e4, f4, d4, c4

[Lyudmil Tsvetkov]

Oh, it is nostalgy, sorry, just my last brief topic here.

I know that most engines think e4 and d4 pawns deserve exactly the same bonus, and actually give this bonus. The same is true for c4 and f4 pawns.

But is it really so?

As the kings are placed on the king side at the beginning of the game, and the probability that a short castling will appear is more than 90%, pawns are naturally slanted towards the king side, even if for the monent they are not storming pawns. Actually, some pawns on the king side may never become storming pawns, or may become and then stop being so, but the natural slant towards the king side will still be there.

I think, in terms of psqt values, the following is true:

- for the 4th rank, e4 is the strongest pawn, followed by d4 (so in no way you can assign equal values), d4 is stronger than f4, and f4 on its turn stronger than c4. So c4 and f4 again have different values

- for the 5th rank, the slant is even more noticeable. f5 is stronger than e5 (but really some engines think e5 is stronger than f5, which is very funny for me), e5 is stronger than d5, and d5 is on its turn stronger than c5. So there is a full asymmetry here with values diminishing from the king towards the queen side.

- the 6th rank follows the pattern for the 5th rank, f6 is stronger than e6 (f6 is actually the strongest pawn on the board, passers excluded), e6 is stronger than d6, and d6 stronger than c6

OK, I will not ask for your expert opinion, but just how funny the above seems to you?

[jorose]

I disagree out of a number of reasons.

First because in principle I don't think you should base PST values based off of relative piece placement. Specifically your logic will crumble the moment black decides to castle queenside. Instead you could evaluate things pawn distance to king or some other random king safety term if you really wanted to evaluate that.

Second attacking with pieces tends to be more effective then with pawns. Your getting ahead of yourself if you think an attack will be more justified starting with f4 compared to c4. d4, e4 and Nf3 all control the center and help get your pieces into the game which should increase chances for an attack much more then pawns being "slanted towards the kingside".

Finally it's exceptionally easy to argue the contrary. f4 might easily offer black more chances for an attack then white. Specifically the f-pawn is an important defender of the white king. There are many lines where white may get crushed do to an early f4 weakening the a7-g1 or h4-e1 diagonals. In fact due to this weakening black could consider a gambit as early as move 1! [pgn] 1.f2f4 e7e5 2.fxe5 d6 3.exd6 Bxd6 [/pgn] is a very dangerous line for the first player who is already faced with the mate threat 4. ... Qh4+ 5.g3 Bxg3+ 6.hg Qxh3#. By contrast 1.c4 d5 2.cxd5 e6 3.dxe6 Bxe6 might just be objectively winning for white as he is just up a pawn with two central pawns against none. In fact in human play 1.f4 is extremely rare at top level and has a very dubious reputation whereas 1.d4, 1.e4, 1.Nf3, 1.c4 are all very popular and even less popular moves like 1.g3 tend to have a decent reputation.

[Lyudmil Tsvetkov]

I disagree out of a number of reasons.

First because in principle I don't think you should base PST values based off of relative piece placement. Specifically your logic will crumble the moment black decides to castle queenside. Instead you could evaluate things pawn distance to king or some other random king safety term if you really wanted to evaluate that.

Second attacking with pieces tends to be more effective then with pawns. Your getting ahead of yourself if you think an attack will be more justified starting with f4 compared to c4. d4, e4 and Nf3 all control the center and help get your pieces into the game which should increase chances for an attack much more then pawns being "slanted towards the kingside".

