A balanced approach to imbalances

[hgm]

I don't know if black could have won this, and which move was the mistake that lead to a draw instead of a win, if there is any such single mistake here.

I don't think that it is so much a matter of a wrong move, but more of a wrong strategy. I remeber now that to make QueeNy play well with the Knights, I had to remove all of its King safety. The key to winning is to gang up with all the Knights against the opponent King. You don't have sufficient power to overwhelm the defences of the latter if you have to keep some Knights back to protect your own King. So the King must not be afraid to march to the center, surrounded by its army of Knights. In fact it must even be encouraged to do so, counting the tactical ability of the engine to provide sufficient protection to keep the King safe. So QueeNy uses the end-game PST for the King from the start.

The point in the game where it goes wrong is in the 5-vs-2 stage, when the Knights leave the King completely unprotected behind, and the Queens then attack from behind, so that it can only be saved at the expense of a hastily withdrawn Knight. If the King would have marched together with the cavalary, such a thing would never happen.

[hgm]

Intuition does not suck, actually intuition, judging by the Latin word it is derived from, means insight, careful concentration, higher knowledge. People who have intuition by definition know more than people who do not have it, because intuition is based on fact and is the product of either genetic, naturally conditioned factors (like astrological influences), or hard labour.

Well, it seems then that you take your intuition as an infallibe oracle, and that your claims about advantages in chess positions indeed should be considered at the same level as the daily horoscope in the newspaper...

I think the engines simply play bad with such an unnatural imbalance for which they have no knowledge. I analysed a bit the position with the 2 queens and 5 knights (where the knights are still excellently placed), and did not in any way find a winning continuation for black, I do not know if white could win. My main line is as follows:
1. b3 Nbd5 2.g3 a5 3. c4 Ne7 4.Qe3 Nef5 5. Qc3 Ned4 6.a3 Nde4 7.Qe1 g5 8.b4 ab4 9.ab4 b5 10.cb5 Nb5 11.Qc2 Ncd4 12.Qce4 Ne4 13.Qe4 Kg7 14.Kf1, and you tell me what happens here, I do not think black can win.

[d]8/2p2pk1/7p/1n3np1/1P1nQ3/6PP/5P2/5K2 b - - 0 14

But again, at the beginning of the game the black knights were excellently placed in distinction to the white queens.

Yes, the Knights are well placed here (although having Pawns on both wings is a well-know factor that disadvantages Knights, and you placed so many of them on each wing that they are not likely to disappear before you get to the one-Queen stage...), and yes, the engines do play it badly.

But your line is full of ambiguous moves, and I don't feel like sorting it out. As long as the black moves were also played by you, the value of the final position is completely meaningless, and if it is not won to black it proves at best that your main line sucks.

Note furthermore that I never claimed that 5 Knights in general have the advantage over 2 Queens. If I would have to make an assessment based on scarce empirical information, I would say they are about equal. Meaning that sometimes the Knights win, sometimes the Queen, and many factors (such as the Pawn structure) could swing the statstical advantage to one or the other. (And in individual games, blind chance would play a major role.)

Which of course leaves plenty to explain, as the classical value of 5 Knights is only 5x3 = 15, while 2 Queens are 2x9 = 18. So naive additive material evaluation suggests that the Knights are about 1 Knight short of equality, which usually would be an totally losing disadvantage. And the further bonus that your writings claim for the pair of Queens seems another astrological myth, working in the opposite direction of what is needed in real life.

If there is some point about the elephantiasis effect, it is that the extremely large number of pieces of lower power (absolutely unrealistic with any game situation) by definition defend each other well, so that it is difficult to attack them, while they can attack the enemy while being defended. But this is all about defending bonus points, nothing more. For example 7N vs 3 Q is better for the knights than 5 knights vs 2Q, for the simple reason that the knights defend each other better by definition when in a large quantity. Similarly, 5N vs 2Q is better for the knights than 3N vs 1Q, as you can judge by the positions and the necessity of the queen side to exchange. With a low number of minors, the rule already does not hold true, as the minors already do not defend each other, although theoretically they should still be able to interdict queen activity. It is as simple as that, it is all about mutual defence.

Now this is at least a conjecture that can be tested. Let me first remark that 'mutual defense' is of course one aspect of interdiction: the Knights can take shelter on squares that are interdicted to the Queens by other Knights, so they cannot be captured. But interdiction is more, and in many cases can cause that the Knights cannot even be attacked by the Queens. This is for instance used to keep the King safe (against 3 Queens!) while marching to the center, as protection is not really helpful on Kings.

Now the crucial test that can distinguish your 'mutual defense' theory from the theory of the elephantasis effect is this:

Take a set of positions of 3 Knights versus a Queen that are about equal (using number or quality of Pawns to tune this). No doubt the Knights benefit from mutual defense, like the Queen benefits from her higher mobility, but you balanced that out by other circumstances.

Now add a Queen to each side, or better yet, two Queens. So that it becomes 3Q vs 2Q+3N. Who has the advantage now? There are still only 3 Knights, so their 'mutual defense' has not gone up. The elephantiasis theory, however, predicts that the extra Queens for the Queen side are devaluated by the presence of the opposing Knights, while the extra Queens of the Knights side do not suffer a similar drawback. (With 3 Queens plus King can for instance be forked by a Knight in 6 different combinations, where with only 1 Queen she had to worry only about one possible fork. In fact the extra Queens have become a liability, rather than an asset.) So the predictions of both theories are clearly different.

Now when you thorougly investigate this, by playing thousands of engine-engine games from such positions, as I have done, and not just by devine revelation, astrogical wizardry or brainwave intuition, you will see that it is the elephantiasis theory that makes the correct prediction. The extra Queens disadvantage the Queen side. (And as everyone can determine that easily for himself, I am NOT going to post any games on it.) Now explain that!

Regarding the new position you posted, I think the black king shelter, with 7 knights in it, is much safer than the white one, so black is better even in terms of king safety. But I will again say it is a draw at most.

Yeah, sure. The Knights are weaker, and it is just because they protect each other better, provide stronger King shelter, make multiple attacks on Pawns that cannot be effectively protected, fork the Queens, checkmate the opponent King, and more of such naughty mischieve that they always win. But they are weaker for sure! Wake up to reality: this is what Knights do...

Making an impenetrable fortress wouldn'thelp them to a win, btw. If you let QueeNy play the Knights here it immedialy starts breaking down the fortress, to march its King and Knights to the center. So the King fortress isn't really a factor. What is a factor is that in the initial position all Knights are now sufficiently protected, so that the Queens don't have any quick tactics to force a trade, and QueeNy can itself decide how to safely deploy them, rather than getting a position dumped in its lap where it immediately loses two Knights just because your intuition tells you that it is such a great position.

[hgm]

The question is if 7 knights are strong or maybe 3 queens are weak.
I wonder if white is winning in the following positions when white has no queens and computers evaluates white as better based on common material values.

[d]nnnnknnn/pppppppp/8/8/8/8/PPPPPPPP/RNB1KBNR w - - 1 1

[d]nnnnknnn/pppppppp/8/8/8/8/PPPPPPPP/RR2KRRR w - - 1 1

Yes, these are good questions. Without really having investigated the matter, I would say that in the first position white should have little trouble: it has enough minors itself to trade away any pushy Knight of the opponent. While it is easy to deploy 7 Knights such that they are impervious to Queen attack for 2-vs-1 trading (because twice protected), there is no way to protect them from 1-vs-1 trading without keeping them locked up and not using them. So basically there is an easy 'trading gradient' towards 3N vs 2R, which (according to normal Chess logic, which should now apply) should be about equal.

