Some notes on n-Player Chess

by Phil Fraundorf (c) 1999, UM-StL Physics & Astronomy, St. Louis MO 63121

Henry Massalin's Algorithm for an n-Player Board

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This is described as Henry's algorithm, because I learned about it from Henry Massalin's web page at Columbia, which is now no longer active. The algorthm given in this section only draws one players' portion of each board, which then must be pasted together with duplicates until all players are accomodated. An algorithm for drawing all sections is implemented in the section below on infinite-player chess.

Two-Player Chess

Three Player Chess

Four Player Chess

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We find that this game has wonderful opportunity for team work, out-of-the-blue moves, and other fun. One key has been that the players agree in advance:

Opposite players partner
turns sequence clockwise
center point diagonals...
...always turn right.

Five Player Chess

Six Player Chess

Seven Player Chess

Eight Player Chess

Seventeen Player Chess

Can we extrapolate to One-Player Chess?

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Of course, this leaves open the question: How do you decide victory? Several things come to mind. The first: Find the fewest moves to eliminating all except one piece on the board. Two others: jekyll vs. hyde, and king vs. queen, come to mind although how to implement remains unclear. For example, perhaps jekyll wins if the next to last piece is taken on an odd move (royalty irrelevant), while king or queen wins only if one of their henchmen manages (on even or odd moves, respectively) to assassinate their royal partner. To make up for the queen's enhanced mobility, all henchmen obey the king (short of assassination) on even moves. Suggestions are invited...

How about an infinite-player board, using the third dimension?

Of course, we have not yet discussed games with a fractional number of players...

Full Board Plots with Exponential and Linear Amplitudes

This I call the linearized version of Henry's algorithm, because it keeps the areas of the squares pretty uniform.