower, instead.

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Each figure can attack as many times as possible and even one attack can be lead by as many figures as necessary. To attack an opponent's figure successfully, one must reduce its rating exactly to zero each figure that still has a negative or positive rating at the end of the opponents turn, will regenerate to its full rating.

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Since the ratings vary that much, it is rather difficult to attack another figure successfully. Various possibilities for a single attack of a figure do exist, each with the goal of reducing the target's rating to If you have found out any mathematical properties concerning Rhythmomachia, or know any alternative rules then please tell me.

Also if you know about additional sources on the web, I can include a link to them. Some hints if try to solve some puzzles: a simple mathematical connection in Rhythmomachia concerns the starting arrangements of the figures. Some of the pieces' ratings follow up a sequence like:.

## Game Theory in Philosophy

What figures are the most effective ones? Which can attack the most opponents and which can be attacked by the least? Which figures can be used best for winning orders? What value do these figures have then? Can you compute a list of all possible combinations for winning orders? My computer printed out this list of winning orders. Be sure to click the End Turn button at the end of each turn. See David Dyers' recent Rhythmomachia The Rules of the Game Rhythmomachia is a complex strategic game played on a board similar to a chessboard.

The Moves For making a move, use your mouse to drag pieces to their new position according to the following moves: An Infantry man , represented by a circle, moves exactly two fields in horizontal or vertical direction. A Cavalier , represented by a triangle, moves exactly three fields in diagonal direction.

A Chariot , represented by a square, moves exactly four fields in any direction including diagonal. The Pyramid , represented by a pyramidal tower, contains six or less units and can choose like which of those it wants to move, every time. If a figure contained in the pyramidal tower is attacked successfully, then it is removed and cannot be used for moving, any more.

Note: The number of fields moved includes the starting and ending position! So a Cavalier has moved three fields if it has simply stepped over one empty field in between.

## Game Theory in Philosophy | SpringerLink

This strange calculation is important for attacks. Each figure has a rating that determines its combat values, whereas hardly any two figures have the same ratings. Various possibilities for a single attack of a figure do exist, each with the goal of reducing the target's rating to 0: Direct confrontation is used if a movement of a figure would lead exactly onto the target figure and the ratings are equal. This attack can only be lead by a single figure at once. A figure's combat value will be subtracted from the target's rating. Reinforcement Attack uses addition for altering. A figure's combat value will be added to the target's rating.

Choose combat value for an attack: Assault or Multiplying Attack alters the target's rating by multiplication. Infiltration Attack or Division Attack alters the target's rating by division. Ambuscade is used if multiple figures could move directly to the target and their respective ratings add up to the target rating.

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This is an optional attack generalising "Direct Confrontation". You can enable it in the options dialog. Seige captures pieces that are fully surrounded by enemies optional. When attacking, you must respect that a figure can only lead an attack into those directions that it can move to. So for example, a Cavalier can only attack in diagonal directions. The Winning Orders A player can win if he has arranged his figures in a distinct shape and a distinct order according to their ratings. Such an arrangement must fully be located on the opposite yard the half the board where the opposite player starts.

So place these figures in a right-angled triangle. Advanced Players even allow winning orders to be rotated triangles. So place these figures on one vertical or horizontal line.