A balanced approach to imbalances

[Lyudmil Tsvetkov]

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

Play 10 games with the above position, featuring the imbalance of 2 queens vs 5 knights in a neutral environment, and report the result.
I would be happy with the following conditions: 1 to 5 minute games (1 minute per each side for the entire game would be fine), 10 games of Queeny with black vs Stockfish + 9 other engines of your choice that are not weaker than Queeny.

I played a 10 game match from this position with alternating colors between QueeNy and TQueeny. Time control was 40 moves in 7 minutes, repeating. TQueeny won 9.5-0.5. I think this at least shows that it is not an easy win for the black side.
http://dl.dropboxusercontent.com/u/8968 ... Arena1.pgn

Thank you.

Obviously TQueeny is much stronger than Queeny.
The amount of tactics with correct play with such positions is unbelievable, certainly at times not human-like.

[petero2]

You could try this one:

[d]3nkn2/2pnpnp1/3nnn2/8/8/8/3PPP2/1Q1QK1Q1 w - - 0 1
Very bad for black! All its pawns are isolated, while white has a nice King shield of connected Pawns! :lol:

This seems better for black than the other two positions I tested, but it still is not an easy win for QueeNy playing black against TQeeny playing white.

In a 10-game alternating color match with time control 40 moves in 7 minutes repeating, Queeny scored 3.5/5 when playing black and 0/5 when playing white.

http://dl.dropboxusercontent.com/u/8968 ... Arena3.pgn

The draws all ended with KNNK. The two games that QueeNy won got to the end game KQKNNNN. Is this endgame generally won for the knights?

[hgm]

OK, so TQueeny is obviously much stronger than Queeny. (Which is no surprise, as Spartacus, from which QueeNy actually is an early, unfinished version, gets whipped by Texel each month in the on-line engine blitz.) Being stronger doesn't help you in a lost position, however. Even micro-Max can beat Houdini in KRK. An engine that only search 2 ply probaby couldn't. In a won position there is a certain minimum depth that is required to secure the win even against perfect play. At 40/7' apparenlt that level of play is not yet reached for QueeNy, as it seems to make unnecessary tactical blunders that TQueeNy can recognize. I will give it a try to see what happens at longer TC.

Lyudmil's strategy to draw is interesting. But IMO it cannot conclusively show that the initial position is well balanced. By stonewalling positions that otherwise would be very unbalanced can become dead draws. Like most Chess engines QueeNy is totally naive against this. Closing the position like this is furthermore only possible when each side has more than 5 Pawns.

I have kind of lost track of what we are trying to prove here. According to simple addition of any reasonable piece values the Queens should have an overwhelming advantage here, of more than two minors. Yet now it seems to be already considered an achievement if you can draw such a position in a small minority of the cases where there are so many Pawns that it can be closed against a weak engine that is completely naive in this respect. If we really want to get an idea of whether the Knights or Queens are stronger with this many Pawns, it should at least be tested with an engine that recognizes the danger of closing, and makes some attempt to resist it.

It is also not clear to me what the effect of the Pawn configuration 1s supposed to be. Is the consensus now that whether the position is won for Queens or Knights is critically dependent on the Pawn chain or on the initial positioning of the Knights? Why not test it with each side just 4 Pawns in the center? (To eliminate the danger of highly unbalanced games ending in draws by stonewalling.) If that would give an unfair advantage to the Knights because of a better King fortress (I don't see why, because the white King is behind those Pawns too), why not move the Kings into a corner then, keeping the Knights in the center?

And above all, is the claim that it depends on the Pawn configuration not an admission that the position is close to equality, and thus that the Queens are very strongly devaluated?

It would be supressed, if the position is won for the knights.

Why not if it is draw? Surely a single Queen is worth 3 Knights, so that the Knights side seems to be two minors short of equality. Normally that would be well outside the draw margin, especially in the presence of Pawns.

A single queen trades for 2 knights for the simple reason that, if that is not done, in a reasonable amount of time the queen value would really be supressed to below 2 knights, however, the trade avoids precisely that. The knights would be strong, if they manage to cooperate well, only when abundantly defending each other, otherwise they would not. The queen exchange avoids precisely that. Say it that way: 7 well placed knights would suppress the value of 3Qs, but not 7 randomly placed knights. The knights would suppress the queen value, if they necessarily placed well, but there is no proof for that.
The trade is an attempt not to allow good coordination for the knights side, or good defence, an immaterial factor, that should be taken into account when calculating the piece values.

