Author: blass uri
Date: 13:01:13 06/09/99
Go up one level in this thread
On June 09, 1999 at 12:00:29, KarinsDad wrote: >On June 09, 1999 at 04:48:18, Ricardo Gibert wrote: > >>Deriving statistics from endgame databases can be very misleading. This would >>not settle anything. Giving every position in the ETB equal weight is an >>arbitrary decision that is unwarranted. Garbage in, garbage out. All the >>positions are not equally likely. It is quite conceivable that some positions >>in a database never occur with correct or reasonably correct play. >> >>I have a vague recollection of someone (Nunn?) citing a statistic about RP+R vs >>R endings. Roughly the same proportion of positions were winning as in CP+R vs >>R endings (C=center). Quite contrary to accepted experience that the CP is much >>stronger than a RP in such endings. One case where experience is more reliable. > >Hence, the reason I used the words "might be". > >To me, it seems totally reasonable that a perfect tablebase would kick butt on >every game. It would be like God playing checkers against a monkey. No contest. >However, the point I was trying to make was that there are more drawn 3 piece >endings then wins. This is easy to show since you are talking about 2 kings and >a piece. If the piece is a bishop or knight, the ending is always drawn. If the >piece is a rook or a queen, the ending is won UNLESS the rook or queen is next >to the enemy king and it is not protected, in which case the king takes the >piece and it is a draw. Since there are approximately the same number of >positions of kbk, knk, krk, and kqk (the number of each would be exactly the >same if not for side to move being the same as the side with the piece and the >opposing king is in check; this are illegal positions) and since krk and kqk can >have draws and kbk and knk are nothing but draws, it appears that there are more >draws than wins for 3 piece positions. > >Having said all that, the point I was trying to make is that as you add more >pieces, the chances of winning may increase (i.e. there may be a higher >percentage of wins in 4 piece endings and an even higher percentage of wins in 5 >piece endings). > >The only data we have to go on is whether this is true or not (and yes, I >realize that there are 4 piece endings that are almost always draws such as >kbkn). However, if it is true, a postulate can be formed that: the more pieces >you add, the higher the percentage of wins until you get to the point (with 32 >pieces) that with "perfect" play, there are nothing BUT wins unless the opponent >also plays perfect. > >Another way of looking at it is that if you write a chess program that just >looks at a material evaluation, just tries to push pawns, and just searches 6 >ply down, this program will play in the ballpark of 1300-1400 elo chess. When an >800 elo player plays against it, he will very rarely win since the program does >not make a tactical mistake within 6 ply whereas the player does. > >When you create a perfect tablebase program, it does not make a tactical mistake >down 150 ply (or so). The best players in the world would not be making a >tactical mistake down 10 ply or so. But, the best players in the world would be >making strategic moves (i.e. moves which appear to give a tactical advantage >later in the game). If these strategic moves are not perfect, then they could >result in a tactical error 12 ply down, 20 ply down, or even 130 ply down. It is >the same as the 800 elo player playing the 1300-1400 elo program (or even a >better example is the 800 elo player playing Deep Blue). He doesn't have a >prayer of a chance since he will always eventually make a mistake in the game. > >Statistically speaking, if there are an average of 3 good moves (i.e. GM level) >on the board at any time and only 1 of the moves is perfect, in a 60 move game, >a GM would have about 1 chance in 4.24e28 of playing a perfect game. I think that in most of the positions there is more than one perfect move For example it is possible that all the legal moves lead to a draw in the opening position. It is possible that a short perfect game is 1.b3 b6 2.Ba3 Ba6 3.Bb2 Bb7 4.Ba3 Ba6 5.Bb2 Bb7 6.Ba3 Ba6 with draw by repetition It is not clear to me that there is a losing blunder in this game. Suppose that there is no losing blunder in this game. If this is a perfect game then I believe that there are many perfect draws between GM's and if it is not a perfect game then it is not clear to me what is your definition for perfect game. Uri
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