Finally it's exceptionally easy to argue the contrary. f4 might easily offer black more chances for an attack then white. Specifically the f-pawn is an important defender of the white king. There are many lines where white may get crushed do to an early f4 weakening the a7-g1 or h4-e1 diagonals. In fact due to this weakening black could consider a gambit as early as move 1! [pgn] 1.f2f4 e7e5 2.fxe5 d6 3.exd6 Bxd6 [/pgn] is a very dangerous line for the first player who is already faced with the mate threat 4. ... Qh4+ 5.g3 Bxg3+ 6.hg Qxh3#. By contrast 1.c4 d5 2.cxd5 e6 3.dxe6 Bxe6 might just be objectively winning for white as he is just up a pawn with two central pawns against none. In fact in human play 1.f4 is extremely rare at top level and has a very dubious reputation whereas 1.d4, 1.e4, 1.Nf3, 1.c4 are all very popular and even less popular moves like 1.g3 tend to have a decent reputation.

The From Gambit you cite is unsound, that is known theory; it is dangerous only for novices.

e4 and c4 are clearly stronger first moves for white than d4. On e4, you can defend with black only with the Berlin possibly in the Ruy Lopez, or some very specific lines of the Sicilian. Most other lines should be very inferior for black.

The Moderm Defense with g6 gives you fair chances on e4, unless white plays the Austrian Attack with, please note, f4, before Nf3, deliberately weakening the king shelter according to you. That is also a known theory, check Fischer and Bronstein games for example. That is the only reason why the Modern Defense is not that sound.

On c4 black also has very difficult time to equalise.

Not so on d4. Black should equalise easily in the KID (that is why Kasparov and Fischer played extensively the KID, I think both are not such weak players, and excellent theoreticians btw.; same is true of Bronstein, possibly the greatest theoretician overall, who also liked the KID)

Critical for the black KID is only the Saemisch with f3 and castling away from the black pawn chain, and some fianchettoe lines.

Other moves on d4 should give white advantage, for example the NimzoIndian or the Queen's Indian, although engines and many GMs might think just the opposite, finding the Queen's Indian for example for sufficient. It is not, for reference see Kasparov, Fischer and Bronstein games.

Why KID-like structures are very dangerous you might understand when you replay the Caruana-Carlsen game from the last TataSteel. For a long time neither Komodo, SF or Houdini see anything, but Carlsen's KID-type attack still wins as if out of the blue. With a, please note well, f4 black pawn.

Nf3 and g3, though a bit inferior in terms of the move order, can both lead to King's Indian Attack for white, the mirror image of the KID for black, with plus tempo. It is not in vain that Fischer employed that system so often, almost every time he could do so.

Black castling long is a nice presumption, unfortunately this happens only some 5% of cases.

d4 and e4 pawns are not equal, that is for certain, and it would be wrong to assign both squares equal values in the psqt.

The initial position in chess is asymmetric, as there are 2 pairs of minors and a pair of rooks symmetrically placed, but also a king and queen, the most important pieces, asymmetrically placed. When the king castles short, this asymmetry is further highlighted, and you know that everything revolves around the king. Why use symmetric piece/pawn tables for positions that are actually asymmetric?

[bob]

I disagree out of a number of reasons.

First because in principle I don't think you should base PST values based off of relative piece placement. Specifically your logic will crumble the moment black decides to castle queenside. Instead you could evaluate things pawn distance to king or some other random king safety term if you really wanted to evaluate that.

Second attacking with pieces tends to be more effective then with pawns. Your getting ahead of yourself if you think an attack will be more justified starting with f4 compared to c4. d4, e4 and Nf3 all control the center and help get your pieces into the game which should increase chances for an attack much more then pawns being "slanted towards the kingside".

Finally it's exceptionally easy to argue the contrary. f4 might easily offer black more chances for an attack then white. Specifically the f-pawn is an important defender of the white king. There are many lines where white may get crushed do to an early f4 weakening the a7-g1 or h4-e1 diagonals. In fact due to this weakening black could consider a gambit as early as move 1! [pgn] 1.f2f4 e7e5 2.fxe5 d6 3.exd6 Bxd6 [/pgn] is a very dangerous line for the first player who is already faced with the mate threat 4. ... Qh4+ 5.g3 Bxg3+ 6.hg Qxh3#. By contrast 1.c4 d5 2.cxd5 e6 3.dxe6 Bxe6 might just be objectively winning for white as he is just up a pawn with two central pawns against none. In fact in human play 1.f4 is extremely rare at top level and has a very dubious reputation whereas 1.d4, 1.e4, 1.Nf3, 1.c4 are all very popular and even less popular moves like 1.g3 tend to have a decent reputation.

