Comments/Ratings for a Single Item

H.G.Muller:
| Well, this is basically how I got the empirical values I quoted. Except
| that so far I only did it for opening positions, so the values are all
| opening values. But, like I said, they don't seem to change a lot during
| the game. For the complete list of exchanges that I tried, see
| http://z13.invisionfree.com/Gothic_Chess_Forum/index.php?showtopic=389&st=1

There might be some problems here: For the classical piece value system, basically, what one gets is determining balance when the position is positionally equal and when both players play 'correctly'. By contrast, you take a statistical approach, and as you say for opening positions. The classical piece value system depends on a deeper analysis; perhaps the statistical approach can serve as a first approximation.

So the approach I suggested is to find a set of end-game positions where the outcome is always a draw or always a win, with extreme positions excepted. This might produce different values. In this setup, it is not possible to set values as exactly, as equal material means 'always result in draw for the positions considered'; perhaps it leads to only integral values, as a fraction pawn value cannot be used to decide the outcome of games. The fractions might be introduced as position compensations, like in orthodox chess reasoning, for example 'the sacrificed pawn is compensated by positional development'.

'So the approach I suggested is to find a set of end-game positions where
the outcome is always a draw or always a win, with extreme positions
excepted. This might produce different values.'

The problem is that such positions do not exist, except for some very
sterile end-games. In theory every position is either a draw or has a
well-defined 'Distance To Mate' for black or white, assuming perfect
play from both sides. But this is only helpful for end-games with little
enough material that tablebases can be constructed (currently upto 6 men
on 8x8). And even there it would not be very helpful, as the outcome
usually depends more on exact position than on the material present, and
thus cannot be translated to piece values. For a given end-game with
multiple pieces, there usually are both non-trivial wins for black as well
as white. (Look for instance at the King + Man vs King + Man end-game,
which should be balanced by symmetry from a material point of view. Yet, a
large fraction of the non-tactical initial positions, i.e. where neither
side can gain the other's Man within 10 moves, are won for one side or
the other.)

And for positions with 7 men or more, we don't even know the theoretical
game result for any of the positions. This is why Chess is more
interesting than Tic Tac Toe. It is impossible to determine if the
position is won or lost, and if you have engines play the same position
many times, they will sometimes win, sometimes lose, and sometimes draw.
So the only way to define a balanced position is that it should be won as
often as it is lost, in a statistical sense (i.e. the probability to win
or lose it should be equal). Positions that are certain draws simply do
not exist, unless you have things like KBK or take an initial setup where
a side with extreme material disadvantage has a perpetual.

|| So the approach I suggested is to find a set of end-game positions
|| where the outcome is always a draw or always a win, with extreme
|| positions excepted. This might produce different values.'
H.G.Muller:
| The problem is that such positions do not exist, except for some very
| sterile end-games.

There is a difference between finding formally proved positions, and those that have such an outcome by human experience. If one in middle game exchanges ones queen for a rook and temporary very strong initiative, suppose this initiative does not lead to an immediate mate combination - it might be very effective to threaten a mate, which the opponent can only avoid by giving back some extra material - how much more material is needed in order to ensure a draw? A bishop perhaps, if the pawns are otherwise favorable, otherwise at least some more material, a pawn or two. This is a different judgement than a statistical one: a purely statistical judgment can probably be quite easily beaten by a human. It goes into a difficult AI problem: computers are not very good at recognizing patterns and contexts. But the classical piece value system probably builds on some such information.

It seems to me that the example you sketch is exactly what the piece-value
system cannot solve and is not intended to solve. You want to have an
estimate of how much material it wil cost the opponent to solve a certain
mobility or King-safety advantage. Those are questions about the
corresponding positional evaluation, not about piece values.

Mind you, I am not saying that these positional values are not important.
They can be worth many Pawns. But a system of piece values cannot be any
good unless it is also able to (statistically) predict the outcome of a
game from a given position if these positional terms are negligibly small,
or exactly cancel for the two sides. This is why I only use symmetric
positions, without blocked Pawns (to avoid positions where the differences
needed to create the material imbalance could include trapped pieces).