The second position is more difficult to predict. I haven't investigated it, and QueeNy wouldn't be the right tool to do it, as I only upped the Knight & Bishop value it uses, not the Rook value, so that it considers Knights more valuable then Rooks. While 1-vs-1 N for R trades are the obvious winning path for the Knights here, while 2N-vs-1R trades are the winning path for the Rooks. (Which is not unlike what normal engines should think, so I guess these could be used to evaluate the position.) Like against the Queens, 7 Knights should be able to prevent the latter, however. Forcing a R-vs-N trade is of course much less helpful for the Knights than forcing a Q-vs-N trade. But that is of course incorporated in the elephantiasis theory by devaluating a Rook much les by the presence of the same number of Knights than a Queen.

But the rational approach to this would be to fit the parameters of the elephantiasis theory by empirical evaluation of such extreme positions (where the contribution of the terms is largest). If there is nothing to it, all parameters will simply converge on zero in that case. In fact one could fit a general second-order polynomial function, containing cross terms between all (colored) piece types (where unlike Bishops are treated as different piece types), as well as square terms.

[Lyudmil Tsvetkov]

Well, it seems then that you take your intuition as an infallibe oracle, and that your claims about advantages in chess positions indeed should be considered at the same level as the daily horoscope in the newspaper...

Well, I will not go into astrological details. But a matter of fact is, for example, that the current WC match Carlsen-Anand features 2 Scorpios.

Yes, the Knights are well placed here (although having Pawns on both wings is a well-know factor that disadvantages Knights, and you placed so many of them on each wing that they are not likely to disappear before you get to the one-Queen stage...), and yes, the engines do play it badly.

You are wrong here: pawns on both wings disadvantage knights in normal situations, for the simple reason that they are attackable, but not in this extraordinary situation, when the pawns can easily be defended by the large number of knights. Therefore, this rule does not hold true here. Why do you take it out of the context?

But your line is full of ambiguous moves, and I don't feel like sorting it out. As long as the black moves were also played by you, the value of the final position is completely meaningless, and if it is not won to black it proves at best that your main line sucks.

Moves for both sides were played by me, the final position is not won for black, and I think rightly so, because black does not have more than a draw in the initial position. Please note, that although I easily admit I play much weaker tactically than most engines, I would argue that it is possible that I handle a range of positions (as well as many other humans), for which engines do not have specific knowledge, better than them. It is actually very probable that engines that do not have any particular knowledge about playing an imbalance of 7 knights vs 3 queens misplay it badly. Something wrong will go with the search when evaluation is not appropriate. If engines do not know what is valuable and what not, what and where to change, what pawn structure is best with such an imbalance, chances are big that they will play it wrong. And indeed, if you do not try exhanging Q for 2Ns at the earliest possibility and somehow limit the mobility of knights close to the own king with the help of pawns, the Q side is bound to fail. If you know what strategy to follow, you might achieve something better. I still claim the 5 Ns vs 2Qs position, with some psqt advantage for the knights, is a draw at most, while the position Lucas posted lately is a win for white with correct play.

Note furthermore that I never claimed that 5 Knights in general have the advantage over 2 Queens. If I would have to make an assessment based on scarce empirical information, I would say they are about equal. Meaning that sometimes the Knights win, sometimes the Queen, and many factors (such as the Pawn structure) could swing the statstical advantage to one or the other. (And in individual games, blind chance would play a major role.)

So that you actually acknowledge that the 5Ns do not win against the 2Qs.

Which of course leaves plenty to explain, as the classical value of 5 Knights is only 5x3 = 15, while 2 Queens are 2x9 = 18. So naive additive material evaluation suggests that the Knights are about 1 Knight short of equality, which usually would be an totally losing disadvantage. And the further bonus that your writings claim for the pair of Queens seems another astrological myth, working in the opposite direction of what is needed in real life.

I already told you, but it seems you did not pay attention to this: 7 knights, or even 5 knights, by definition defend each other extremely well. I would say 7 knights would defend themselves 10-12 times at least. If you score defending bonus points with some 1/10 the value of the piece defended, that would make an additional immaterial defence bonus in the range of 10x30cps= full3 pawns material. I.e., defence matters. It is a very simple and very true explanation. But at the same time you did not answer why you claim that the knights would interdict access of queens to squares on the board, when I showed with counting mobile squares in the 3 diagrams I posted that mobility even with this strange imbalance is still a function of centralisation (quite explicable, as the piece values themselves are a function of a measurement of average mobility performance on an empty board), while at the same time in all 3 positions the knights enjoy extremely good defence. So that, actually, elephantiasis is due to unnaturally high mutual piece defence (with its corresponding bonus points), and not to square interdiction. Would you admit your theory was wrong?

And the further bonus that your writings claim for the pair of Queens seems another astrological myth, working in the opposite direction of what is needed in real life.

More than 1 queens really deserve a bonus for their unusual interaction on the board and increase in speed of attacking operations, but in a normal environment. Please note, that a position with 3 queens is much more normal than a position with 7 knights. In the particular imbalance situation the attacking speed of the queens is already irrelevant, as they more or less have nothing to attack, as all objects of the knights side, including the king, are extremely well defended. So that, yes, more than 1 queen deserve a bonus, but not here, as their efficiency here vanishes. Again, you have to specify further.

Now add a Queen to each side, or better yet, two Queens. So that it becomes 3Q vs 2Q+3N. Who has the advantage now? There are still only 3 Knights, so their 'mutual defense' has not gone up. The elephantiasis theory, however, predicts that the extra Queens for the Queen side are devaluated by the presence of the opposing Knights, while the extra Queens of the Knights side do not suffer a similar drawback. (With 3 Queens plus King can for instance be forked by a Knight in 6 different combinations, where with only 1 Queen she had to worry only about one possible fork. In fact the extra Queens have become a liability, rather than an asset.) So the predictions of both theories are clearly different.

Now when you thorougly investigate this, by playing thousands of engine-engine games from such positions, as I have done, and not just by devine revelation, astrogical wizardry or brainwave intuition, you will see that it is the elephantiasis theory that makes the correct prediction. The extra Queens disadvantage the Queen side. (And as everyone can determine that easily for himself, I am NOT going to post any games on it.) Now explain that!

Now, this is very easy to explain, moreover that the suggested imbalance of 3Qs vs 2Qs + 3Ns is of practical importance, or iny case somewhat realistic.
Indeed, my theory would also hold that 2Qs +3Ns have the advantage over 3Qs. In the first place, you consider complementarity. In the 2Qs + 3Ns you have 3 piece capacities - linear and diagonal in the queens and knight capacity. In the 3Qs you have just 2 capacities - linear and diagonal in the queens, so that the knights and queens complement themselves better. Furthermore, as I told you, you always have to specify further: and in the present case, according to my theory, you would dispense a bonus for 3Qs, but also a bonus for 2Qs, and when you have an imbalance of 3Qs vs 2Qs it is quite possible that additional queen bonus points are even not due. It is a matter of further necessary specification. So that this quite easily explains it - the 2Qs + 3Ns, for once complement better, and twice, the 3Ns still offer excellent defence, including as a shelter to the king. With no pawns, or few pawns, I think the side with the 3Qs will suffer greatly from a lack of king shelter, while the side with knights will have one.