The From Gambit you cite is unsound, that is known theory; it is dangerous only for novices.

e4 and c4 are clearly stronger first moves for white than d4. On e4, you can defend with black only with the Berlin possibly in the Ruy Lopez, or some very specific lines of the Sicilian. Most other lines should be very inferior for black.

The Moderm Defense with g6 gives you fair chances on e4, unless white plays the Austrian Attack with, please note, f4, before Nf3, deliberately weakening the king shelter according to you. That is also a known theory, check Fischer and Bronstein games for example. That is the only reason why the Modern Defense is not that sound.

On c4 black also has very difficult time to equalise.

Not so on d4. Black should equalise easily in the KID (that is why Kasparov and Fischer played extensively the KID, I think both are not such weak players, and excellent theoreticians btw.; same is true of Bronstein, possibly the greatest theoretician overall, who also liked the KID)

Critical for the black KID is only the Saemisch with f3 and castling away from the black pawn chain, and some fianchettoe lines.

Other moves on d4 should give white advantage, for example the NimzoIndian or the Queen's Indian, although engines and many GMs might think just the opposite, finding the Queen's Indian for example for sufficient. It is not, for reference see Kasparov, Fischer and Bronstein games.

Why KID-like structures are very dangerous you might understand when you replay the Caruana-Carlsen game from the last TataSteel. For a long time neither Komodo, SF or Houdini see anything, but Carlsen's KID-type attack still wins as if out of the blue. With a, please note well, f4 black pawn.

Nf3 and g3, though a bit inferior in terms of the move order, can both lead to King's Indian Attack for white, the mirror image of the KID for black, with plus tempo. It is not in vain that Fischer employed that system so often, almost every time he could do so.

Black castling long is a nice presumption, unfortunately this happens only some 5% of cases.

d4 and e4 pawns are not equal, that is for certain, and it would be wrong to assign both squares equal values in the psqt.

The initial position in chess is asymmetric, as there are 2 pairs of minors and a pair of rooks symmetrically placed, but also a king and queen, the most important pieces, asymmetrically placed. When the king castles short, this asymmetry is further highlighted, and you know that everything revolves around the king. Why use symmetric piece/pawn tables for positions that are actually asymmetric?

You are over-emphasizing PST values. PSTs are simply general guidance. Nothing more, nothing less. King safety is not going to be handled well with PST values, ever. Too many other things are far more important that the general-case PST type of information.

The general idea behind PSTs is NOT attacking or anything else. It is more a matter of "what to do when there is nothing to do?" as opposed to being knowledge that helps specific plans of attack or defense. I wouldn't disagree with any of your assessment in general, except that PSTs are NOT the place to express those concepts. If one side castles long, all of that is out the window. With the black king at b8, black doesn't care that white has a pawn chain pointing toward g7/h7 at all. In fact that pawn chain is pointing the wrong way entirely. That's why most programs do their "king safety pawn shelter" evaluation at run-time where they know where the kings are at the moment, and can use that to derive how the pawns ought to look to enable an attack...

[Adam Hair]

Oh, it is nostalgy, sorry, just my last brief topic here.

I know that most engines think e4 and d4 pawns deserve exactly the same bonus, and actually give this bonus. The same is true for c4 and f4 pawns.

But is it really so?

As the kings are placed on the king side at the beginning of the game, and the probability that a short castling will appear is more than 90%, pawns are naturally slanted towards the king side, even if for the monent they are not storming pawns. Actually, some pawns on the king side may never become storming pawns, or may become and then stop being so, but the natural slant towards the king side will still be there.

