Author: Graham Laight
Date: 08:39:57 05/11/00
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.
-g
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