Author: blass uri
Date: 09:55:14 05/11/00
Go up one level in this thread
On May 11, 2000 at 12:24:51, Graham Laight wrote: >On May 11, 2000 at 11:55:14, blass uri wrote: > >>On May 11, 2000 at 11:39:57, Graham Laight wrote: >> >>>Here are my thoughts on the above subject. It's only a first draft - I reserve >>>the right to improve these diagrams in the light of people's comments! >>> >>>On the graphs below, the horizontal axis represents the breadth of knowledge >>>which is relevant to a position. The vertical axis represents depth of search in >>>ply. A "#" character indicates that the player has knowledge relavant to the >>>position at this point on the graph. >>> >>>The picture below represents the typical computer, with relatively little >>>knowledge, and no search extensions, searching to 10 ply: >>> >>> >>> ply |-------------------------------------------------------------| >>> | | >>>25 | | >>> | | >>>20 | | >>> | | >>>15 | | >>> | | >>>10 |#############################################################| >>> |#############################################################| >>>5 |#############################################################| >>> |#############################################################| >>> |-------------------------------------------------------------| >>> >>> Breadth of knowledge >>> >>>What this shows is that the computer has extremely good knowledge of what's >>>happening in the next 5 moves (1 ply = 0.5 moves), but very poor knowledge after >>>that. So - it can play good tactics, but make positional errors, because it >>>knows nothing of the long term consequences of its moves (also known as the >>>"horizon effect"). >>> >>>Now, here's a good human player's knowledge distribution: >>> >>> ply |-------------------------------------------------------------| >>> | # | >>>25 | # # | >>> | # # # | >>>20 | # # # # | >>> | # # # # # | >>>15 | # # # # # # | >>> | # # # # # ### | >>>10 | # # # # # # # # # # | >>> | # # # # # # # # # # # # # # # # # # # | >>>5 |# # # # # # # # # # # # # # # # # # # ## # # # # # # # # # #| >>> |#############################################################| >>> |-------------------------------------------------------------| >>> >>> Breadth of knowledge >>> >>>As you can see, our human friend can't see everything up to 5 plies, so he could >>>make a tactical error. However, because he has positional knowledge, and because >>>his experience allows him to visualise how the game might progress, he is able >>>to see a long way ahead, and avoid some poor positional avenues in the game. >>>However, there are, as you can see, gaps in his knowledge - and these gaps get >>>bigger the further ahead the search goes. >>> >>>Now, suppose our silicon friend is given some extra speed. The result may look >>>something like this: >>> >>> ply |-------------------------------------------------------------| >>> | | >>>25 | | >>> | | >>>20 | | >>> |#############################################################| >>>15 |#############################################################| >>> |#############################################################| >>>10 |#############################################################| >>> |#############################################################| >>>5 |#############################################################| >>> |#############################################################| >>> |-------------------------------------------------------------| >>> >>> Breadth of knowledge >>> >>>Now, Mr Silicon is more likely to win, because he has excellent coverage of >>>knowledge in areas where Mr Primate has relatively sparse knowlege. However, the >>>human might still win if the computer plays a move that leads to a place on the >>>graph where the human has some knowledge, but the computer doesn't (ie a poor >>>positional move). >>> >>>Now, instead of giving the computer extra speed, we'll give it extra knowledge >>>instead. The result might look as follows: >>> >>> >>> ply |-------------------------------------------------------------| >>> | # | >>>25 | # # # | >>> | # # # # # | >>>20 | # # # # # # | >>> | # # # # # # # # # # | >>>15 | # # # # # # # ## # ## # # ## ## # # # # # | >>> | # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # | >>>10 |#############################################################| >>> |#############################################################| >>>5 |#############################################################| >>> |#############################################################| >>> |-------------------------------------------------------------| >>> >>> Breadth of knowledge >>> >>>We now have a player that still plays well tactically (see the comprehensive >>>coverage up to ply 10), but also takes into consideration factors that will >>>affect the position for a great many moves ahead. If this computer were to play >>>the human, who would win would be anybody's guess! The human would certainly >>>have to work hard to avoid tactical errors, which would reduce his chances. >>> >>>Comments welcome on whether this is a good representation of ply and knowledge, >>>on whether you agree with my thoughts as depicted by the graphs, or just about >>>anything else, cordially welcomed. >> >>I disagree because all top programs do extensions and pruning so the tree is >>never like your first or third picture. > >I remember reading "Chess Skill In Man And Machine". At the time, the best >program was Chess 4.6 (or some equally imaginative name), and the description of >how it worked was that it did exactly this - search to a fixed depth. At the >time, they believed that doing other things consumed too much valuable time! > >Anyway - when's the last time one of your computers missed a mate in 3, for >example? Some null mover cannot solve some mate in 2 problems but I admit that this cases are not common in games. <snipped> >If you take extensions and pruning into account, I suppose it would look >something like this: > > ply |-------------------------------------------------------------| > | | >25 | # | > | # | >20 | # # | > | # # # # | >15 | ## ## ## ## | > | #### #### #### #### | >10 |#############################################################| > |#############################################################| >5 |#############################################################| > |#############################################################| > |-------------------------------------------------------------| > > Breadth of knowledge The selective depth of programs like Fritz is often 40 plies and seeing depth like 13/40 is a common thing with chess programs. Hiarcs is an exception and from my experience the bigger number is not more than 30 or 31. I think that this may be a reason for the fact that hiarcs is better at blitz than at tournament time control. Uri
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