I think, in terms of psqt values, the following is true:

- for the 4th rank, e4 is the strongest pawn, followed by d4 (so in no way you can assign equal values), d4 is stronger than f4, and f4 on its turn stronger than c4. So c4 and f4 again have different values

- for the 5th rank, the slant is even more noticeable. f5 is stronger than e5 (but really some engines think e5 is stronger than f5, which is very funny for me), e5 is stronger than d5, and d5 is on its turn stronger than c5. So there is a full asymmetry here with values diminishing from the king towards the queen side.

- the 6th rank follows the pattern for the 5th rank, f6 is stronger than e6 (f6 is actually the strongest pawn on the board, passers excluded), e6 is stronger than d6, and d6 stronger than c6

OK, I will not ask for your expert opinion, but just how funny the above seems to you?

Here is a midgame piece-square table for pawns that I extracted from a PGN of ~450,000 high quality engine-engine matches. I took the cumulative game results when a pawn was on a square for 6 or more half moves during the midgame (which for these purposes were the moves from 13 to 40):

Code: Select all

A8                                             H8
   0,     0,     0,     0,     0,   0,    0,  0
  118,   121,   173,   168,   107,  82,  -16, 22
   21,    54,    72,    56,    77,  95,   71, 11
	9,    30,    23,    31,    31,  23,   17, 11
	1,    14,     8,     4,     5,   4,   10,  7
	1,     1,    -6,   -19,    -6,  -7,   -4, 10 
   -1,    -7,   -11,   -35,   -13,   5,    3, -5 
    0,     0,     0,     0,     0,   0,    0,  0
A1                                              H1

[jorose]

e4 and c4 are clearly stronger first moves for white than d4. On e4, you can defend with black only with the Berlin possibly in the Ruy Lopez, or some very specific lines of the Sicilian. Most other lines should be very inferior for black.

Thats a claim every top 50 player as well as every top 20 engine disagree with Id suspect. You are basing this off of what? You also mentioned the following which Ill leave without commentary as I addressed it previously.

- for the 4th rank, e4 is the strongest pawn, followed by d4 (so in no way you can assign equal values), d4 is stronger than f4, and f4 on its turn stronger than c4. So c4 and f4 again have different values

Not so on d4. Black should equalise easily in the KID (that is why Kasparov and Fischer played extensively the KID, I think both are not such weak players, and excellent theoreticians btw.; same is true of Bronstein, possibly the greatest theoretician overall, who also liked the KID)

Bronstein and Fischer were great theoreticians but only for their own time. Nowadays there is a massively greater amount of theory. Also those players themselves would disagree that it's easy to equalise with the KID, it's not why they played the opening, they played it to get a struggle where they felt they could outplay their opponent. Fischer himself avoided the KID when he was looking for equality out of the opening opting for the Grunfeld.

Nf3 and g3, though a bit inferior in terms of the move order, can both lead to King's Indian Attack for white, the mirror image of the KID for black, with plus tempo. It is not in vain that Fischer employed that system so often, almost every time he could do so.

Pretty sure Fischer played 1.e4 most exclusively before he faced Spassky.

Critical for the black KID is only the Saemisch with f3 and castling away from the black pawn chain, and some fianchettoe lines.

Currently it seems the top players disagree in general opting for other lines.

Black castling long is a nice presumption, unfortunately this happens only some 5% of cases.

So you want an assymetric evaluation function for white and black?

d4 and e4 pawns are not equal, that is for certain, and it would be wrong to assign both squares equal values in the psqt.

The initial position in chess is asymmetric, as there are 2 pairs of minors and a pair of rooks symmetrically placed, but also a king and queen, the most important pieces, asymmetrically placed. When the king castles short, this asymmetry is further highlighted, and you know that everything revolves around the king. Why use symmetric piece/pawn tables for positions that are actually asymmetric?

Your looking at this incorrectly. You can claim e4 to be better than d4 (even if I disagree) however you need to reason WHY you think e4 is better than d4. If its due to the pawn being closer the the enemy king then add an evaluation term for that. If you think its because your queen is more active then add an evaluation term for that.