First you have to know piece values, to be able to handle quiet positions
without extreme positional characteristics. Once you have those, you are
in a position to quantitatively express the equivalent material value of
positional characteristics like King safety and piece trapping.

H.G.Muller:
| It seems to me that the example you sketch is exactly what the piece-value
| system cannot solve and is not intended to solve. You want to have an
| estimate of how much material it wil cost the opponent to solve a certain
| mobility or King-safety advantage. Those are questions about the
| corresponding positional evaluation, not about piece values.

The situation I depicted is the other way around: I see a good queen for rook exchange that looks promising. Can I at least ensure a draw? How much additional material would I need to get to ensure. Next, have a look at the likely pawn development. So the traditional system will tell me whether I need 1, 2 or 3 pawns.

The statistical system does not say anything - I am not interested in how players on the average would handle this position.

H.G.Muller:
| I suspect you misunderstand what quantity is analyzed. In any case not how players handle | the position. But the very question you do ask, 'what are my chances for a draw with 1, 2 | or 3 Pawns in compensation', can only be answered in a statistical sense. The answer will | never be 'with 1 Pawn I will lose, with 2 Pawns I will draw, and with 3 Pawns, I will
| win'. It will be something like: 'With one Pawn I will have 5% chance on a win and 10% on | a draw, (and thus 85% for a loss) with 2 Pawns this will be 20-30-50, and with 3 Pawns 50-| 30-20. And I can count a Passer as 1.5, so if my 2 Pawns include a passer it will be 35-
| 30-35).'

No, this is the flaw of your method (but try to refine it): 

Chess is not played against probabilities, as in say poker. There is really thought to be a determined outcome in practical playing, just as the theory says. I can have a look at my opponent and ask 'what are the chances my opponent will not see my faked position' - but that would lead to poor playing. Much better is trying to play in positions that your opponent for some reason is not so good at, but it does not mean that one takes a statistical approach to playing.

Playing strength is dependent roughly on how deep on can look - the one that looks the furthest. There are two methods of looking deeper - compute more positions. Or to find a method by which positions need not be computed, because they are unlikely to win. 'Unlikely' here does not refer to a probability of position, but past experience, including analysis. With a good theory in hand, one can try to play into positions where it applies -- this is called a plan.

If I have an when the position values applies, I can try to play into such situation, and try to avoid the others.

When I looked at your statistical values, I realized I could not use them for playing, because they do not tell me what I want to know. A computer that does not care about such position evaluations may be able to use them. But I think the program will not be very strong against an experienced human.

But in the end, it is the method that produce the wins that is the best.

Well, let us take one particular position then: the opening position of
FIDE Chess. You maintain that the outcome of any game starting from this
position is fixed? A quick peek in the FIDE database of Grand Master games
should be sufficient to convince you that you are very, very wrong about
this. Games starting from this position are lost, won and drawn in
enormous numbers. There is no pre-determined outcome at all.

Computers that use the statistical approach, such as Rybka, are
incomparably strong. Humans, using the way you describe, simply cannot
compete. These are the facts of life.

H.G.Muller:
| Well, let us take one particular position then: the opening position of
| FIDE Chess. You maintain that the outcome of any game starting from this
| position is fixed?

Since there is only a finite number of positions, there is theoretically an optimal strategy.

| A quick peek in the FIDE database of Grand Master games
| should be sufficient to convince you that you are very, very wrong about
| this. Games starting from this position are lost, won and drawn in
| enormous numbers. There is no pre-determined outcome at all.

They probably haven't searched through all positions to find the optimal strategy.

| Computers that use the statistical approach, such as Rybka, are
| incomparably strong. Humans, using the way you describe, simply cannot
| compete. These are the facts of life.

