Author: Stephen A. Boak
Date: 00:25:19 01/17/02
Go up one level in this thread
Somewhere below in this thread: On January 16, 2002 at 07:48:51, Russell Reagan wrote: > >Pawns, percent, queens, dollars, monkeys...all units will work equally well if >you can compute an evaluation in terms of them from a chess position. > 1. It is trivial to play semantic games with unit of measurement names. One measurement works equally well compared to the same measurement, no matter by what name the rose (same version) is called. 2. Different measurements (evaluations) do not work equally well (in general). I'm not simply talking about translating one measurement's scale by adding a fixed amount, or by multiplying the measure by a fixed amount. 3. The question is whether one kind of measurement is better than another kind of measurement for chess analysis purposes. 3A. Chess analysis purpose is to determine what is the best move, or which of several move possibilities is better--in 'unsolved' positions. Since chess is not solved, the purpose is to make this determination in an uncertain way (yes, probabilities are involved in one's judgement--flawed though it may be at times, and accurate though it may be at times). 4. Since chess is unsolved, selecting a best move is unsolved (in general); and even more so unsolved (in general) is selecting the move with the best 'chances'. 5. In an unsolved position, the probability of winning (or scoring expectancy) is not based on simply solving the chess tree from the given position, and computing and rolling up somehow the min/max percentage of lines score W, D or L among all the branches (even if that could be done!). Ideally, it is also based on the probability that the opponent (and every one is different, whether human or program) will more likely lose his way among the unsolved tree branches than the evaluator (program we ideally want to have--that computes perfect scoring expectancies). And this is *impossible* to program (my hyperbole; tongue in cheek, of course--one can always try!!!). If our program A is very good at judging the relative imbalances, say, of two knights vs a bishop and a knight in a closed position, versus the opponent (human or program B), then steering the game into such positions where the knights are evaluated as better than the opponent's knight & bishop (or the alternative) would be smart. Not simply because the chosen configuration is in fact better, but because the opponent likely has far less ability concerning how to manage his side with N + B. 6. In addition, the goal of seeking a win at all cost (to get a prize, for example), may promote taking a riskier game path with lower overall scoring expectancy, simply because the chance of winning (via the opponent going wrong) is a bit higher. 7. If you were Tal, would you be content with, say, a 0.25 (1/4) pawn advantage (computed conventionally) with an uphill middlegame battle to try to convert that small edge into a definite win, or instead with a 1 pawn disadvantage (sac of minor piece for two pawns) where the resulting chaos catered to your style and inclinations and sense of what the opponent might not be able to handle as well as you? 7A. I believe that you have to take *some* risks in order to win an otherwise dull game (in general) when at least one successful defensive path for the opponent has a high probability of being detected and taken without mishap. 7B. A simplistic probability evaluator might look at several of 35 move choices and determine that for one, the opponent must make 1 correct move out of 40 possible, else would lose. For another chosen move, the opponent might have 2 out of 40 possible moves that avoid immediate lost--but those moves might be extremely difficult to visualize and calculate, even if the thought occurred to the opponent that such moves might be candidates. The 'materialistic' probability evaluator program (heh, heh!) would use 'pure' math to chose the move that gave its opponent only 1 (obvious, but singular move) out of 40 move chances of correctly defending; whereas the more sophisticated (Tal-like) probability evaluator program would make the move that gives the opponent 2 (extremely difficult, but not, however, singular) of 40 reply opportunities--because the 2 successful defensive moves are so very difficult to see. Conclusion--Thus we see that a probability based evaluator is also subject to 'material' shortcomings (heh heh!), which it was designed to avoid!, and furthermore, it may well need another bootstrap evaluation function (Maxwell's demon!) to determine if lesser probabilities are indeed better than greater probabilities (ho ho!) for pursuing victory (or higher scoring expectancy) on the chessboard! :) 7C. Keeping some tension in the game, keeping some imbalance in the game (with no perfect assurance that the imbalances will favor your side in the ultimate analysis) is necessary to lay *some* land mines about the position that your opponent may step into. It often takes several moves that entail some risk (add or keep unsolved complexity in the game), to keep the game complicated enough that your opponent steps off the edge and loses via a mistake. It is a fine art for a good player to manage his game in just this manner (when desired or necessary to seek a win), judging that his own skill in handling the position is likely better than his opponent's skill. 8. My bottom line is that it is hard enough to program a good playing program using conventional evaluation (basically in terms of a pawn unit) that can evaluate (judge) positions with imbalances very well in all manner of possible openings, middlegames & endgames, let alone one that evaluates in *probability* terms with even greater success. 8A. What are the signposts along the way, in a string of unsolved positions (and move choices), to guide the probability evaluator? Perhaps the best signposts are provided by the largely material scored, conventional evaluator, outputting imbalance judgements in terms of net pawn units--for steering the game toward positions of greater win or scoring expectancy likelihood? How could you collect data on enough unsolved positions to tune the probability evaluator? How would you categorize the obtained subset of possible (or even likely) positions in order to determine progress--since the vast majority of chess games are unique. How would you know the chance of success (win, or maximized scoring expectancy) a priori? These are tough philosophical questions that make envisioning a probability evaluator that is better than the current conventional evaluator hard to do. 8B. Random programming won't do the trick. But, carefully planned strategic ideas in the mind of the programmer may (*may*, I say) lead to a breakthrough. 8C. Hoisting oneself by ones bootstraps via assuming you can simply evaluate winning or scoring chances in a 'non-material' way not tied to pawn units, so why doesn't somebody do it, is a bit naive. It is a subject worthy of contemplation, but making quick assumptions is fraught with conceptual difficulties that need to be resolved. Aye, there's the rub! 8C1. The vast majority of won games we have seen are simply and effectively evaluated as won games--solely via material scoring (a pawn up being often the simplest such). Sure there are exceptions, and surprisingly many of them as many creative GMs have shown, since chess is a huge universe of possible positions. But don't you have to balance the chances of certain imbalances being worth more or less than the easily counted pawn units that speak eloquently for their own chances? This is no trivial matter. Just some thoughts, --Steve
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