The thing that I do not understand is how elephantiasis sufficiently explains the imbalance, as there are only 3 knights, so that its impact would be minimal at most.

Making an impenetrable fortress wouldn'thelp them to a win, btw. If you let QueeNy play the Knights here it immedialy starts breaking down the fortress, to march its King and Knights to the center. So the King fortress isn't really a factor. What is a factor is that in the initial position all Knights are now sufficiently protected, so that the Queens don't have any quick tactics to force a trade, and QueeNy can itself decide how to safely deploy them, rather than getting a position dumped in its lap where it immediately loses two Knights just because your intuition tells you that it is such a great position.

I would enjoy a further analysis of some more equal position with this imbalance, for example the position Lucas posted. I think white has excellent chances there. Having 7 knights in the king shelter and white king shelter in the center, where it is easiest to attack it, is not a very equal position.

[Lyudmil Tsvetkov]

I post again the 3 positions with Ns-Qs imbalance.

[d]8/2p2pk1/7p/1n3np1/1P1nQ3/6PP/5P2/5K2 b - - 0 14

Here I count 10 mobile squares for the Q and 8 for the Ns, with both sides almost optimally placed, i.e. equally

[d]6k1/ppp2pp1/1nnnnn1p/8/8/7P/PPP2PP1/3QQ1K1 w - - 0 1

Here I count 12 mobile squares for the Qs, and 26 for the Ns, with the knights placed much more centrally

[d]2n2nk1/n1p1nnp1/1n3p1n/8/1P1PQ3/1Q3P2/3Q4/6K1 w - - 0 1

Here I count 32 mobile squares for the Qs, and 15 for the Ns, this time with the queens placed much more centrally.

Again, elephantiasis, to the point where it is valid in positions with extremely large amount of pieces of lower power, is not a function of square interdiction, as mobility in the 3 positions is directly proportional to centralisation, but to abundant, unusually high mutual piece defence. While mobility changes with centralisation in the 3 positions, in all 3 diagrams the knights enjoy unsually high piece defence (in one of the cases knights are defended by pawns).

[d]2n2nk1/n1p1nnp1/1n3p1n/8/1P1PQ3/1Q3P2/3Q4/6K1 w - - 0 1
Count this one, the knights are defended 8 times in all, and in the center that number will rise further! But their mobility is still lower than the queens', because they are less centralised (I count only safe mobile squares).

In this way, I would be willing to admit certain relevance of the rule, but only to the point where it is connected to piece defence. An extremely large number of pieces of lower power not only would defend each other, but even more importantly defend almost all available friendly pawns, so that penetration for the other side becomes very difficult. But again, this would be valid only in situations with unnaturally high number of pieces of lower power. In normal situations, in distinction to a posistion with 7 knights where the knights by definition defend each other well, a queen would always be stronger than 3 minors (excluding the bishop pair), i.e., stronger than 3 knights, and stronger than 2 knights + bishop. Of course, if the pawns and minor pieces defend each other well, the minors side might be better, but in most cases that will not be the case. In fact, I think a queen would be stronger than 2Ns + B in some 70-80% of cases. And also stronger than 3Ns (although unnatural), in a similar amount of cases.

For people liking extreme experience, I recommend coming to grasps with the following diagram, the most natural imbalance of Q vs 3Ns. I guess the white side has some advantage here, but do not know if winning.

[d]1nn1k1n1/pppppppp/8/8/8/8/PPPPPPPP/3QK3 w - - 0 1

[Lyudmil Tsvetkov]

I modified the starting position:
* turn all black pieces into knights
* changed white rooks into queens and removed its minor pieces

It was quite a fascinating game to watch:
[pgn]
[White "Discocheck"]
[Black "Discocheck"]
[Result "1/2-1/2"]
[FEN "nnnnknnn/pppppppp/8/8/8/8/PPPPPPPP/Q2QK2Q w - - 0 1"]

1. b3 Nfe6 2. g4 Kf8 3. h4 Nab6 4. a4 c5 5. a5 Na8 6. f4 Nbc6 7. f5 Nec7 8.
e4 e6 9. Qg1 d6 10. c3 Nc8e7 11. Qf3 exf5 12. gxf5 Nf6 13. d4 Nce8 14. Kd1
cxd4 15. cxd4 Nac7 16. d5 Ne5 17. Qe2 a6 18. Kc2 Nfg4 19. Kc1 f6 20. Kb2 g6
21. fxg6 hxg6 22. h5 gxh5 23. Qh1 f5 24. Qxh5 Nhf7 25. exf5 Nef6 26. Qhh1
Nf2 27. Qh4 Nfd3+ 28. Kb1 Nexd5 29. Qg3 Nb5 30. Qexd3 Nxd3 31. Qxd3 Ne5 32.
Qh3 Ndc6 33. Qb2 Nxa5 34. Qh8+ Ke7 35. Qc8 Ne4 36. Qh2 Nbc3+ 37. Ka1 Nxb3+
38. Kb2 Nbc5 39. Qh7+ Nf7 40. Qhg8 Kf6 41. Qce8 Kxf5 42. Qgxf7+ Ndf6 43.
Qg6+ Kf4 44. Qh6+ Kf3 45. Qeg6 Nd1+ 46. Kb1 Ndf2 47. Qc1 Ncd3 48. Qc7 Ndc5
49. Qe7 Kf4 50. Qh6+ Kf5 51. Ka1 b5 52. Qe3 Nfd3 53. Qh3+ Kg5 54. Qf7 Kf4
55. Qe7 Kg5 56. Qg2+ Kf5 57. Qf1+ Kg6 58. Qg2+ Kf5 59. Qf1+ Kg6 60. Qg1+
Kf5 61. Qh2 b4 62. Qh3+ Kg5 63. Qf7 b3 64. Qe3+ Kf5 65. Qc4 a5 66. Qh3+ Kg6
67. Qg2+ Kf5 68. Qf1+ Ke5 69. Qe2 a4 70. Kb1 a3 71. Qh2+ Kf5 72. Qh3+ Kg6
73. Qg2+ Kf5 74. Qf3+ Kg6 75. Qg2+ Kf5 76. Qf3+ Kg6 77. Qcxd3 Nxd3 78. Qxd3
Kg5 79. Ka1 Nc5 80. Qxd6 Nfe4 81. Qb8 Kg4 82. Qb4 a2 83. Qe1 Kf4 84. Qh4+
Ke3 85. Qh3+ Kd4 86. Qh8+ Kc4 87. Qh4 Kd4 88. Qh8+ Kd3 89. Qb2 Ke3 90. Qh2
Nc3 91. Qe5+ Kd3 92. Qf5+ N3e4 93. Qe5 Nc3 94. Qg3+ Kc4 95. Qh4+ N3e4 96.
Qg4 Kc3 97. Qg2 Kc4 98. Qe2+ Kd4 99. Qb2+ Nc3 100. Qf2+ Kd3 101. Qf1+ Kd4
102. Qf7 Nd5 103. Qg7+ Ke4 104. Qg6+ Kd4 105. Qg4+ Kd3 106. Qg6+ Kc4 107.
Qg4+ Kd3 108. Qd1+ Kc4 109. Qg4+ Kb5 110. Qe2+ Kb4 111. Qe8 Nd3 112. Qe4+
Kc3 113. Qg4 Nc5 114. Qg8 Nd3 115. Qg4 Nb6 116. Qg7+ Kc4 117. Qc7+ Kb5 118.
Qf7 Nc5 119. Qe8+ Kc4 120. Qe2+ Kd4 121. Qg4+ Kd5 122. Qg8+ Kc6 123. Qg5
Kb5 124. Qg4 Nd5 125. Qh5 Nc3 126. Qh4 N3e4 127. Qd8 Kc4 128. Qe8 Nc3 129.
Qg8+ Kd4 130. Kb2 Nd3+ 131. Kxb3 a1=Q 132. Qc4+ Ke3 133. Qxc3 Qa8 134. Kc4
Qa4+ 135. Kd5 Qb5+ 136. Kd6 Qb8+ 137. Ke7 Qg8 138. Kd7 Qb8 139. Ke7 Qb6
140. Kd7 Qb7+ 141. Kd6 Qa6+ 142. Kc7 Qa7+ 143. Kd6 Qb7 144. Ke6 Qg2 145.
Kd6 Qg3+ 146. Kd7 Qf4 147. Ke7 Qe4+ 148. Kd6 Qf4+ 149. Kd7 Qa4+ 150. Kc7
Qf4+ 151. Kd7 Qh2 152. Ke7 Qh6 153. Qf6 Qh7+ 154. Kd6 Qh2+ 155. Kc6 Qc2+
156. Kb6 Qc5+ 157. Kb7 Qd5+ 158. Qc6 Qe5 159. Qc4 Nf4 160. Qb3+ Ke4 161.
Qc2+ Kf3 162. Qb3+ Ke2 163. Qc2+ Kf3 164. Qb3+ Kg4 165. Kc6 Qe8+ 166. Kc5
Kg5 167. Qc4 Qd7 168. Kb4 Nd5+ 169. Kb3 Qh3+ 170. Kb2 Qh8+ 171. Ka2 Qe5
172. Qc1+ Ne3 173. Qg1+ Kf5 174. Qf2+ Kg4 175. Qe2+ Kg5 176. Qb2 Qc7 177.
Qb5+ Nf5 178. Qb2 Kh4 179. Qb3 Nd6 180. Qb2 Nf5 181. Qb3 Nd6 182. Qb2 Nf5
1/2-1/2
[/pgn]
Although it ended in a draw, it is clear that black had the better side of it. The problem however, is that in order to win, black must find a way to shield his king from constant perpetual check threats, while pushing his passed pawns to promotion.

