Crazy theories

[PK]

"landing squares" for rooks are basically rook outposts, and are mentioned in "My system". I have included them in evaluation function of Rodent, with a small bonus of 5-10 centipawns, increasing towards the wing (as suggested by Nimzowitsch). Benefit was very small, but it is definstely not a regression.

[carldaman]

I would think Komodo probably uses a lot of what you're describing in its eval. Larry Kaufman is an authority on the relative value of the pieces, piece redundancies, etc.

[Lyudmil Tsvetkov]

I would think Komodo probably uses a lot of what you're describing in its eval. Larry Kaufman is an authority on the relative value of the pieces, piece redundancies, etc.

My impression is that Komodo (at least the version I saw at the 3Champs) does great with piece imbalances (definitely much better than both Stockfish and Houdini, which have, if any, only a basic understanding of the phenomenon).

However, I do not think any of those engines uses (if practically feasible, and I think it is) colour complementarity or general square complementarity (sorry for the slang, you have to use some notions). Just like piece imbalances, for me those and similar notions might be useful, even in only a tiny portion of positions (just as many other terms btw.)

[Lyudmil Tsvetkov]

I think play based on compensation is a very interesting and largely unexplored way of handling the game. In most cases, sacrificing material for some kind of positional or tactical compensation is a situation difficult to assess with full precision, and consequently difficult to play. Probably that is the reason why most humans and engines avoid playing such lines.

Concerning engines, they would sacrifice, but only if they see something concrete, i.e. that they will have their material back in a certain number of moves. One exception from the leading engines for me is Stockfish, which I have quite frequently watched, even in longer games, sacrifice material (usually a pawn, but sometimes more) for no visible compensation that would materialise into concrete moves. In most cases, however, even in 30-50-70 moves, Stockfish would be proven right. Probably this kind of play is based on some exceptional understanding of open files, rooks on the 7th rank, etc., on its very good search that might be somewhat different from other engines, also maybe on a bit of speculation, but the important thing is that it really works, is fun to watch, provides a vein of originality and brings some additional points that would otherwise not come.

I am not in the position to talk here about the merits of the Stockfish kind of tactical compensation, as humans are as a rule much less proficient than engines in similar situations involving abundant tactics, but will discuss a bit instead another, and not less important type of positional compensation.

My theory is that whenever one of the sides has the following large number of positional assets, it has the full right to at least doubly increase the bonus points for those assets because of a latent effect of the snowball, that would make such assets of significantly bigger value in the long term, thus providing objective compensation:

- 2 or more enemy backward (backward-fated) pawns
- 2 or more own minor pieces on outposts into the enemy camp (gaining space advantage on the 5th and 6th ranks)
- at least 3 own pawns gaining space advantage on the 5th and 6th ranks

The reason that such compensation is due is that similar situations are an exception, occur very infrequently, and their mere presence indicates the existence of assets that are unusually big taken as a whole, will last a very long time and certainly bring about the effect of the snowballing increase of score as the game progresses.

Below some relevant positions.

[d]r2q2k1/p2r1pbp/1p1p2p1/1PpNp1P1/2P1P2P/5Q2/8/R4RK1 w - - 0 1
White is 3 pawns down, with no specific visible compensation in sight, at least a tactical one. But I think the position is at least equal. What would be able to compensate for the full 3 points advantage of black in terms of material?

White has an excellent knight outpost on d5 (50cps), 4 black penalised backward pawns: d6, actually backward-fated (35-40cps), f7, also backward-fated, as white has predominant control of the square in front of the pawn (so that predominant piece control of the square in front of a backward pawn will render it backward-fated), a7, and h7. The penalties for f7 and h7 might be increased by 2/3 as they are part of the king shelter, making it inflexible; there are also 2 white pawns gaining space advantage, b5 and g5, but that will only make up for slightly over 1.5 pawns. Where will the other 1.5 pawns to fully compensate come from?

I think here you might introduce the concept of positional compensation in terms of large number of assets. The penalties for the 4 black backward pawns can actually be increased doubly, because of their long-term consequences and the impending snowballing effect. Thus, the 4 backward pawns will add another 1.5 pawns to white's score, equalising. If you do not use a similar technique, you will not see the compensation, but it will be there.

