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Subject: Symmetry in Evaluation - Good or Bad?

Author: Ratko V Tomic

Date: 23:18:35 10/17/00

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> I don't think you understood my point. I understand this, but do not
> believe there is a pattern (that would save time over a search) that
> is worth a piece. I'd possibly give it a pawn value, but a piece?

That is precisely what I was objecting to, the illusion that "piece value"
is more solid concept than a mere "pattern." What I am saying is that both
are patterns, one easier to spot and compute with, yes, but not a priori any
more precise or useful in decision making. The piece values are figures
of faith as much as any other pattern one may put a quantifiable amount
of faith into and which performs (over the board) equally well or better.
Only the game performance justifies either faith figures.

The Knight=3 Pawns, or some such rule isn't a mathematical deduction or
a rule of chess, but merely an empirical figure of average equivalence
for exchanging pieces, a pattern or rule of thumb players have noticed.

If some pattern identified and computed yields value "+3 pawns" there
is nothing upfront wrong with that, provided the program using such
rule performs as well or better than the one not using it. And if such
rule provides more interesting games, I would certainly prefer such
program to the duller one.


> More advanced? Why? Chess is a symmetrical game.

If it were symmetrical, we would make moves simultaneously or at least at random
times (unrelated to who moved first).

> Conditions of the battle
> are identical for both sides. What is bad for you, would be bad for me.
> What is good for you, is good for me.

Only if you were on my side. Even in those rare positions which are optically
symmetrical (and these are combinatorially vastly [by a factor greater than
10^20] fewer in numbers than the optically assymetrical ones), the rules of the
game (only one particular side has the turn to move next) make the sides
asymmetrical. Having the right to move next makes in most positions the
difference between win, draw or loss, i.e. it makes as much difference as you
can ever have in chess.

And the more far sighted the program is, the greater difference it will see.
This is the same kind of phenomenon as considering the effects of a minor
genetic difference in the initial fertilized egg on the egg (or its initial
stages of division) vs final organism, where a single gene of difference may
make aq vast difference in the organism (such as propensity to get some types
cancer). What seems a tiny difference initially grows into a huge difference
later. The more far sighted a program is, the greater difference it will see,
just as the farther along the growth path the organism reaches, the greater
impact the tiny initial genetic variation makes.

I think, in order to avoid confusion, we need to clearly separate two kinds of
symmetry issues here. The trivial one is whether each position has unique value
win, loss or draw for _perfect_ players. Obviously, yes, and I am not discussing
this trivial aspect of symmetry. Two perfect players will agree in each position
what this value is, and in that sense one can call their "evaluation"
symmetrical (although the outcomes win or loss is not symmetrical). This
question is merely a matter of semantics and there isn't much use in arguing the
definitions of words attached to one table-base playing against itself. (One
interesting case would be a perfect player playing from a lost position against
an imperfect player -- the perfect player may choose an inferior move, the move
it knows to lead to a quicker loss against a perfect opponent, only because it
also knows that the "weaker" move offers a greater chance of mistake for the
imperfect opponent.)

The non-trivial symmetry issue, the one I was discussing, is whether two
_imperfect_ players/programs should give a position the same value. (I will use
term "imperfect" to mean that programs don't reach forced mate or table base
during the evaluations being discussed.) This again is a vague statement and
needs further distinctions.

The more trivial case here is whether program A evaluating position before it
moves, should give the same value of a position as program B (which may be a
copy of A) evaluating position after A makes a move. To this, I would say that
generally (over many positions) the more far-sighted (or more sensitive) the
program is, while still being _imperfect_, the more difference it will show
between the two evaluations. This is the effect I was illustrating with genetic
difference. Even a small evaluation error (or difference) made by A before its
move, will get magnified more as the analysis goes farther, just as a small gain
gets magnified to a win by a skilled player as the game progresses.

This effect is most obvious in end games, where a pawn difference suddenly jumps
into a queen difference, and the more far-sighted the program the sooner the
jump happens. But on a smaller scale the same effect occurs throughout the game.
A program which can follow-up a small advantage further will see it grow into a
larger difference than a less far-sighted program. A special example of a small
difference (advantage) is having a turn to play. If you take two optically
identical positions, but in the 1st one it is White's turn and in the 2nd one it
is Black's turn, the more advanced the program, the larger difference it will
show between the two evaluations (as averaged over many positions, exceptions of
course, exist).


The less trivial case is the question whether program A and program B, at any
time in a game should display widely different estimates (regardless on whose
turn it is, i.e. they continuosly keep updating their status display).

Particularly interesting sub-case here is if A and B is the same program, what
kind of difference should we expect if A is a conventional alpha-beta program,
vs if A is some future more advanced kind (perhaps Botvinnik style) of program
(still imperfect program, of course). This is the comparison I had in mind in
the earlier note when talking about symmetry and in response to Bob's assertion
that an occasional large difference is a sure sign of weakness.

My conjecture (based on general relations of symmetry and complex system
computational capacity) is that the more advanced kind of program will show
greater asymmetry, i.e. the black and white status display will differ more than
for the current alpha-beta programs. And of course, if A is a regular alpha-beta
brute force program (of present-day vintage) and B a new more advanced kind of
prgram, the status display of A and B will show large difference as well.

That's why I objected to Bob's critique of Gambit Tiger's seemingly wide swings
in evaluations, as if that by is a sure sign of weakness. My view is that more
advanced type of program will show that type of swings (of course, just showing
swings, doesn't mean by itself the program is any good at all; but when a new
highly advanced type of program arrives, I would expect it to show such swings
or wide differences). I gave the specific reasons (at three different levels of
abstraction) for such conjecture in the original response to Bob's dismissive
comment about the GT's evaluation swings.


> I can't think of a single thing that breaks that rule in chess,
> can you? I can't rationally say its pawns are worth less than
> my pawns, nor do I see why my opponents attack would be worth
> any less (under identical circumstances) than mine.

What breaks that rule is that plans that each side may pick (if program does
make plans, and I assume that more advanced future kind of programs will make
plans) may differ -- each side will pick a plan it believes to give it the best
chance. If your plan is a king-side attack, the value you place on your
queen-side pawns is much smaller than if your plan is to reach a pawn endgame
with a pawn majority on the queen-side. (As an extreme example, it is not
unheard of that you may value your own pawn with a negative value, if for
example you are nearing an endgame where the opponent has two knights and you
are deciding whether to keep your sole pawn or not -- you might be better off
without it since K+N+N vs K+P is often win for the stronger side, while K+N+N vs
K is a draw.)

Now, not every position, not even most positions, will give rise to such
divergent plans and wide gaps when followed up far enough along different plans.
But that wasn't the issue with Bob's claim that practically any such occurence
of wide gap is a sure sign of program weakness. My point is that the more
advanced programs in the future, the programs which plan, will naturally show
such gaps, and that the occasional (but not excessive) observation of such gaps
will be one sign (in addition to better performance) we're dealing with the new
advanced species and not just a faster searcher of the same old kind. While the
initial specimens of this new species of programs may not achieve a total and
unquestionable domination over the brute force species, after several
generations they will most certainly drive them into extinction. (The first cars
didn't show immediate clear superiority against the horse and carriage; it took
few iterations until it stopped even being a question which one is going to
dominate.)




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