I don't know if black could have won this, and which move was the mistake that lead to a draw instead of a win, if there is any such single mistake here.

I think white should be better here.
I would play with a strong pawn center for white, but first of all I would place my king to safety on g1, for example after 1.g3, Qf3, Kf1-g1. Disco leaves its king in the center and that creates quite some trouble. I would also change a queen for 2 knights at the first opportunity, and a second queen for another 2 knights at the next opportunity. In this way black already would not defend itself too well.

[hgm]

You are wrong here: pawns on both wings disadvantage knights in normal situations, for the simple reason that they are attackable, but not in this extraordinary situation, when the pawns can easily be defended by the large number of knights. Therefore, this rule does not hold true here. Why do you take it out of the context?

That is not how Chess works. Having Pawns on both wings is a strategic trait, i.e. one that is not likely going to change in the subsequent play, which eventually will trade down the abundance of pieces to modest proportions, where the rule will apply. It makes a huge difference whether after trading Q for 2N a won or a lost position remains. It is quite hard for 3 Knights to defend against a Queen, with Pawns on both wings. While with connected Pawns (or even just a single one) the King and Knights would march up as a single unstoppable army, supporting the Pawn to promotion and clearing its way, as could be seen in one of the games I posted. It makes all the difference in the world if the only trade you might have hope to force will leave you in a won or a lost position!

..., I would argue that it is possible that I handle a range of positions (as well as many other humans), for which engines do not have specific knowledge, better than them.

Well, 'is possible' in no proof of any kind. It is also possible that you completely mishandle them. To prove anything, you should first let the engine (in particular QueeNy) play the Knights, and only after you would win that with the Queens there would be any reason to cast doubt on the abilities of the engine and suggesting you could do better. Just starting with your own lousy moves because "it is possible that you handle it better" is not going to cut it.

It is actually very probable that engines that do not have any particular knowledge about playing an imbalance of 7 knights vs 3 queens misplay it badly. Something wrong will go with the search when evaluation is not appropriate. If engines do not know what is valuable and what not, what and where to change, what pawn structure is best with such an imbalance, chances are big that they will play it wrong.

So use QueeNy, which does have such knowledge, and is tuned for playing well with Knights in 7-3, and with Queens in 6-3, and as well as can be expected in a badly lost position with Queens in 7-3. Only when that loses for a given side there is reason to find improvements by hand for the side that lost. And no reason at all to start bungling it by playing moves yourself for the side that won.

And indeed, if you do not try exhanging Q for 2Ns at the earliest possibility and somehow limit the mobility of knights close to the own king with the help of pawns, the Q side is bound to fail. If you know what strategy to follow, you might achieve something better.

Well, at least we agree about that. Which, like I said before, is an admission on your part that in these kind of positions the marginal value of a Queen is less than the marginal value of two Knights. With does beg for an explanation.

I still claim the 5 Ns vs 2Qs position, with some psqt advantage for the knights, is a draw at most, while the position Lucas posted lately is a win for white with correct play.

A claim without proof... Show us a game that the Queens won without bungling it yourself for the Knights! And even then, it could just be because the Pawns-on-both-wings position disadvantage the Knights. Even if you don't believe it, I claim that with connected Pawns the Knights would win much easier, and that to really prove anything, you should show a win for the Queens from
[d]1nnnknn1/2pppp2/8/8/8/8/2PPPP2/3QKQ2 w
If you are right about that being worse for the Knights, it should only make it easier!

So that you actually acknowledge that the 5Ns do not win against the 2Qs.

Do not always win. Yes, of course. I said that from the beginning. This is why arguing about the 5-2 case is such an utter waste of time. 5-vs-2 is about equal, which is amazing enough in itself (additive evaluation 18-15 in favor of the Queens). Meaning there are many quiet positions where the Knights would win, but about equally many where the Queens would win. Equality is by no means a synonym for 'certain draw'.

I already told you, but it seems you did not pay attention to this: 7 knights, or even 5 knights, by definition defend each other extremely well. I would say 7 knights would defend themselves 10-12 times at least. If you score defending bonus points with some 1/10 the value of the piece defended, that would make an additional immaterial defence bonus in the range of 10x30cps= full3 pawns material. I.e., defence matters.

I thought I did respond to that. What you propose here is essentially a term in the evaluation that is quadratic in the number of Knights. My criticism was that such a term could not explain another empirical fact: why with Q vs 3N the advantage lies with the Q, while with 3Q vs 2Q+3N it would lie with the Knights.

It is a very simple and very true explanation. But at the same time you did not answer why you claim that the knights would interdict access of queens to squares on the board, when I showed with counting mobile squares in the 3 diagrams I posted that mobility even with this strange imbalance is still a function of centralisation (quite explicable, as the piece values themselves are a function of a measurement of average mobility performance on an empty board), while at the same time in all 3 positions the knights enjoy extremely good defence. So that, actually, elephantiasis is due to unnaturally high mutual piece defence (with its corresponding bonus points), and not to square interdiction. Would you admit your theory was wrong?

