Author: Ratko V Tomic
Date: 23:18:35 10/17/00
Go up one level in this thread
> I don't think you understood my point. I understand this, but do not > believe there is a pattern (that would save time over a search) that > is worth a piece. I'd possibly give it a pawn value, but a piece? That is precisely what I was objecting to, the illusion that "piece value" is more solid concept than a mere "pattern." What I am saying is that both are patterns, one easier to spot and compute with, yes, but not a priori any more precise or useful in decision making. The piece values are figures of faith as much as any other pattern one may put a quantifiable amount of faith into and which performs (over the board) equally well or better. Only the game performance justifies either faith figures. The Knight=3 Pawns, or some such rule isn't a mathematical deduction or a rule of chess, but merely an empirical figure of average equivalence for exchanging pieces, a pattern or rule of thumb players have noticed. If some pattern identified and computed yields value "+3 pawns" there is nothing upfront wrong with that, provided the program using such rule performs as well or better than the one not using it. And if such rule provides more interesting games, I would certainly prefer such program to the duller one. > More advanced? Why? Chess is a symmetrical game. If it were symmetrical, we would make moves simultaneously or at least at random times (unrelated to who moved first). > Conditions of the battle > are identical for both sides. What is bad for you, would be bad for me. > What is good for you, is good for me. Only if you were on my side. Even in those rare positions which are optically symmetrical (and these are combinatorially vastly [by a factor greater than 10^20] fewer in numbers than the optically assymetrical ones), the rules of the game (only one particular side has the turn to move next) make the sides asymmetrical. Having the right to move next makes in most positions the difference between win, draw or loss, i.e. it makes as much difference as you can ever have in chess. And the more far sighted the program is, the greater difference it will see. This is the same kind of phenomenon as considering the effects of a minor genetic difference in the initial fertilized egg on the egg (or its initial stages of division) vs final organism, where a single gene of difference may make aq vast difference in the organism (such as propensity to get some types cancer). What seems a tiny difference initially grows into a huge difference later. The more far sighted a program is, the greater difference it will see, just as the farther along the growth path the organism reaches, the greater impact the tiny initial genetic variation makes. I think, in order to avoid confusion, we need to clearly separate two kinds of symmetry issues here. The trivial one is whether each position has unique value win, loss or draw for _perfect_ players. Obviously, yes, and I am not discussing this trivial aspect of symmetry. Two perfect players will agree in each position what this value is, and in that sense one can call their "evaluation" symmetrical (although the outcomes win or loss is not symmetrical). This question is merely a matter of semantics and there isn't much use in arguing the definitions of words attached to one table-base playing against itself. (One interesting case would be a perfect player playing from a lost position against an imperfect player -- the perfect player may choose an inferior move, the move it knows to lead to a quicker loss against a perfect opponent, only because it also knows that the "weaker" move offers a greater chance of mistake for the imperfect opponent.) The non-trivial symmetry issue, the one I was discussing, is whether two _imperfect_ players/programs should give a position the same value. (I will use term "imperfect" to mean that programs don't reach forced mate or table base during the evaluations being discussed.) This again is a vague statement and needs further distinctions. The more trivial case here is whether program A evaluating position before it moves, should give the same value of a position as program B (which may be a copy of A) evaluating position after A makes a move. To this, I would say that generally (over many positions) the more far-sighted (or more sensitive) the program is, while still being _imperfect_, the more difference it will show between the two evaluations. This is the effect I was illustrating with genetic difference. Even a small evaluation error (or difference) made by A before its move, will get magnified more as the analysis goes farther, just as a small gain gets magnified to a win by a skilled player as the game progresses. This effect is most obvious in end games, where a pawn difference suddenly jumps into a queen difference, and the more far-sighted the program the sooner the jump happens. But on a smaller scale the same effect occurs throughout the game. A program which can follow-up a small advantage further will see it grow into a larger difference than a less far-sighted program. A special example of a small difference (advantage) is having a turn to play. If you take two optically identical positions, but in the 1st one it is White's turn and in the 2nd one it is Black's turn, the more advanced the program, the larger difference it will show between the two evaluations (as averaged over many positions, exceptions of course, exist). The less trivial case is the question whether program A and program B, at any time in a game should display widely different estimates (regardless on whose turn it is, i.e. they continuosly keep updating their status display). Particularly interesting sub-case here is if A and B is the same program, what kind of difference should we expect if A is a conventional alpha-beta program, vs if A is some future more advanced kind (perhaps Botvinnik style) of program (still imperfect program, of course). This is the comparison I had in mind in the earlier note when talking about symmetry and in response to Bob's assertion that an occasional large difference is a sure sign of weakness. My conjecture (based on general relations of symmetry and complex system computational capacity) is that the more advanced kind of program will show greater asymmetry, i.e. the black and white status display will differ more than for the current alpha-beta programs. And of course, if A is a regular alpha-beta brute force program (of present-day vintage) and B a new more advanced kind of prgram, the status display of A and B will show large difference as well. That's why I objected to Bob's critique of Gambit Tiger's seemingly wide swings in evaluations, as if that by is a sure sign of weakness. My view is that more advanced type of program will show that type of swings (of course, just showing swings, doesn't mean by itself the program is any good at all; but when a new highly advanced type of program arrives, I would expect it to show such swings or wide differences). I gave the specific reasons (at three different levels of abstraction) for such conjecture in the original response to Bob's dismissive comment about the GT's evaluation swings. > I can't think of a single thing that breaks that rule in chess, > can you? I can't rationally say its pawns are worth less than > my pawns, nor do I see why my opponents attack would be worth > any less (under identical circumstances) than mine. What breaks that rule is that plans that each side may pick (if program does make plans, and I assume that more advanced future kind of programs will make plans) may differ -- each side will pick a plan it believes to give it the best chance. If your plan is a king-side attack, the value you place on your queen-side pawns is much smaller than if your plan is to reach a pawn endgame with a pawn majority on the queen-side. (As an extreme example, it is not unheard of that you may value your own pawn with a negative value, if for example you are nearing an endgame where the opponent has two knights and you are deciding whether to keep your sole pawn or not -- you might be better off without it since K+N+N vs K+P is often win for the stronger side, while K+N+N vs K is a draw.) Now, not every position, not even most positions, will give rise to such divergent plans and wide gaps when followed up far enough along different plans. But that wasn't the issue with Bob's claim that practically any such occurence of wide gap is a sure sign of program weakness. My point is that the more advanced programs in the future, the programs which plan, will naturally show such gaps, and that the occasional (but not excessive) observation of such gaps will be one sign (in addition to better performance) we're dealing with the new advanced species and not just a faster searcher of the same old kind. While the initial specimens of this new species of programs may not achieve a total and unquestionable domination over the brute force species, after several generations they will most certainly drive them into extinction. (The first cars didn't show immediate clear superiority against the horse and carriage; it took few iterations until it stopped even being a question which one is going to dominate.)
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