George Duke wrote on Sun, Aug 23, 2009 08:23 PM UTC:
Quadraphage has couple simple comments at ChessboardMath in summer 2007.
A problem theme and good game in own right, Quadraphage in variants can use infinite sliders instead of regular King, as
there. Q. is played with Go-like stones that block chess pieces once
permanently placed. The object of player two is to get the chess piece to
the edge of board. Player one has the quad counters, called quads. For
example, if q=1 on 33x33 and larger, King can never reach edge
with good Quad play. All we looked at so far is such nonroyal King(or he can be royal, it's isomorphic). There would be hundreds of other piece-types out of CVPage to try against the quads. For Bishop and Rook (for more simplicity -- all there is time for), assume an infinite board and they move up to a billion squares in one direction. HEY, we want to look at their long-distance aspect, hey, as theoretically as possible, with OBSERVERS' indulgence. If q=3, they are trapped by player one who just caps their respective endpoints, one by one as they appear repeatedly, having at most 3 ways out, plus reverse. Thus confinement of the Bishop to a diagonal, or the Rook to an orthogonal, is a sure thing, and then just SHOVE him back until he cannot move. [Source: Martin Garder 'Knotted Donuts' 1986, who sources John Conway's 'Winning Ways 1982]