Seems to me you are confusing strategic traits with tactical traits. Of course centralization is important for Knights, like mobility is for Queens. But it is a tactical concern, as inactively placed Knights will eventually move towards the center, to achieve their full potential, without the Queen side being able to prevent it. It is just a matter of time. That the mutual defense is already large in all discussed positions is because you selected them that way. And like I said before, it is just one aspect of the interdiction effect, which interdicts access to both empty and occupied squares, the latter being synonymous for 'mutual defense'.

In the following position there is zero mutual defense. And no engine playing white ever stood any chance against QueeNy playing black, not even QueeNy versions with 10 times longer thinking. It is utterly lost for white.
[d]nnnnknnn/pppppppp/8/8/8/8/PPPPPPPP/1Q1QK1Q1 w

More than 1 queens really deserve a bonus for their unusual interaction on the board and increase in speed of attacking operations, but in a normal environment. Please note, that a position with 3 queens is much more normal than a position with 7 knights. In the particular imbalance situation the attacking speed of the queens is already irrelevant, as they more or less have nothing to attack, as all objects of the knights side, including the king, are extremely well defended. So that, yes, more than 1 queen deserve a bonus, but not here, as their efficiency here vanishes. Again, you have to specify further.

These are just words, astrological mumbo-jumbo not backed up by proof. I am sure it is what you think, but considering your track record of judgement of N vs Q positions, why would I lend that any credibility?

Now, this is very easy to explain, moreover that the suggested imbalance of 3Qs vs 2Qs + 3Ns is of practical importance, or iny case somewhat realistic.
Indeed, my theory would also hold that 2Qs +3Ns have the advantage over 3Qs. In the first place, you consider complementarity. In the 2Qs + 3Ns you have 3 piece capacities - linear and diagonal in the queens and knight capacity. In the 3Qs you have just 2 capacities - linear and diagonal in the queens, so that the knights and queens complement themselves better. Furthermore, as I told you, you always have to specify further: and in the present case, according to my theory, you would dispense a bonus for 3Qs, but also a bonus for 2Qs, and when you have an imbalance of 3Qs vs 2Qs it is quite possible that additional queen bonus points are even not due. It is a matter of further necessary specification. So that this quite easily explains it - the 2Qs + 3Ns, for once complement better, and twice, the 3Ns still offer excellent defence, including as a shelter to the king. With no pawns, or few pawns, I think the side with the 3Qs will suffer greatly from a lack of king shelter, while the side with knights will have one.

The thing that I do not understand is how elephantiasis sufficiently explains the imbalance, as there are only 3 knights, so that its impact would be minimal at most.

But elephantiasis is not a small effect. Note that even in the simple Q vs 3N case the Queen suffers from elephantiasis, so that renormalization of the base value is necessary to remain with the effective value at the classical 9. If the elephantiasis term would be c*nQ*nN, then the 'bare' Q value should be 9+3*c. If for the sake of argument we consider 5N vs 2Q, where the elephantiasis term is c*2*5 = 10*c as equality, it would mean that 2*(9+3*c) - 10*c = 18-4*c = 5*3 = 15. So 4*c = 3, or c = 0.75.

The extra Queens of the Knight side, in absense of opponent Knights to devaluate them, would have their bare value, which is 3*c = 3*0.75 = 2.25 above that of the extra Queens for the opponent each. So the predicted effect could be as large as 4.5 Pawn, with this very course calculation. That is more than enough to cause complete reversal of the chances. (I have no doubt that using more precise values for N and Q values plus a more accurate determination how far 2Q vs 5N is from equality, would lower this prediction, as even to me it seems on the high side.)

As to your 'explanation': it seems to me you drag in a lot of new effects, each associated with a new and independent arbitrarily tunable parameter. With as many parameters as material composition one can of course always fit anything, but the predictive value is zero. It is symptomatic of 'sick science'. At least the elephantiasis theory makes numerical predictions about this whithout any mumbo-jumbo.

I would enjoy a further analysis of some more equal position with this imbalance, for example the position Lucas posted. I think white has excellent chances there. Having 7 knights in the king shelter and white king shelter in the center, where it is easiest to attack it, is not a very equal position.

Not sure I understand what you mean here. Which position are you referring to, and who exactly has the advantage there?

[Lyudmil Tsvetkov]

You are wrong here: pawns on both wings disadvantage knights in normal situations, for the simple reason that they are attackable, but not in this extraordinary situation, when the pawns can easily be defended by the large number of knights. Therefore, this rule does not hold true here. Why do you take it out of the context?

That is not how Chess works. Having Pawns on both wings is a strategic trait, i.e. one that is not likely going to change in the subsequent play, which eventually will trade down the abundance of pieces to modest proportions, where the rule will apply. It makes a huge difference whether after trading Q for 2N a won or a lost position remains. It is quite hard for 3 Knights to defend against a Queen, with Pawns on both wings. While with connected Pawns (or even just a single one) the King and Knights would march up as a single unstoppable army, supporting the Pawn to promotion and clearing its way, as could be seen in one of the games I posted. It makes all the difference in the world if the only trade you might have hope to force will leave you in a won or a lost position!

..., I would argue that it is possible that I handle a range of positions (as well as many other humans), for which engines do not have specific knowledge, better than them.

Well, 'is possible' in no proof of any kind. It is also possible that you completely mishandle them. To prove anything, you should first let the engine (in particular QueeNy) play the Knights, and only after you would win that with the Queens there would be any reason to cast doubt on the abilities of the engine and suggesting you could do better. Just starting with your own lousy moves because "it is possible that you handle it better" is not going to cut it.

It is actually very probable that engines that do not have any particular knowledge about playing an imbalance of 7 knights vs 3 queens misplay it badly. Something wrong will go with the search when evaluation is not appropriate. If engines do not know what is valuable and what not, what and where to change, what pawn structure is best with such an imbalance, chances are big that they will play it wrong.

So use QueeNy, which does have such knowledge, and is tuned for playing well with Knights in 7-3, and with Queens in 6-3, and as well as can be expected in a badly lost position with Queens in 7-3. Only when that loses for a given side there is reason to find improvements by hand for the side that lost. And no reason at all to start bungling it by playing moves yourself for the side that won.

And indeed, if you do not try exhanging Q for 2Ns at the earliest possibility and somehow limit the mobility of knights close to the own king with the help of pawns, the Q side is bound to fail. If you know what strategy to follow, you might achieve something better.

Well, at least we agree about that. Which, like I said before, is an admission on your part that in these kind of positions the marginal value of a Queen is less than the marginal value of two Knights. With does beg for an explanation.

I still claim the 5 Ns vs 2Qs position, with some psqt advantage for the knights, is a draw at most, while the position Lucas posted lately is a win for white with correct play.

A claim without proof... Show us a game that the Queens won without bungling it yourself for the Knights! And even then, it could just be because the Pawns-on-both-wings position disadvantage the Knights. Even if you don't believe it, I claim that with connected Pawns the Knights would win much easier, and that to really prove anything, you should show a win for the Queens from
[d]1nnnknn1/2pppp2/8/8/8/8/2PPPP2/3QKQ2 w
If you are right about that being worse for the Knights, it should only make it easier!

So that you actually acknowledge that the 5Ns do not win against the 2Qs.

