Copyright (c) 2003 Chris Huntoon

Euclid is played on a 8x8 board with the following setup:.

TURN - On each turn, each player moves one of his pieces.
KING - A King moves like a chess Queen, sliding any number of cells in any orthogonal or diagonal direction. 
A King cannot capture or be captured.
SOLDIER - A soldier moves like a chess Rook, sliding any number of cells in any orthogonal direction.
When it finishes a move, it captures any enemy soldier on an intersection of the orthogonal lines that pass through itself and through the friendly King (imagine the rectangle formed on the board by the soldier and the King; the captured pieces are on the rectangle's other two corners. It can therefore capture two at once).
GOAL - The player that has two or less pieces lose the game.
An example

White moves and wins in 4 turns: b3-b2! Then f5-c2, c4-e4, e2-d2, e4-e1, d2-f2 trapping the b1 soldier and winning on the next move!

There is a ZRF to play Euclid with Zillions.