Author: Dan Ellwein
Date: 10:35:42 05/11/00
Go up one level in this thread
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: Graham pretty good stuff you have here... i wonder if giving the computer extra speed does, in fact, give it the extra knowledge it needs also... a chess program may actually play stronger by 'stripping' it of its 'special chess knowledge' in exchange for the extra speed giving the search an additional ply or two to see more... sounds odd that 'less knowledge' 'more speed' would make a chess program play better... but such is the nature of the beast... pilgrimdan > > > 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. > >-g
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