PSTs should only be a very small part of your evaluation code. They are great because they can be evaluated incrementally and cheaply. In the case of Knight and King they are also very useful. If you make them asymmetric however your engine will lose generality. It will be weaker if you ever teach it FRC and it will make it harder to tune your parameters.

If you have completely assymettric tapered eval PSTs (no queenside kingside symmetry, no top bottom symmetry,no color symmetry and differing values for opening and endgame) you will have 256 parameters for JUST your pawn PSTs. Assuming you want to use this information incrementally during make move you will probably have this many variables for each piece so you are looking at 1536 variables to tune just for your PSTs.

[Lyudmil Tsvetkov]

I disagree out of a number of reasons.

First because in principle I don't think you should base PST values based off of relative piece placement. Specifically your logic will crumble the moment black decides to castle queenside. Instead you could evaluate things pawn distance to king or some other random king safety term if you really wanted to evaluate that.

Second attacking with pieces tends to be more effective then with pawns. Your getting ahead of yourself if you think an attack will be more justified starting with f4 compared to c4. d4, e4 and Nf3 all control the center and help get your pieces into the game which should increase chances for an attack much more then pawns being "slanted towards the kingside".

Finally it's exceptionally easy to argue the contrary. f4 might easily offer black more chances for an attack then white. Specifically the f-pawn is an important defender of the white king. There are many lines where white may get crushed do to an early f4 weakening the a7-g1 or h4-e1 diagonals. In fact due to this weakening black could consider a gambit as early as move 1! [pgn] 1.f2f4 e7e5 2.fxe5 d6 3.exd6 Bxd6 [/pgn] is a very dangerous line for the first player who is already faced with the mate threat 4. ... Qh4+ 5.g3 Bxg3+ 6.hg Qxh3#. By contrast 1.c4 d5 2.cxd5 e6 3.dxe6 Bxe6 might just be objectively winning for white as he is just up a pawn with two central pawns against none. In fact in human play 1.f4 is extremely rare at top level and has a very dubious reputation whereas 1.d4, 1.e4, 1.Nf3, 1.c4 are all very popular and even less popular moves like 1.g3 tend to have a decent reputation.

The From Gambit you cite is unsound, that is known theory; it is dangerous only for novices.

e4 and c4 are clearly stronger first moves for white than d4. On e4, you can defend with black only with the Berlin possibly in the Ruy Lopez, or some very specific lines of the Sicilian. Most other lines should be very inferior for black.

The Moderm Defense with g6 gives you fair chances on e4, unless white plays the Austrian Attack with, please note, f4, before Nf3, deliberately weakening the king shelter according to you. That is also a known theory, check Fischer and Bronstein games for example. That is the only reason why the Modern Defense is not that sound.

On c4 black also has very difficult time to equalise.

Not so on d4. Black should equalise easily in the KID (that is why Kasparov and Fischer played extensively the KID, I think both are not such weak players, and excellent theoreticians btw.; same is true of Bronstein, possibly the greatest theoretician overall, who also liked the KID)

Critical for the black KID is only the Saemisch with f3 and castling away from the black pawn chain, and some fianchettoe lines.

Other moves on d4 should give white advantage, for example the NimzoIndian or the Queen's Indian, although engines and many GMs might think just the opposite, finding the Queen's Indian for example for sufficient. It is not, for reference see Kasparov, Fischer and Bronstein games.

Why KID-like structures are very dangerous you might understand when you replay the Caruana-Carlsen game from the last TataSteel. For a long time neither Komodo, SF or Houdini see anything, but Carlsen's KID-type attack still wins as if out of the blue. With a, please note well, f4 black pawn.

Nf3 and g3, though a bit inferior in terms of the move order, can both lead to King's Indian Attack for white, the mirror image of the KID for black, with plus tempo. It is not in vain that Fischer employed that system so often, almost every time he could do so.

Black castling long is a nice presumption, unfortunately this happens only some 5% of cases.

d4 and e4 pawns are not equal, that is for certain, and it would be wrong to assign both squares equal values in the psqt.