[d]2r1r1k1/1p1q2bp/pB1p2p1/P2Np1P1/2P1BpR1/1P1P1P2/R7/7K w - - 0 1

Black has a queen and pawn for 2 white minor pieces, but I think the positions is at least equal. Where will the compensation for the black material superiority come from? Well, white has the 2 bishops (50cps), somewhat better imbalance (but its king is not very safe), 2 great outposts on b6 and d5 (75cps in all), and 4 black penalised backward pawns: b7 (actually backward-fated, because of predominant piece control, 35cps), d6 (also backward-fated for the same reason, another 35cps), e5 (backward-fated, because d6 is backward, 35cps), and h7 (backward part of the king shelter, 40cps). 2 white pawns gain space advantage on a5 and g5, but in total that would some up to slightly less than 3 pawns. We still need more than a pawn to compensate, where do we get that pawn from?

Again, I think here the above-mentioned compensatory mechanism might come in useful. The bonus points for the 2 white minor pieces on outposts into the enemy camp, as well as the penalties for the 4 black backward pawns could objectively be increased doubly because of the snowballing effect. This will add some 2 pawns to white's score, and already white could be in advantage. In any case, the position should not be lost.

If you do not consider something similar in terms of compensation, there is nowhere to take those additional 2 pawns from, and you will regard the position as simply lost for white, which it is not.

[d]1rqn1bbk/3p2p1/2pP1pPp/RpP2P2/1P3PP1/2Q5/8/R5K1 w - - 0 1

White has a rook and pawn for 3 enemy minor pieces, a difference of 3.5 pawns in terms of material, but I think the position is at least equal. Where will yo take those 3.5 pawns compensation from?

Well, white has control of the a file (the double rooks would not score more than 60cps), 4 pawns gaining space advantage: c5 (10cps), d6 (30cps), f5 (15cps because on the king side), g6 (45cps for the same reason; those should not be considered as storming pawns, for me, as they are blocked, but g4 is, another 40cps for the 4th rank, 60 when it goes to the 5th; f4, however, does nothing, it is not a storming pawn, as it is blocked by an own pawn that in its turn is blocked by an enemy one). Black has 2 very passive minor pieces, and the penalties for passivity, extremely low mobility for both pieces could go to 1.5 pawns in total, but at the same time the white king has poor safety and black has the 2 bishops (another full pawn in black's favour).

So that, all calculated, white will miss some 1 full pawn in order to be able to compensate completely. Where will it take this pawn from?

I think here again you might resort to the above-mentioned principle of dispensing compensation for the snowball effect with long-range consequences. The 4 white pawns gaining space advantage (because of their number, which is unusual and supposes compensation, as with cramped positions) could well duplicate their bonus points, adding another full pawn to white's score. Thus, white is able to equalise at least.

If you do not consider similar compensatory rules, however, or something of the kind, most probably you will think black has the advantage here (unless you see something tactical), which might not be the case.

Any comments very much appreciated.
What is your/your engine's conception of compensation? Any specific rules built in? Would be interesting to share. I think this is one of the topics widely neglected by both humans and engines of all calibre, but it promises unchartered waters, higly intriguing positions and a lot of points.

Best, Lyudmil

PS. I am not completely certain of the validity of the positions tactically, had to improvise something, there might be some flaws, but the important thing are the undelying principles, which I think are valid. I know there are better-suited positions in my database, but I could not find them right now.

[Lyudmil Tsvetkov]

I think basically the same approach could be applied with tactical compensation.

Using the rule of the snowball effect (if theoretically correct, which is questionable, but all theories are questionable), one could dispense additional bonus points in tactically relevant positions for the presence of at least 3 of a number of factors, among which the following could be included:

- rook on the 7th rank
- rook on an open file
- bad enemy king safety (king in the center - c-f files, or just one pawn of the immediate shelter)
- 2 storming pawns already on the 5th rank (or even better one of them on the 6th)
- pawn gaining space advantage on the 6th rank on the side where the enemy king has castled

The presence of 3 of those might suggest the validity of increasing the score for all of those by some 1/3 to 2/3, as they would very well exhibit a snowball effect in the long term. The idea would be that a number of factors larger than certain limit would provide a quality leap in their overall influence on the board, and not just represent the sum of the values of the separate factors.

I think Stockfish, knowingly or unknowingly, resorts to something having a similar effect. For example (and that is my pure hypothesis, the Stockfish authors will excuse my ignorance or wrong assumptions), Stock might play some positions based on tactical compensation well, because it scores heavier than usual rooks on open files, 7th rank, bad enemy king safety, etc. When only one or 2 of those are present, the engine might show a bit higher score than normal, that could be beneficial sometimes, or not lead to dire consequences in other situations, because of the small number of terms; however, where more such factors are present, the engine might very well find moves that would allow it to play chess along the lines of tactical compensation, sacrificing a pawn or other material with no visible compensation.