Do not always win. Yes, of course. I said that from the beginning. This is why arguing about the 5-2 case is such an utter waste of time. 5-vs-2 is about equal, which is amazing enough in itself (additive evaluation 18-15 in favor of the Queens). Meaning there are many quiet positions where the Knights would win, but about equally many where the Queens would win. Equality is by no means a synonym for 'certain draw'.

I already told you, but it seems you did not pay attention to this: 7 knights, or even 5 knights, by definition defend each other extremely well. I would say 7 knights would defend themselves 10-12 times at least. If you score defending bonus points with some 1/10 the value of the piece defended, that would make an additional immaterial defence bonus in the range of 10x30cps= full3 pawns material. I.e., defence matters.

I thought I did respond to that. What you propose here is essentially a term in the evaluation that is quadratic in the number of Knights. My criticism was that such a term could not explain another empirical fact: why with Q vs 3N the advantage lies with the Q, while with 3Q vs 2Q+3N it would lie with the Knights.

It is a very simple and very true explanation. But at the same time you did not answer why you claim that the knights would interdict access of queens to squares on the board, when I showed with counting mobile squares in the 3 diagrams I posted that mobility even with this strange imbalance is still a function of centralisation (quite explicable, as the piece values themselves are a function of a measurement of average mobility performance on an empty board), while at the same time in all 3 positions the knights enjoy extremely good defence. So that, actually, elephantiasis is due to unnaturally high mutual piece defence (with its corresponding bonus points), and not to square interdiction. Would you admit your theory was wrong?

Seems to me you are confusing strategic traits with tactical traits. Of course centralization is important for Knights, like mobility is for Queens. But it is a tactical concern, as inactively placed Knights will eventually move towards the center, to achieve their full potential, without the Queen side being able to prevent it. It is just a matter of time. That the mutual defense is already large in all discussed positions is because you selected them that way. And like I said before, it is just one aspect of the interdiction effect, which interdicts access to both empty and occupied squares, the latter being synonymous for 'mutual defense'.

In the following position there is zero mutual defense. And no engine playing white ever stood any chance against QueeNy playing black, not even QueeNy versions with 10 times longer thinking. It is utterly lost for white.
[d]nnnnknnn/pppppppp/8/8/8/8/PPPPPPPP/1Q1QK1Q1 w

More than 1 queens really deserve a bonus for their unusual interaction on the board and increase in speed of attacking operations, but in a normal environment. Please note, that a position with 3 queens is much more normal than a position with 7 knights. In the particular imbalance situation the attacking speed of the queens is already irrelevant, as they more or less have nothing to attack, as all objects of the knights side, including the king, are extremely well defended. So that, yes, more than 1 queen deserve a bonus, but not here, as their efficiency here vanishes. Again, you have to specify further.

These are just words, astrological mumbo-jumbo not backed up by proof. I am sure it is what you think, but considering your track record of judgement of N vs Q positions, why would I lend that any credibility?

Now, this is very easy to explain, moreover that the suggested imbalance of 3Qs vs 2Qs + 3Ns is of practical importance, or iny case somewhat realistic.
Indeed, my theory would also hold that 2Qs +3Ns have the advantage over 3Qs. In the first place, you consider complementarity. In the 2Qs + 3Ns you have 3 piece capacities - linear and diagonal in the queens and knight capacity. In the 3Qs you have just 2 capacities - linear and diagonal in the queens, so that the knights and queens complement themselves better. Furthermore, as I told you, you always have to specify further: and in the present case, according to my theory, you would dispense a bonus for 3Qs, but also a bonus for 2Qs, and when you have an imbalance of 3Qs vs 2Qs it is quite possible that additional queen bonus points are even not due. It is a matter of further necessary specification. So that this quite easily explains it - the 2Qs + 3Ns, for once complement better, and twice, the 3Ns still offer excellent defence, including as a shelter to the king. With no pawns, or few pawns, I think the side with the 3Qs will suffer greatly from a lack of king shelter, while the side with knights will have one.

The thing that I do not understand is how elephantiasis sufficiently explains the imbalance, as there are only 3 knights, so that its impact would be minimal at most.

But elephantiasis is not a small effect. Note that even in the simple Q vs 3N case the Queen suffers from elephantiasis, so that renormalization of the base value is necessary to remain with the effective value at the classical 9. If the elephantiasis term would be c*nQ*nN, then the 'bare' Q value should be 9+3*c. If for the sake of argument we consider 5N vs 2Q, where the elephantiasis term is c*2*5 = 10*c as equality, it would mean that 2*(9+3*c) - 10*c = 18-4*c = 5*3 = 15. So 4*c = 3, or c = 0.75.

The extra Queens of the Knight side, in absense of opponent Knights to devaluate them, would have their bare value, which is 3*c = 3*0.75 = 2.25 above that of the extra Queens for the opponent each. So the predicted effect could be as large as 4.5 Pawn, with this very course calculation. That is more than enough to cause complete reversal of the chances. (I have no doubt that using more precise values for N and Q values plus a more accurate determination how far 2Q vs 5N is from equality, would lower this prediction, as even to me it seems on the high side.)

As to your 'explanation': it seems to me you drag in a lot of new effects, each associated with a new and independent arbitrarily tunable parameter. With as many parameters as material composition one can of course always fit anything, but the predictive value is zero. It is symptomatic of 'sick science'. At least the elephantiasis theory makes numerical predictions about this whithout any mumbo-jumbo.

I would enjoy a further analysis of some more equal position with this imbalance, for example the position Lucas posted. I think white has excellent chances there. Having 7 knights in the king shelter and white king shelter in the center, where it is easiest to attack it, is not a very equal position.

Not sure I understand what you mean here. Which position are you referring to, and who exactly has the advantage there?

You are wrong here: pawns on both wings disadvantage knights in normal situations, for the simple reason that they are attackable, but not in this extraordinary situation, when the pawns can easily be defended by the large number of knights. Therefore, this rule does not hold true here. Why do you take it out of the context?

That is not how Chess works. Having Pawns on both wings is a strategic trait, i.e. one that is not likely going to change in the subsequent play, which eventually will trade down the abundance of pieces to modest proportions, where the rule will apply. It makes a huge difference whether after trading Q for 2N a won or a lost position remains. It is quite hard for 3 Knights to defend against a Queen, with Pawns on both wings. While with connected Pawns (or even just a single one) the King and Knights would march up as a single unstoppable army, supporting the Pawn to promotion and clearing its way, as could be seen in one of the games I posted. It makes all the difference in the world if the only trade you might have hope to force will leave you in a won or a lost position!

..., I would argue that it is possible that I handle a range of positions (as well as many other humans), for which engines do not have specific knowledge, better than them.

Well, 'is possible' in no proof of any kind. It is also possible that you completely mishandle them. To prove anything, you should first let the engine (in particular QueeNy) play the Knights, and only after you would win that with the Queens there would be any reason to cast doubt on the abilities of the engine and suggesting you could do better. Just starting with your own lousy moves because "it is possible that you handle it better" is not going to cut it.

It is actually very probable that engines that do not have any particular knowledge about playing an imbalance of 7 knights vs 3 queens misplay it badly. Something wrong will go with the search when evaluation is not appropriate. If engines do not know what is valuable and what not, what and where to change, what pawn structure is best with such an imbalance, chances are big that they will play it wrong.

So use QueeNy, which does have such knowledge, and is tuned for playing well with Knights in 7-3, and with Queens in 6-3, and as well as can be expected in a badly lost position with Queens in 7-3. Only when that loses for a given side there is reason to find improvements by hand for the side that lost. And no reason at all to start bungling it by playing moves yourself for the side that won.