The initial position in chess is asymmetric, as there are 2 pairs of minors and a pair of rooks symmetrically placed, but also a king and queen, the most important pieces, asymmetrically placed. When the king castles short, this asymmetry is further highlighted, and you know that everything revolves around the king. Why use symmetric piece/pawn tables for positions that are actually asymmetric?

You are over-emphasizing PST values. PSTs are simply general guidance. Nothing more, nothing less. King safety is not going to be handled well with PST values, ever. Too many other things are far more important that the general-case PST type of information.

The general idea behind PSTs is NOT attacking or anything else. It is more a matter of "what to do when there is nothing to do?" as opposed to being knowledge that helps specific plans of attack or defense. I wouldn't disagree with any of your assessment in general, except that PSTs are NOT the place to express those concepts. If one side castles long, all of that is out the window. With the black king at b8, black doesn't care that white has a pawn chain pointing toward g7/h7 at all. In fact that pawn chain is pointing the wrong way entirely. That's why most programs do their "king safety pawn shelter" evaluation at run-time where they know where the kings are at the moment, and can use that to derive how the pawns ought to look to enable an attack...

Fully right, the big problem is how to tune asymmetric psqt tables with the remaining eval terms. There should be a way to do this sucessfully, but extremely hard.

Still, it seems to me asymmetric psqts are the right way to proceed.
There is no denying that:

1. the initial position in chess is asymmetric
2. in some 95% of cases the king castles short by dint of an inevitable force of objective circumstances, meaning that looking for the fastest way to bring the king to safety is the right strategy, and the fastest way is castling short, castling long is much more difficult to do, especially for black

[Lyudmil Tsvetkov]

Oh, it is nostalgy, sorry, just my last brief topic here.

I know that most engines think e4 and d4 pawns deserve exactly the same bonus, and actually give this bonus. The same is true for c4 and f4 pawns.

But is it really so?

As the kings are placed on the king side at the beginning of the game, and the probability that a short castling will appear is more than 90%, pawns are naturally slanted towards the king side, even if for the monent they are not storming pawns. Actually, some pawns on the king side may never become storming pawns, or may become and then stop being so, but the natural slant towards the king side will still be there.

I think, in terms of psqt values, the following is true:

- for the 4th rank, e4 is the strongest pawn, followed by d4 (so in no way you can assign equal values), d4 is stronger than f4, and f4 on its turn stronger than c4. So c4 and f4 again have different values

- for the 5th rank, the slant is even more noticeable. f5 is stronger than e5 (but really some engines think e5 is stronger than f5, which is very funny for me), e5 is stronger than d5, and d5 is on its turn stronger than c5. So there is a full asymmetry here with values diminishing from the king towards the queen side.

- the 6th rank follows the pattern for the 5th rank, f6 is stronger than e6 (f6 is actually the strongest pawn on the board, passers excluded), e6 is stronger than d6, and d6 stronger than c6

OK, I will not ask for your expert opinion, but just how funny the above seems to you?

Here is a midgame piece-square table for pawns that I extracted from a PGN of ~450,000 high quality engine-engine matches. I took the cumulative game results when a pawn was on a square for 6 or more half moves during the midgame (which for these purposes were the moves from 13 to 40):

Code: Select all

A8                                             H8
   0,     0,     0,     0,     0,   0,    0,  0
  118,   121,   173,   168,   107,  82,  -16, 22
   21,    54,    72,    56,    77,  95,   71, 11
	9,    30,    23,    31,    31,  23,   17, 11
	1,    14,     8,     4,     5,   4,   10,  7
	1,     1,    -6,   -19,    -6,  -7,   -4, 10 
   -1,    -7,   -11,   -35,   -13,   5,    3, -5 
    0,     0,     0,     0,     0,   0,    0,  0
A1                                              H1

No doubt you are the originator of the asymmetric psqt idea, Adam, thanks!

