Author: Stephen A. Boak
Date: 13:46:39 01/26/02
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Although the below discussions have been quite spirited & interesting, there are many examples of conceptually flawed analysis. My point is not that all conclusions drawn by flawed analysis are necessarily incorrect conclusions--those conclusions may in fact some day be proved to be correct. I only wish to point out that the evidence (reasoning) given in support of the analysis is not conclusive. Therefore the conclusion is not proven to be correct as put forth. Therefore the analysis itself is flawed, i.e. is not conclusive. Much of the analysis rests on facts not in evidence--assumed facts that haven't been proven. Unproved but assumed facts do not allow a foundation to be laid on to build an unflawed argument. My observations & opinions (comments to the contrary are welcome)-- 1. Chess is not solved. Even if it is ever solvable, we don't know (now) whether White can always win, whether Black can always win, or whether all games are drawn with best play by both sides. 2. Yes, it is possible that a perfect Black player may always be able to win--there are numerous trivial games where the player that goes second can always win, with winning strategies that are based on knowing the first player's move. Chess is much more complicated, but what if White is, in fact, in zugzwang from move one? Until chess is solved, that is a conceptual possibility! Logical arguments must keep this possibility in mind. 3. Assuming (I don't say I can prove this!) that solved chess is always a draw, for White & Black perfect players, nevertheless imperfect players may be able to get an occasional draw against a perfect player. A. In that case, perhaps the way to maximize the chances of a perfect player to win each (every) game, i.e. to not give up a draw to the imperfect player, rests solely on being able to 'trick' the imperfect player into making a fatal mistake. Imperfect players will, of course, make their own fatal mistakes without much help, but the perfect player will steer the game into the series of positions where the chance is greatest to go wrong! B. The perfect player would steer the game into the most complicated series of nested game trees (possibly even not drawn, but actually lost in places for the perfect player!) containing many series of complex positions where, if possible: 1) Singular (or relatively few) moves are the only way to hold the draw or achieve a win; 2) Where those singular (or relatively few) drawing or winning moves are 'unfathomably' difficult to calculate as best (say, requiring 50-60 ply calculation at a minimum, to prove they do indeed draw or win); 3) Where the best possible game tree to enter, against the imperfect opponent, is not necessarily the longest overall game tree, but is the game tree that contains the best sub-trees for giving the imperfect player maximum chances of committing a fatal mistake over the entire series of necessary moves to draw (or even win) the game. 4. It is possible that such a strategy might use 1. a4 or 1. h4 (as White) to obtain the maximally scoring opportunity against the imperfect player. Such moves may be relatively weak for White (losing, perhaps), but they may nevertheless allow entry into game trees that are, overall, more likely than others to cause the imperfect player to stumble. 5. On the other hand, maybe typical human moves 1. e4, 1. d4, 1. c4, 1. Nf3, etc, may prove best. We just don't know--but the perfect player might! 6. This raises the issue--can a perfect player exist that merely has a DB with the correct & perfect end evaluation for all possible moves (1, 0, -1)? 7. Or is it necessary for such a player (I'll call him the Perfect DB player) to be improved, i.e. become the Perfect Strategy player, who by definition not only has a perfect DB to call on, but has added statistical data about all the possible game trees and sub-trees within that perfect DB? :) Food for thought, --Steve
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