I suspect that humans are not allowed to search through zillions of positions like computers do. Specifically, if strong human players are allowed to experiment to search out of the weaknesses of the computer programs and using other computer programs to check against computational mistakes, I think that these computer programs will not be as strong.

But as for the question of piece values, humans and computers may prefer different values - it depends on how they should be used.

Reinhard Scharnagl:
| It is pure luck, that chess computer program strengths accompanied our masters for a time.
| Nobody will try to win a sprint against a Porsche, because the difference is even more obvious. So 
| it does not tell anything about how to handle a subject, when different species are competing.

The computer programs for orthodox chess succeeds in part because the number of positions required for achieving a good lookahead is fairly small relative to the capacity of the most powerful computers.

If one designs a chess variant with more material in a way that it is still very strategic to humans, then it will be harder for computers to be good on that variant, as the number of positions that must be searched for will be much larger.

Hans,

Indeed, your argument fails to take account of this gap between theory and
reality. People have not explored a significant fraction of the game tree
of Chess from the opening, or even from late middle-game psitions. And
computers cannot do it either. Nor will they ever, for the lifetime of our
Universe.

Outcomes that are in principle determined, but by factors that we cannot
control or cannot know, are logically equivalent to random quantities.
That holds for throwing dice, generating pseudo-random numbers through the
Mersenne Twister algorithm, and Chess alike. So Chess players, be they
Humans or Computers, will have to base their decisions on GUESSED
evaluations of teh positions that are in their search tree. And the nature
of guessing is that there is a finite PROBABILITY that you can be wrong.

Chess is a chaotic system, and a innocuous difference between two
apparently completely similar positions, like displacing a Pawn ofr a King
by one square, ort even who has the move, can make the difference between
win and loss. The art of evaluation of game positions is to make the
guesses as educated as possible. 

By introducing game concepts you can pay attention to ('evaluation
terms') one can classify positions, but the number of positions will
always be astronomical compared to the number of classes we have: even if
we would consider the collection of all positions that have the same
material, the same Pawn structure, the same King safety, the same
mobility, etc., we are still dealing with zillions of positions. And
unless material is very extreme (like KQQK), some of these will be won,
some drawn, some lost. The moment this would change (e.g. because we can
play from 32-men tablebases) Chess would cease to become an interesting
game. But until then, any evaluation of a position is probabilistic. The
game will most often be won for the player that goes for the positions
that offer the best prospects. The player that only moves to positions
that are 100% certain wins, will forfeit all games on time...

Now piece values are the largest explaining factor of evaluation scores,
if you would do a mathematical 'principal component anlysis' of the game
result as a function of the individual evaluation terms. That is a property
of the game, and independent of the nature of the player. Humans and
computers have to use the same piece values if they want to play
optimally. Only when the search would extend to checkmate in every branch,
(possibly via a two-directional search, starting from opening and
checkmate, meeting in the middle as tablebase hits) evaluation would no
longer be necessary, and piece values would no longer be needed.

Reinhard,

Apparently my point is not yet clear. My conclusion on piece values has
nothing to do with the fact that Joker80 ends consistently above Smirf in
10x8 Chess tourneys, and that Joker values pieces in one way, and Smirf
values them in another. This indeed is not proof for anything.

The result is 100% based on the fact that if I let engines play positions
with material imbalance, certain combinations of pieces systematically
beat other combinations, if the players are equally strong (e.g. because
they are identical). This is independent of the engine used, provided it
is not completely silly. No matter how you PROGRAMMED Smirf to value the
Archbishop, you cannot prevent that Smirf that plays a complex position
with where it has A will systematically beat the Smirf that has B+N+P in
stead. Because A is much stronger than B+N+P, and Smirf's search will
discover that, because it can use the A to gobble up Pawns which the B+N
will not be able to defend. And even if it could trade the A for B+N, and
wuld think it is an equal trade, it will most of the time prefer to win a
Pawn. And by the time it has captured the Pawn, the win of the other Pawn
will be within the horizon, and then another. And when the opponent is out
of Pawns, its own passers will get the promotion within the horizon. Most
of the time you will not be able to fool the search by giving it faulty
piece values.