When I say for the first time your asymmetric tables, I was shocked, the usual way, but on thinking a bit more on this, you are fully right.

Your approach for building the table might not be fully scientific, as engines do not play perfect chess, they avoid some promising setups, etc., the 6 half-moves condition might be not the perfect condition, I do not know, but still, your table generally confirms the king-side asymmetry:

- for the 6th rank, your values show that the f6 square gets the highest value overall, excluding passers values for the 7th rank; strangely enough, d6 in your table is lower than c6

- your 5th rank tables are fully symmetric, but I do not think this is really the case; engines simply can not play the KID, otherwise you would have a strong slide towards the king side here

- I can not comment the 4th rank and other non-central values, as they involve king safety and storming pawns, but I really find the table worth consideration

Interesting what will happen when you repeat the test with a few selected top engines, maybe the first 4 or 6, even with a lower number of games; probably you will have a much more accurate table in this way?

[Lyudmil Tsvetkov]

e4 and c4 are clearly stronger first moves for white than d4. On e4, you can defend with black only with the Berlin possibly in the Ruy Lopez, or some very specific lines of the Sicilian. Most other lines should be very inferior for black.

Thats a claim every top 50 player as well as every top 20 engine disagree with Id suspect. You are basing this off of what? You also mentioned the following which Ill leave without commentary as I addressed it previously.

- for the 4th rank, e4 is the strongest pawn, followed by d4 (so in no way you can assign equal values), d4 is stronger than f4, and f4 on its turn stronger than c4. So c4 and f4 again have different values

Not so on d4. Black should equalise easily in the KID (that is why Kasparov and Fischer played extensively the KID, I think both are not such weak players, and excellent theoreticians btw.; same is true of Bronstein, possibly the greatest theoretician overall, who also liked the KID)

Bronstein and Fischer were great theoreticians but only for their own time. Nowadays there is a massively greater amount of theory. Also those players themselves would disagree that it's easy to equalise with the KID, it's not why they played the opening, they played it to get a struggle where they felt they could outplay their opponent. Fischer himself avoided the KID when he was looking for equality out of the opening opting for the Grunfeld.

Nf3 and g3, though a bit inferior in terms of the move order, can both lead to King's Indian Attack for white, the mirror image of the KID for black, with plus tempo. It is not in vain that Fischer employed that system so often, almost every time he could do so.

Pretty sure Fischer played 1.e4 most exclusively before he faced Spassky.

Critical for the black KID is only the Saemisch with f3 and castling away from the black pawn chain, and some fianchettoe lines.

Currently it seems the top players disagree in general opting for other lines.

Black castling long is a nice presumption, unfortunately this happens only some 5% of cases.

So you want an assymetric evaluation function for white and black?

d4 and e4 pawns are not equal, that is for certain, and it would be wrong to assign both squares equal values in the psqt.

The initial position in chess is asymmetric, as there are 2 pairs of minors and a pair of rooks symmetrically placed, but also a king and queen, the most important pieces, asymmetrically placed. When the king castles short, this asymmetry is further highlighted, and you know that everything revolves around the king. Why use symmetric piece/pawn tables for positions that are actually asymmetric?

Your looking at this incorrectly. You can claim e4 to be better than d4 (even if I disagree) however you need to reason WHY you think e4 is better than d4. If its due to the pawn being closer the the enemy king then add an evaluation term for that. If you think its because your queen is more active then add an evaluation term for that.

PSTs should only be a very small part of your evaluation code. They are great because they can be evaluated incrementally and cheaply. In the case of Knight and King they are also very useful. If you make them asymmetric however your engine will lose generality. It will be weaker if you ever teach it FRC and it will make it harder to tune your parameters.

If you have completely assymettric tapered eval PSTs (no queenside kingside symmetry, no top bottom symmetry,no color symmetry and differing values for opening and endgame) you will have 256 parameters for JUST your pawn PSTs. Assuming you want to use this information incrementally during make move you will probably have this many variables for each piece so you are looking at 1536 variables to tune just for your PSTs.