And indeed, if you do not try exhanging Q for 2Ns at the earliest possibility and somehow limit the mobility of knights close to the own king with the help of pawns, the Q side is bound to fail. If you know what strategy to follow, you might achieve something better.

Well, at least we agree about that. Which, like I said before, is an admission on your part that in these kind of positions the marginal value of a Queen is less than the marginal value of two Knights. With does beg for an explanation.

I still claim the 5 Ns vs 2Qs position, with some psqt advantage for the knights, is a draw at most, while the position Lucas posted lately is a win for white with correct play.

A claim without proof... Show us a game that the Queens won without bungling it yourself for the Knights! And even then, it could just be because the Pawns-on-both-wings position disadvantage the Knights. Even if you don't believe it, I claim that with connected Pawns the Knights would win much easier, and that to really prove anything, you should show a win for the Queens from
[d]1nnnknn1/2pppp2/8/8/8/8/2PPPP2/3QKQ2 w
If you are right about that being worse for the Knights, it should only make it easier!

So that you actually acknowledge that the 5Ns do not win against the 2Qs.

Do not always win. Yes, of course. I said that from the beginning. This is why arguing about the 5-2 case is such an utter waste of time. 5-vs-2 is about equal, which is amazing enough in itself (additive evaluation 18-15 in favor of the Queens). Meaning there are many quiet positions where the Knights would win, but about equally many where the Queens would win. Equality is by no means a synonym for 'certain draw'.

I already told you, but it seems you did not pay attention to this: 7 knights, or even 5 knights, by definition defend each other extremely well. I would say 7 knights would defend themselves 10-12 times at least. If you score defending bonus points with some 1/10 the value of the piece defended, that would make an additional immaterial defence bonus in the range of 10x30cps= full3 pawns material. I.e., defence matters.

I thought I did respond to that. What you propose here is essentially a term in the evaluation that is quadratic in the number of Knights. My criticism was that such a term could not explain another empirical fact: why with Q vs 3N the advantage lies with the Q, while with 3Q vs 2Q+3N it would lie with the Knights.

It is a very simple and very true explanation. But at the same time you did not answer why you claim that the knights would interdict access of queens to squares on the board, when I showed with counting mobile squares in the 3 diagrams I posted that mobility even with this strange imbalance is still a function of centralisation (quite explicable, as the piece values themselves are a function of a measurement of average mobility performance on an empty board), while at the same time in all 3 positions the knights enjoy extremely good defence. So that, actually, elephantiasis is due to unnaturally high mutual piece defence (with its corresponding bonus points), and not to square interdiction. Would you admit your theory was wrong?

Seems to me you are confusing strategic traits with tactical traits. Of course centralization is important for Knights, like mobility is for Queens. But it is a tactical concern, as inactively placed Knights will eventually move towards the center, to achieve their full potential, without the Queen side being able to prevent it. It is just a matter of time. That the mutual defense is already large in all discussed positions is because you selected them that way. And like I said before, it is just one aspect of the interdiction effect, which interdicts access to both empty and occupied squares, the latter being synonymous for 'mutual defense'.

In the following position there is zero mutual defense. And no engine playing white ever stood any chance against QueeNy playing black, not even QueeNy versions with 10 times longer thinking. It is utterly lost for white.
[d]nnnnknnn/pppppppp/8/8/8/8/PPPPPPPP/1Q1QK1Q1 w

More than 1 queens really deserve a bonus for their unusual interaction on the board and increase in speed of attacking operations, but in a normal environment. Please note, that a position with 3 queens is much more normal than a position with 7 knights. In the particular imbalance situation the attacking speed of the queens is already irrelevant, as they more or less have nothing to attack, as all objects of the knights side, including the king, are extremely well defended. So that, yes, more than 1 queen deserve a bonus, but not here, as their efficiency here vanishes. Again, you have to specify further.

These are just words, astrological mumbo-jumbo not backed up by proof. I am sure it is what you think, but considering your track record of judgement of N vs Q positions, why would I lend that any credibility?

Now, this is very easy to explain, moreover that the suggested imbalance of 3Qs vs 2Qs + 3Ns is of practical importance, or iny case somewhat realistic.
Indeed, my theory would also hold that 2Qs +3Ns have the advantage over 3Qs. In the first place, you consider complementarity. In the 2Qs + 3Ns you have 3 piece capacities - linear and diagonal in the queens and knight capacity. In the 3Qs you have just 2 capacities - linear and diagonal in the queens, so that the knights and queens complement themselves better. Furthermore, as I told you, you always have to specify further: and in the present case, according to my theory, you would dispense a bonus for 3Qs, but also a bonus for 2Qs, and when you have an imbalance of 3Qs vs 2Qs it is quite possible that additional queen bonus points are even not due. It is a matter of further necessary specification. So that this quite easily explains it - the 2Qs + 3Ns, for once complement better, and twice, the 3Ns still offer excellent defence, including as a shelter to the king. With no pawns, or few pawns, I think the side with the 3Qs will suffer greatly from a lack of king shelter, while the side with knights will have one.

The thing that I do not understand is how elephantiasis sufficiently explains the imbalance, as there are only 3 knights, so that its impact would be minimal at most.

But elephantiasis is not a small effect. Note that even in the simple Q vs 3N case the Queen suffers from elephantiasis, so that renormalization of the base value is necessary to remain with the effective value at the classical 9. If the elephantiasis term would be c*nQ*nN, then the 'bare' Q value should be 9+3*c. If for the sake of argument we consider 5N vs 2Q, where the elephantiasis term is c*2*5 = 10*c as equality, it would mean that 2*(9+3*c) - 10*c = 18-4*c = 5*3 = 15. So 4*c = 3, or c = 0.75.

The extra Queens of the Knight side, in absense of opponent Knights to devaluate them, would have their bare value, which is 3*c = 3*0.75 = 2.25 above that of the extra Queens for the opponent each. So the predicted effect could be as large as 4.5 Pawn, with this very course calculation. That is more than enough to cause complete reversal of the chances. (I have no doubt that using more precise values for N and Q values plus a more accurate determination how far 2Q vs 5N is from equality, would lower this prediction, as even to me it seems on the high side.)

As to your 'explanation': it seems to me you drag in a lot of new effects, each associated with a new and independent arbitrarily tunable parameter. With as many parameters as material composition one can of course always fit anything, but the predictive value is zero. It is symptomatic of 'sick science'. At least the elephantiasis theory makes numerical predictions about this whithout any mumbo-jumbo.

I would enjoy a further analysis of some more equal position with this imbalance, for example the position Lucas posted. I think white has excellent chances there. Having 7 knights in the king shelter and white king shelter in the center, where it is easiest to attack it, is not a very equal position.

Not sure I understand what you mean here. Which position are you referring to, and who exactly has the advantage there?

I will not bury my head into endless discussions about mumbo-jumbos, sick science, bungling, mishandling, etc. Moreover that you were not quite specific in your answers.

The only thing that is worth answering for me is the following abstract:

My criticism was that such a term could not explain another empirical fact: why with Q vs 3N the advantage lies with the Q, while with 3Q vs 2Q+3N it would lie with the Knights.

