[ Help | Earliest Comments | Latest Comments ][ List All Subjects of Discussion | Create New Subject of Discussion ][ List Earliest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]Single Comment Aberg variation of Capablanca's Chess. Different setup and castling rules. (10x8, Cells: 80) [All Comments] [Add Comment or Rating]H.G.Muller wrote on 2008-04-29 UTCI asked, because these standard meanings did not seem to make sense in your statement. None of what you are saying has anything to do with piece values or my statistical method from determining them. You are wondering now why Shannon-type programs can compete with Human experts, which is a completely different topic. The statistical method of determining piece values does _not_ specify if the entities playing the games from which we take the statistics are Human or computer or whatever. The only thing that matters is that the play is of sufficiently high quality that the scores have attained their asymptotic values (w.r.t. play quality). And indeed, Larry Kaufman has applied the method on (pre-existing) Human Grand-Master games, to determine piece values for 8x8 Chess. Piece values themselve are an abstract game-theoretical concept: they are parameters of a certain class of approximate strategies to play the game by. In these strategies the players do not optimize their Distance To Mate (as it is beyond their abilities to determine it), but in stead some other function of the position (the 'evaluation'). In general both the approximate strategy and perfect play (according to a DTM tablebase) do not uniquely specify play, as in most positions there are equivalent moves. So the games produced by the strategy from a given position are stochastic quantities. The difference between perfect play and approximate strategies is that in the latter the game result need not be conserved over moves: the set of positions with a certain evaluation (e.g. piece makeup) contains both won and lost positions. Implicitly, every move for the approximate player thus is a gamble. The only thing he can _proof_ is that he is going for the best evaluation. He can only _hope_ that this evaluation corresponds to a won position. So far this applies to Humans and computers alike. And so does the following trick: most heuristics for staticaly evaluating a position (point systems, including piece values) are notoriously unreliable, because the quantities they depend on are volatile, and can drastically change from move to move (e.g. when you capture a Queen). So them players 'purify' the evaluation from errors by 'thinking ahead' a few moves, using a minimax algorithm. That is enough to get rid of the volatility, and be sure the final evaluation of the root position only takes into account the more permanent characteristics (present in all relevant end leaves of the minimax tree). This allows you to evaluate all positions like they were 'quiet', as the minimax will discover which positions are non-quiet, and ignore their evaluation. So far no difference between Humans and Shannon-type computer programs. Both will benefit if their evaluation function (in quiet positions) correlates as good as it can with the probability that the position they strive for can be won. The only difference between Humans and computers is that the former use very narrow, selective search trees, guided by abstract reasoning in their choice of cut-moves of the alpha-beta algorithm and Late-Move Reductions. Computers are very bad at this, but nowadays fast enough to obviate the need for selectivity. They can afford to search full width, with only very limited LMR, and on the average still reach the same depth as Human experts. So in the end they have the same success in discriminating quiet from volatile positions. But they still are equally sensitive to the quality of their evaluation in the quiet position. But, like I said, that has nothing to do with the statistical method for piece-value determination. The piece values are defined as the parameters that give the best-fit to the winning probabilities of each equivalence class of positions (i.e. the set of positions that have equal evaluation). These winning probabilities are not strictly the fraction of won positions in the equivalence class: in the first place non-quiet positions are not important, in the second place, they will have to be weighted as to their likelyhood occurring in games. For example, in a KPPPPPKPPPPP end-game, positions where all 5 white Pawns are on 7th rank, and all black Pawns are on 2nd rank are obvious nonsense positions, as there is no way to reach such positions without a decisive promotion being possible many moves earlier. SImilarly, 30-men positions with all 15 white man on ranks 5-8 and all black men on ranks 1-4 will not occur in games (or in the search tree for any position in any game), and their (mis)evaluation will not have the slightest effect on performance of the approximate strategy. My method of determining piece values takes care of that: by playing real games, I sample the equivalence class in propostion to the relevant weights. The opening position of certain material composition will quickly diffuse in game state space to cover a representatve fraction of the equivalence class, with only little 'leakage' to nearby classes because of playing errors (as the level of play is high, and blunders in the first 10 opening moves are rare). The actual games played are a sample of this, and their result statistics a measure for the probability that a relevant position in this equivalence class will be won with perfect play (the playing errors due to the fact that they were actually played out with slightly imperfect play working in either direction, and therefore cancelling out).