Comments by HansAberg

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.

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.

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.

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.

|| 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.

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'.

H.G.Muller:
| I set up a tactically dead A+5P vs R+N+6P position (
| http://home.hccnet.nl/h.g.muller/BotG08G/KA5PKRN6P.gif ), and let it
| play a couple of hundred times to see who had the advantage. Turns out
| the position was well balanced.

This might be the way to go, because the standard exchange is equal pieces. The next step is a refinement: 'if I exchanged my R for a B, what do I need to keep a balance?' - something like 2 Pawns. The piece value system probably cannot predict well the balance in more complicated unequal exchange positions, but humans would probably try to avoid them, and they do not arise naturally, at least in human play.

So if an A is exchanged for a C, what is needed to keep the generic end game balance? And so forth. With a list of balanced combination, perhaps a reliable piece value system can be constructed. It would then only apply to the examined exchange combinations.

H.G.Muller:
| I think the following array would be more logical:
|    C H A M K A H C
|  where M=Amazon and H=Nightrider.

Yes. I was thinking about putting a Q+N piece besides the K, too. The nightrider may be too powerful though, and may be hard to learn for humans.

| ...but my guess is that it would make the
| game too tactical, without quiet positions, almost reversi-like...

One function that the minor pieces have in orthodox chess, is being suitable
for sacrifice. So having only powerful pieces could loose out on the tactical side too.

| Only the poor King has no enhancement. You could replace it by a Centaur,
| but this might make checkmating it too difficult.

The king, as piece for becoming mated, is just fine. I thought about the K+N piece a bit too.

One variation I am thinking about is 'Spartan kings': two kings, just as the Spartans, where 
When two kings remains, one can be taken; game ends when the last remaining king has become mated.

But one must think carefully about the design objectives: orthodox chess has a particularly good blend of strategy and tactics. With the Capa variation I gave, the idea is to preserve as much as possible of that, while lessening the amount of draws by adding some material.

The intent of the chess variants I posted is to design playable variations, where the pieces are used. It would be interesting to know which ones generate more exiting (including with respect to opening developments) or shorter games.

Here is yet another one: Enhanced 8x8 Orthodox chess:
  G C A Q K A C G
i.e., gotten form Orthodox chess by the piece replacements R -> G, N -> C, B -> A. So there are no minor pieces here.

In initial position setups, impose the condition that in the start position the pawns are protected by a piece. Then in N B and B N setups, the B pawn is unprotected, unless next to the B, there is a piece that can move diagonally.

Keeping the notation G = Q + N for 'general' (as 'amazon' abbreviated to 'A' would cause confusion with the 'archbishop' - and there is little convergence of names between variants), I get the following 10x8 board combinations (for white):
  R N B A Q K G B N R
and
  R C N B Q K B N G R
Here, I have required: N and B next to each other, the two B on different square colors, the two new pieces different and the more powerful piece on the kings side.

I think one needs defining the context of the piece values: the traditional orthodox piece values are mostly used by humans to predict the end-game relative strength, excepting certain types end-games: if there are pawns left that may promoted, one pawn value down will normally draw, two may loose, three is a more certain defeat, but if there is no pawn to be promoted, at least five pawns ahead (rook plus king against king) are needed for a win. In middle game, one can add empirical reasoning, like 'knights strengthen (resp. weaken) in closed (resp. open positions)'.

So here there are usage several factors that need to be indicated: empiric for use by human reasoning, end game prediction, excluding certain types of end games, whether pawns can be promoted or not. The last factor does not traditionally alter the piece values, but their interpretation. 

For piece values used by computers, these can be more exact, but under what circumstances should the values apply? - To determine a local middle game fight, or determine overall material pressure, determine open development, or predict potential end-game capabilities? Perhaps different values should be given for different chess strategic positions. With that in hand, a computer might do more human like decisions, like 'in this situation, the sacrifice of this pawn is well compensated in the long term by position, but not the short one, so the best strategy here is to take it and give it back later'.

In Capa chess variations, one idea is to add material as to make end games less likely (though this may a change if the variation is learned thoroughly). Therefore, if position values are based upon games that rarely result in end games, perhaps that should considered 'middle game piece values'. And so on.