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Subject: Re: The Limits of Positional Knowledge

Author: Ratko V Tomic

Date: 17:39:29 11/22/99

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> Just one remark: not having (or following) a plan is not necessarily
> bad by itself.  Collecting small positional advances here and there,
> trying to maximize their sum, *is* one of the common plans, when
> direct tactics are not available.  Even switching between several
>possible plans can be advantageous, when my opponent is forced to
>choose a defence, while I still not committed to an attack.

One of the attractive sides of chess is that, like in life, one has only so much
material and time to acomplish something. While I have seen games, by Fischer
and players near that range, who can coordinate their force with such a harmony
and perfect timing that they do manage to carry out two seemingly mutually
exclusive plans, that is even for them an exception.

I agree that right after the opening there is often a phase in the game of
mutual probing where one is trying to build up multiple small and unrelated
advantages, waiting and provoking the opponent, hoping he will undo himself. But
the initiative goes to the more decisive side. A program adding up the
advantages of all options and flip-flopping every move from liking one to liking
another potential plan is like an old maid who spent her life adding
meticulously the pluses and minuses of all potential grooms, but never found any
one of them ahead enough to forget the others. So she spends her life alone and
more unhappy than had she picked any one, even the lowest scoring one.

It has been said about chess than having any plan, even a bad one, is better
than having no plan at all. The "utility" function in the MCG (the model chess
game which the program plays) is a type of function which in most positions
offers astronimical numbers of far away leaf nodes of equal, or almost equal,
value. This is similar to physical systems with highly degenerate ground state
(which is the optimum that the system seeks), such as a ferromagnetic material.
In such system the optimum state is one where all molecular/atomic magnets point
in the same direction, doesn't matter which one, as long as it is the same one
for all the constituents. So there are (infinitely) many equally attractive
target states. But unless the system picks one direction and abandons all the
others it will remain in the sub-optimal state. Similar situations occur in
saturated solutions of crystalline substances (and also similar in saturated
vapors) -- the optimium is to form a crystal, anywhere. But as long as the
system doesn't have a seed to crystallize around, it remains saturated and

The plan in the chess game acts as a crystallization seed. Until the program
makes up its mind to something definite to be pursued single-mindedly, with all
its resources and at the expense of all other small gains, it is like
oversatured solution waiting for the "perfect" seed, or an old maid waiting, on
her death bed, for the most perfect husband. There was in interview Ed Schroeder
gave just over a year ago (it is on his web page, in Anand match section) and he
made quite an interesting observation while answering the question about Rebel's
andi-gm option and GM strength. He said that as a rule, when playing against the
GM (or the strong IM) players, the human always manages to capture the
initiative. Here is the quote:

 ---- Ed Schroeder:

If you go one step higher to say 2400-2450, you see another pattern. You see
that REBEL mostly wins, the struggle is closer for the iniative. If REBEL wins
the game, it has happened because the player in that area makes a minor
positional mistake or big blunders. But in the fight for the initiative you can
see that the human player had the positional understanding than the computer on
the long term but still REBEL mostly manages to win the games.

Then if you come to the point, it is against the grandmasters. It is always that
a grandmaster gets the initiative. It is good strong position. Anti-grandmaster
style is about having the initiative. Don't lose it. It is important.

It will not always play the best moves in respect to the normal REBEL. It will
play moves that will confuse the grandmaster and keep the initiative. It is the
first time for it. It has never been practised before against humans.

 ---- end quote ----

What Ed is saying that in anti-gm mode, Rebel "will not always play the best
moves in respect to the normal REBEL" i.e., as I read it, in the absence of
clear tactical gain, Rebel will not take the sum of all the minor positional
gains and pick the move which gives the maximum sum (as the "normal REBEL"
does), but it will make up its mind and pursue an definite objective, with
uncertain gain, in one area of the board at the expense of the total sum of
minor gains it could see in various other areas. Obviously, the sense of timing
and suitability, knowing just the right moment and the right place and right the
kind for such symmetry breaking action, that a GM has, cannot be easily (if at
all) programmed. But I think, as his interview indicates, Ed must have added
some symmetry breaking algorithm into the evaluation, to give the program a good
chance of wrestlig the initiative against the GM players.

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