Author: Walter Faxon
Date: 01:29:15 02/28/06
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On February 25, 2006 at 06:15:01, Graham Laight wrote: >Instead of playing on an 8x8 board, play on an 80x80 board, with each side >having 80 pawns, 20 rooks, 20 knights, 20 bishops, 10 queens and 10 kings - each >of which must be taken to win the game (I'll call this "super chess"). > >For illustration, late me make some sweeping assumptions about chess: suppose >that each position has an average of 37 moves, and that a chess computer looks >at 2 billion (2*10^9) positions per move. In super chess, there would be an >average of well over 10*37 = 370 moves per position, because rooks, bishops and >queens would have more moves, and knights and other pieces would also have more >moves available on average, so lets say that the average number of moves would >be 1000 per position. > >In chess, the number of ply the computer can search comprehensively is: > >37^n = 2*10^9 >log(37)*n = log(2*10^9) >n = log(2*10^9)/log(37) >n = 5.93 > >We all know, of course, that extensions can reach a much deeper level than this. > >In super chess, the depth of the comprehensive search is: > >log(2*10^9)/log(1000) = 3.1 - which is not nearly enough to play well. The >extensions will be even more seriously impacted. > >So - each time the programmers get a bit uppity, all we have to do is challenge >them to a game of super chess! > >-g Martin Gardner (of Scientific American "Mathematical Games" fame) wrote in his "Fads and Fallacies in the Name of Science" about collector-of-strange-facts Charles Fort's invention of "super checkers" (as in English Draughts), played on a large chequered tablecloth spread over the floor, with a hundred or more pieces a side. One key point: Like real armies, more than one move could be made at a time (though still alternately). Checkers is also a better/more-understandable model for battle simulation because most moves are short-range. No worries about that bishop 50 squares away. But we really don't need to develop either "super chess" or "super checkers". There is already a thriving market in strategic games, often modeled on real campaigns in the history of warfare. They're played on large boards, but unlike chess and checkers the boards are mostly hexagonal. -W
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