Well, because knights with queens complement better. In the Q vs 3Ns you have 2 capacities in the queen - diagonal and linear, and only one in the 3 knights. In the 3Qs vs 2Qs + 3Ns you have 2 capacities for the Q side, and 3 capacities for the Q+Ns side. This brings an added value. Actually, while with a single queen or 3 queens you still have 2 capacities, in the 3Ns you have only one capacity, but in the 2Qs + 3Ns you have full 3 capacities! That makes a difference of 2 capacities, and that is very important. Do you agree now with my explanation?

You still did not answer why you claim that the knights would interdict access of queens to squares on the board, when I showed with counting mobile squares in the 3 diagrams I posted that mobility even with this strange imbalance is still a function of centralisation (quite explicable, as the piece values themselves are a function of a measurement of average mobility performance on an empty board), while at the same time in all 3 positions the knights enjoy extremely good defence. So that, actually, elephantiasis is due to unnaturally high mutual piece defence (with its corresponding bonus points), and not to square interdiction. Would you admit your theory was wrong?

I must tell you that I have some problem with very scientific concepts like elephantiasis. Having a high-flown name does not necessarily mean having a big objective significance, although this is still possible. Usually though, simple things, simple names and a simple approach are truer and more natural. I imagine one day having a version of Stockfish_Elephantiasis.

To make things short, let us concentrate again on empirical research. Below are 3 positions:

[d]1nn1k1n1/pppppppp/8/8/8/8/PPPPPPPP/3QK3 w - - 0 1
I do not know why, but in my analysis games I win all with white. It seems that 1.d4 is the best move for white, and it seems that black loses fairly quickly. Do you agree that white is winning here?

[d]1nnnknn1/pppppppp/8/8/8/8/PPPPPPPP/2QQK3 w - - 0 1
2Qs vs 5Ns. Natural initial position with advantage for neither side in terms of immaterial factors. I do not why, but in my analysis games, I am winning most of the games with white. And I definitely think this is won for white. Do you agree with that?

[d]nnnnknnn/pppppppp/8/8/8/8/PPPPPPPP/Q2QK2Q w - - 0 1
3Qs vs 7Ns in a natural initial position. This is the Lucas position, but you might also use the position you posted with queens on b1 and g1. Do you agree that white is better here? I did not try analysing this extensively, as it is a bit complex, but I think it is still much better for white, although more difficult to play than the 2 other positions. Do you agree that white is better here? I think the fact that Disco managed to draw here points that the 2 other positions favour white even more, and maybe Disco did not play an optimal game for white (Lucas will excuse me, but I have my doubts). I think white is better even here.

So, let us concentrate on factual assessment to see who is right. Any third party posting games/analysis with these 3 positions would of course be of great help.

[Lyudmil Tsvetkov]

[d]1nn1k1n1/pppppppp/8/8/8/8/PPPPPPPP/3QK3 w - - 0 1

[d]1nnnknn1/pppppppp/8/8/8/8/PPPPPPPP/2QQK3 w - - 0 1

[d]nnnnknnn/pppppppp/8/8/8/8/PPPPPPPP/Q2QK2Q w - - 0 1

And again, these 3 positions would be an excellent test to understand if the large number of pieces of lower strength have an additional value because of their large number, or only in situations where they are able to defend both themselves, and the friendly pawns. I would argue that in a natural situation like those on the above diagrams, at least in the fist 2 diagrams white will win or have a significant advantage, because the black knights will not be able to organize and defend efficiently in a short time. If that is true, that would mean that elephantiasis is due to good piece defence, but not to the number of pieces.

I think the first 2 diagrams are fairly easy do solve, so that any engine output, especially at longer TC, would be very nice.

[hgm]

Well, because knights with queens complement better. In the Q vs 3Ns you have 2 capacities in the queen - diagonal and linear, and only one in the 3 knights. In the 3Qs vs 2Qs + 3Ns you have 2 capacities for the Q side, and 3 capacities for the Q+Ns side. This brings an added value. Actually, while with a single queen or 3 queens you still have 2 capacities, in the 3Ns you have only one capacity, but in the 2Qs + 3Ns you have full 3 capacities! That makes a difference of 2 capacities, and that is very important. Do you agree now with my explanation?

Of course not. Because again, these are just words, offered without any proof. Obviously your explanation would fail if all the Queens were substituted by Chancellors, which move as Rook or Knight. Then 2C + 3N would still only have 2 capacities. Can you show evidence that in KCKNNN (+Pawns) that is equal, the chances do not swing strongly in favor of the Knights side when you add two more Chancellors on both sides??? This whole concept of 'capacities' is just sprouting from your imagination, without any basis or validity in real life.

You still did not answer why you claim that the knights would interdict access of queens to squares on the board, when I showed with counting mobile squares in the 3 diagrams I posted that mobility even with this strange imbalance is still a function of centralisation (quite explicable, as the piece values themselves are a function of a measurement of average mobility performance on an empty board), while at the same time in all 3 positions the knights enjoy extremely good defence. So that, actually, elephantiasis is due to unnaturally high mutual piece defence (with its corresponding bonus points), and not to square interdiction. Would you admit your theory was wrong?

Does this anser your question?
[d]8/6p1/p1knn3/2n3n1/2n3P1/2P1nn2/Q7/KQQ5 w - - 0 1

[d]1nn1k1n1/pppppppp/8/8/8/8/PPPPPPPP/3QK3 w - - 0 1
I do not know why, but in my analysis games I win all with white. It seems that 1.d4 is the best move for white, and it seems that black loses fairly quickly. Do you agree that white is winning here?

well, let's say I would not be surprised. The Pawns are spread out, with clearly disadvantages the Knights. Remove the 4 outermost Pawns on each side, and I would not be so sure.

More interesting seems whether you can also win this against Stockfish, when the latter plays black. Are you better at this than an engine, or worse? Is there any merit in listening to your analysis of this, or would it be better to just have the engines battle it out, and collect the statistics?

[d]1nnnknn1/pppppppp/8/8/8/8/PPPPPPPP/2QQK3 w - - 0 1
2Qs vs 5Ns. Natural initial position with advantage for neither side in terms of immaterial factors. I do not why, but in my analysis games, I am winning most of the games with white. And I definitely think this is won for white. Do you agree with that?

Not without proof. Even if with the same Pawn distribution it would be won with Q-3N, it is not obvious at all that you could force conversion to it against an opponent that consciously avoids such conversions. Perhaps you could beat Stockfish, but I don't believe for a minute you could beat QueeNy, (the latter with black). Show us the game where you do so.

[d]nnnnknnn/pppppppp/8/8/8/8/PPPPPPPP/Q2QK2Q w - - 0 1
3Qs vs 7Ns in a natural initial position. This is the Lucas position, but you might also use the position you posted with queens on b1 and g1. Do you agree that white is better here? I did not try analysing this extensively, as it is a bit complex, but I think it is still much better for white, although more difficult to play than the 2 other positions. Do you agree that white is better here? I think the fact that Disco managed to draw here points that the 2 other positions favour white even more, and maybe Disco did not play an optimal game for white (Lucas will excuse me, but I have my doubts). I think white is better even here.

Thousands of games with a variety of engines, and engines that were particularly modified to understand this position, have demonstrated beyond a shadow of a doubt that this position is utterly lost to white. No chance at all. so much for your intuition. QueeNy always wins this with black, even against tactically superior engines that know about the Q for 2N trick.

So, let us concentrate on factual assessment to see who is right. Any third party posting games/analysis with these 3 positions would of course be of great help.

OK, I am waiting for your wins against QueeNy.