I do not need tons of theory, I just look at the games the champions played.

I need to look at some Kasparov games, Fischer games, Smyslov, Karpov and Carlsen games; I leave the rest to you.

You think Kasparov and Fischer will choose a dubious opening just for the sake of offering winning chances, even if risky?
Never, chess at that level is played with only sound, sounder and soundest moves.

For the same reason, I never look at any other games in the current time apart from Carlsen games. Why should I? The best ideas are in Carlsen games, why should I look at weaker ideas?

[Adam Hair]

Oh, it is nostalgy, sorry, just my last brief topic here.

I know that most engines think e4 and d4 pawns deserve exactly the same bonus, and actually give this bonus. The same is true for c4 and f4 pawns.

But is it really so?

As the kings are placed on the king side at the beginning of the game, and the probability that a short castling will appear is more than 90%, pawns are naturally slanted towards the king side, even if for the monent they are not storming pawns. Actually, some pawns on the king side may never become storming pawns, or may become and then stop being so, but the natural slant towards the king side will still be there.

I think, in terms of psqt values, the following is true:

- for the 4th rank, e4 is the strongest pawn, followed by d4 (so in no way you can assign equal values), d4 is stronger than f4, and f4 on its turn stronger than c4. So c4 and f4 again have different values

- for the 5th rank, the slant is even more noticeable. f5 is stronger than e5 (but really some engines think e5 is stronger than f5, which is very funny for me), e5 is stronger than d5, and d5 is on its turn stronger than c5. So there is a full asymmetry here with values diminishing from the king towards the queen side.

- the 6th rank follows the pattern for the 5th rank, f6 is stronger than e6 (f6 is actually the strongest pawn on the board, passers excluded), e6 is stronger than d6, and d6 stronger than c6

OK, I will not ask for your expert opinion, but just how funny the above seems to you?

Here is a midgame piece-square table for pawns that I extracted from a PGN of ~450,000 high quality engine-engine matches. I took the cumulative game results when a pawn was on a square for 6 or more half moves during the midgame (which for these purposes were the moves from 13 to 40):

Code: Select all

A8                                             H8
   0,     0,     0,     0,     0,   0,    0,  0
  118,   121,   173,   168,   107,  82,  -16, 22
   21,    54,    72,    56,    77,  95,   71, 11
	9,    30,    23,    31,    31,  23,   17, 11
	1,    14,     8,     4,     5,   4,   10,  7
	1,     1,    -6,   -19,    -6,  -7,   -4, 10 
   -1,    -7,   -11,   -35,   -13,   5,    3, -5 
    0,     0,     0,     0,     0,   0,    0,  0
A1                                              H1

No doubt you are the originator of the asymmetric psqt idea, Adam, thanks!

When I say for the first time your asymmetric tables, I was shocked, the usual way, but on thinking a bit more on this, you are fully right.

Your approach for building the table might not be fully scientific, as engines do not play perfect chess, they avoid some promising setups, etc., the 6 half-moves condition might be not the perfect condition, I do not know, but still, your table generally confirms the king-side asymmetry:

- for the 6th rank, your values show that the f6 square gets the highest value overall, excluding passers values for the 7th rank; strangely enough, d6 in your table is lower than c6

- your 5th rank tables are fully symmetric, but I do not think this is really the case; engines simply can not play the KID, otherwise you would have a strong slide towards the king side here

- I can not comment the 4th rank and other non-central values, as they involve king safety and storming pawns, but I really find the table worth consideration

To be honest, I am just a dumb stat collector and not able to fully assess why those numbers are what they are.

Interesting what will happen when you repeat the test with a few selected top engines, maybe the first 4 or 6, even with a lower number of games; probably you will have a much more accurate table in this way?

I may do that soon. I have a database that I have roughly sorted by Elo that takes into account time control and processor speed. But I still would have to adjust the minimum Elo so that I have enough samples so that I could extract meaningful statistics.