[d]4r3/5knR/p1q2pp1/1p1p1p2/1P1B4/P1PPP3/1K5Q/8 b - - 0 50
This is from the 4th game of the 3Champs, Stockfish with white against Komodo.

Stockfish shows here an advantage of more than a full pawn, while Komodo thinks it is almost equal. Stockfish won the game (and btw. many other similar games). How does Stockfish sees a white win, when probably there is nothing concrete for the search to veryfy?

It takes Stockfish another 80 moves to achieve a win (whether fully reasonable, I do not know, but the initiative all the way stood with Stockfish, while Komodo only defended), but the point is valuable in any case, while watching developments was at least curious and unusual.

[Lyudmil Tsvetkov]

Engines are renowned for being extremely good tacticians and consequently doing superbly in complicated positions, i.e. positions with large number of attacks. I still think engines could be even better tacticians. I will expose here a short theory of mine concerning complicated positions, that might be of use if not to engines, at least to a stray human reader.

For complicated positions a system might be developed for dispensing bonus points for the capturing potential of each pawn and piece. For a start, the system might be applied whenever there is a certain minimal number of attacks for both sides (for example 6 pawn and piece attacks in total; only direct attacks will be taken into account; but the number could also be set to 8, 10, etc.)

In such a complicated position you check the capturing potential of each object, dispensing points for each captured enemy piece or pawn. You start capturing with a pawn or piece and capture all the way as if having a continuous right to move until there are no more enemy objects to capture. You do all possible capturing ways until they are all exhausted. Then you do the same for the remaining pieces.

For each captured piece or pawn a bonus equal to 1/100 (or maybe even lower value) the value of the respective enemy object will be assigned. If a continuos capturing move ends with a pawn queening, this could bring another 9cps (1/100 the value of the queen, or whatever). Capturing the enemy king will not be considered (but you might experiment by assigning points double those of capturing a queen, with the move ending there).

The suggestion would be that sometimes that might make a difference, and that not always the number of attacks is equivalent to their efficiency. Sometimes, a lower number of attacks might carry bigger attacking/capturing efficiency with it.

[d]r1bq1rk1/1p2p1bp/2n5/1NppN1p1/p2Pnp2/PP2P1P1/2PB1PBP/1R1QR1K1 w - - 0 1

For example, on the above diagram, the black knight on e4 could have the following continuous capturing moves at its disposal:
- g3, done
- d2-b1-a3-b5-d4-b3, done
- d2-b3-d4-c2-e3-d1-f2, done, etc.

How relevant such a factor in complicated positions with a large number of attacks could be might be demonstrated by the capturing capacity of the black and white pawns on the diagram. With both sides' pawns attacking an equal number of enemy pawns (4 each), the attacking efficiency of the black pawns measured in the above-mentioned way is significantly better than that of the white pawns. In a certain type of position, that could already make the distinction.

The white pawns capture just 6cps worth of material along their continuos capturing moves: b3a4, done, d4c5, done, e3-f4-g5, done, g3-f4-g5, done.
At the same time the black pawns would capture the equivalent of some 93.5cps, an astonishing difference!
Possible continuos capturing moves for the black pawns:

- a4-b3-c2-b1Q
- a4-b3-c2-d1Q
- c5-d4-e3-d2-e1Q
- c5-d4-e3-f2-e1Q
- f4-e3-d2-e1Q
- f4-g3-f2-e1Q
- f4-g3-h2

In this way, one might assert that number of attacks and potential attacking/capturing efficiency of those attacks are not one and the same thing. In different situations that might be true for pieces, as well as pawns.

Here I will not appreciate any comments, because it is too complicated for me to further discuss this topic.

Best, Lyudmil

[Lyudmil Tsvetkov]

I am sorry that no one posted here, even a tentative feedback (for example, why it is not possible for engines to introduce a similar approach because of technical considerations).

What I know for sure is that probably some 15-20% of all positions could objectively be played along the lines of compensation. That is maybe the largest still almost completely unexplored field in chess. Knowledge of such positions could bring entertainment, originality and a lot of points.

But, of course, playing similar types of positions is a very complex affair. Of human players up to this day, maybe some games with genuine compensation motives could be found only among the games collections of Kasparov and Carlsen. Of electronic players, Stockfish is about the only engine I have encountered that has some understanding of the concept (but maybe because of a partly speculative approach, or extremely efficient search). Other engines completely ignore play along similar lines, they would like to see something concrete, sacrificed material won back, but in many situations that is about impossible to achieve, as the real compensation would surface in probably some 30-40-50 moves. Thus, all those interesting and promising positions are skipped.

I am convinced this, along with a couple of other position types, is the chess of the future.