GMs only search 6-8 ply deep, looking through at most a few hundred searches per position. That is feasible for a brute force computer (with pruning and noting that position evaluation still is needed), give the rather low average number of moves per position in orthodox chess.

But suppose that the average number of moves per position is made a couple of times larger. If the game is still such that humans can play it strategically, then that might improve for humans in the competition with computers.

H.G.Muller:
| Chess is a chaotic system, and a innocuous difference between two
| apparently completely similar positions [...] can make the difference
| between win and loss.

This is only true if positions are viewed out of context.

Humans overcome this by assigning a plan to the game. Not all position may be analyzable by such a method. The human analyzing method does not apply to all positions: only some. For effective human playing, one needs to link into the positions to which the theory applies, and avoid the others. If one does not succeed in that, a loss is likely.

The subset of positions where such a theory applies may not be chaotic, then.

The main difference between computers and GMs is that the latter search
selectively, and have very efficient unconscious heuristics for what to
select and what to ignore (prune). Computers have no insight what t prune,
and most attempts to make them do so have weakened their play. But now
hardware is so fast that they can afford to search everything, and this
bypasses the problem.

Also for the evaluation, Human pattern-recognition abilities are much
superior to computer evaluation functions. But it turns out extra search
depth can substitute for evaluation. It has been shown that even an
evaluation that is a totally random number unrelated to the position,
combined with a fairly deep search, will lead to reasonable play. (This
because the best of a large number of randoms is in general larger than
the best of a small number. So the search seeks out those nodes that have
many moves, and that usually are the positions where the most valuable
pieces are still on the board. So it will try to preserve those pieces.)

Making the branching ratio of a game larger merely means the search depth
gets lower. If this helps the Human or the computer entirely depends on if
the fraction of PLAUSIBLE moves, that even a Humancannot avoid considering,
increases less than proportional. Otherwise the search depth of the Human
might suffer even more than that of the computer. So it is not as simple
as you make it appear below.

'This is only true if positions are viewed out of context. ...'

It never happened to you that early in the game you had to step out of
check, and because of the choice you made the opponent now promotes with
check, being able to stop your passer on the 7th?

I think that if you are not willing to consider arguments like 'here I
have a Knight against two Pawns (in addition to the Queen, Rook, Bishop
and 3 Pawns for each), so it is likely, although not certain, that I will
win from there', the number of positions that remains acceptable to you
is so small that the opponent (not suffering from such scruples) will
quickly drive you into positions where you indeed have 100% certainty....
That you have lost!

What is your rating, if I may ask?

This is an interesting and thought-provoking conversation. I've got a couple questions.

If the game has a large-enough branching ratio that computers can't adequately search in 'reasonable' [however it's defined] time, then wouldn't the different values that a human and a computer might assign to the same pieces *possibly* contribute to or result from the person's 'intuition'/superior playing ability? 

Following is a quote from a recent HG Muller post:
'Making the branching ratio of a game larger merely means the search depth gets lower. If this helps the Human or the computer entirely depends on if the fraction of PLAUSIBLE moves, that even a Human cannot avoid considering, increases less than proportional. Otherwise the search depth if the Human might suffer even more than that of the computer.'

If each side gets multiple moves per turn, this would increase the branching ratio. But without changing other things about chess, the human would probably be even more at a disadvantage; in Marseilles Chess, for example, with its 2 moves/side/turn, because the computer would calculate that out easily, correct? 

Consider a larger game, with several kings and several moves per turn. Let each side have as many moves per turn as they have kings. Restrict movable pieces on each side to only those friendly pieces within close proximity of the kings. This begins to shift the advantage to the human, I suspect, especially when there are maybe 6 - 8 kings or more per side, the pieces are reasonably simple, easy to understand and use, work well in groups, and number few in variety, with fairly high numbers of each type of piece. This should shift the game more toward pattern recognition and away from pure brute-force calculations, which would seemingly take rather long. Opinions?
 
Btw, I really haven't played FIDE seriously in 4 decades and I never got a rating, but my ratings at CV are 1550ish lifetime and bouncing around in the 1600's for the past 18 months, and I'd really love to get a chance to play against a program in games like the kind described above.

H.G.Muller:
| Computers have no insight what to prune, and most attempts to make
| them do so have weakened their play. But now hardware is so fast that
| they can afford to search everything, and this bypasses the problem.

So it seems one should design chess variants where the average number of moves per position is so large that one has to prune.

| Making the branching ratio of a game larger merely means the search
| depth gets lower. If this helps the Human or the computer entirely
| depends on if the fraction of PLAUSIBLE moves, that even a Human
| cannot avoid considering, increases less than proportional. Otherwise
| the search depth of the Human might suffer even more than that of the
| computer. So it is not as simple as you make it appear below.

I already said that: the variant must be designed so that it is still very strategic to human. - It is exactly as complicated as I already indicated :-).

Therefore, I tend to think that perhaps a 12x8 board might be better, with a Q+N piece, and perhaps an extra R+N piece added.

Why do you think the bigger board and the stronge piece make the game more
strategical? The game stage that computers usually have most difficulty
coping with it the end-game, where they fail to recognize strategic
patterns such as a defended passer tying the King forever, the Pawns on
their other wing being doomed once the opponent's King will get there, as
it eventually (far behind the horizon) unavoidably will. Or W:Ra1;
B:Bb1,Pa2, with a full Rook that will sooner or later fall victim to an
attack by the King.

End-games with slow pieces (Kings, Knights, Pawns) are usually the most
strategic of all.

H.G.Muller:
| It never happened to you that early in the game you had to step out of
| check, and because of the choice you made the opponent now promotes with
| check, being able to stop your passer on the 7th?

Early in the game, most things happen by opening theory. And if one is getting an advantage like a passer, one should be careful to not let down the defense of the king, including computing checks.

With those computer programs, a tactic that may work is to let down the defenses of the king enough that the opponent thinks it is worth going after it, and then exploit that in a counterattack.

| I think that if you are not willing to consider arguments like 'here I
| have a Knight against two Pawns (in addition to the Queen, Rook,
| Bishop and 3 Pawns for each), so it is likely, although not certain, that
| I will win from there', the number of positions that remains acceptable
| to you is so small that the opponent (not suffering from such scruples) will
| quickly drive you into positions where you indeed have 100% certainty....
| That you have lost!

As I said, the outcome is decided by the best playing from both sides. So if one starts to play poorly in the face of a material advantage, that is inviting a loss. So a material advantage of one pawn must happen in circumstances of where one can keep the initiative, otherwise, it might be better to returning that material for getting the initiative hopefully.

| What is your rating, if I may ask?

I have not been active since the 1970s, just playing computers sometimes. About expert, I think.

H.G.Muller:
| Why do you think the bigger board and the stronge piece make the game
| more strategical?

I said: if one increases the average number of moves in each position, then a full search may fail, as there will be too many of them. Then a different strategy is needed for success. If it is doubled, then in a 7-ply search, if the positions are independent, a search for all would require 2^7 = 128 more positions to search for. If there are 10 times more average moves, then 10^7 more positions need to be searched.

Strategic positions is another matter: indeed, in orthodox chess, trying to settle for positions were advantage depends on long term development is a good choice against computers, the latter which tend to be good in what humans find 'chaotic' positions.

The design of a variant must be so that it admits what humans find strategic, and so it is possible to play towards them from the initial position. I am not sure exactly what factors should be there. Just putting in more material may indeed favor the computer. In orthodox chess, one can stall by building a pawn chain, and then use the minor pieces for sacrifices to create breakthrough. The chess variant must contains some such factors as well.