OK, so your position seems to be that it might be possible, but unproven, that the Queen value is suppressed if the Knights are placed well. In that case I wonder why we are focusing on positions where the Knights apparently are not placed well; it seems the first thing that should be done is prove that the suppression indeed occurs with well-placed Knights. Because that is really the claim made by the elephantiasis theory, that it is board control and mutual defense by the Knights that causes the depression. Obviously in a position where no such board control is exercised by the Knights, because they only attack squares already controlled by Pawns, the theory would predict there is no instantaneous suppression. If the Queens can use their undepressed value to strike a decisive blow while that situation exists, it doesn't prove much about elephantiasis.

I still think it should be kind of hard for the Queens to profit from this situation, though. The Knights are not trapped, and can safely move out to before their Pawns, after which they already start to attack a great many squares in the center. Black should not go hunting for Pawns, though, before having deployed most of its Knights.

[Lyudmil Tsvetkov]

OK, so TQueeny is obviously much stronger than Queeny. (Which is no surprise, as Spartacus, from which QueeNy actually is an early, unfinished version, gets whipped by Texel each month in the on-line engine blitz.) Being stronger doesn't help you in a lost position, however. Even micro-Max can beat Houdini in KRK. An engine that only search 2 ply probaby couldn't. In a won position there is a certain minimum depth that is required to secure the win even against perfect play. At 40/7' apparenlt that level of play is not yet reached for QueeNy, as it seems to make unnecessary tactical blunders that TQueeNy can recognize. I will give it a try to see what happens at longer TC.

Lyudmil's strategy to draw is interesting. But IMO it cannot conclusively show that the initial position is well balanced. By stonewalling positions that otherwise would be very unbalanced can become dead draws. Like most Chess engines QueeNy is totally naive against this. Closing the position like this is furthermore only possible when each side has more than 5 Pawns.

I have kind of lost track of what we are trying to prove here. According to simple addition of any reasonable piece values the Queens should have an overwhelming advantage here, of more than two minors. Yet now it seems to be already considered an achievement if you can draw such a position in a small minority of the cases where there are so many Pawns that it can be closed against a weak engine that is completely naive in this respect. If we really want to get an idea of whether the Knights or Queens are stronger with this many Pawns, it should at least be tested with an engine that recognizes the danger of closing, and makes some attempt to resist it.

It is also not clear to me what the effect of the Pawn configuration 1s supposed to be. Is the consensus now that whether the position is won for Queens or Knights is critically dependent on the Pawn chain or on the initial positioning of the Knights? Why not test it with each side just 4 Pawns in the center? (To eliminate the danger of highly unbalanced games ending in draws by stonewalling.) If that would give an unfair advantage to the Knights because of a better King fortress (I don't see why, because the white King is behind those Pawns too), why not move the Kings into a corner then, keeping the Knights in the center?

And above all, is the claim that it depends on the Pawn configuration not an admission that the position is close to equality, and thus that the Queens are very strongly devaluated?

It would be supressed, if the position is won for the knights.

Why not if it is draw? Surely a single Queen is worth 3 Knights, so that the Knights side seems to be two minors short of equality. Normally that would be well outside the draw margin, especially in the presence of Pawns.

A single queen trades for 2 knights for the simple reason that, if that is not done, in a reasonable amount of time the queen value would really be supressed to below 2 knights, however, the trade avoids precisely that. The knights would be strong, if they manage to cooperate well, only when abundantly defending each other, otherwise they would not. The queen exchange avoids precisely that. Say it that way: 7 well placed knights would suppress the value of 3Qs, but not 7 randomly placed knights. The knights would suppress the queen value, if they necessarily placed well, but there is no proof for that.
The trade is an attempt not to allow good coordination for the knights side, or good defence, an immaterial factor, that should be taken into account when calculating the piece values.

OK, so your position seems to be that it might be possible, but unproven, that the Queen value is suppressed if the Knights are placed well. In that case I wonder why we are focusing on positions where the Knights apparently are not placed well; it seems the first thing that should be done is prove that the suppression indeed occurs with well-placed Knights. Because that is really the claim made by the elephantiasis theory, that it is board control and mutual defense by the Knights that causes the depression. Obviously in a position where no such board control is exercised by the Knights, because they only attack squares already controlled by Pawns, the theory would predict there is no instantaneous suppression. If the Queens can use their undepressed value to strike a decisive blow while that situation exists, it doesn't prove much about elephantiasis.

I still think it should be kind of hard for the Queens to profit from this situation, though. The Knights are not trapped, and can safely move out to before their Pawns, after which they already start to attack a great many squares in the center. Black should not go hunting for Pawns, though, before having deployed most of its Knights.

OK, let us test this now:

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

What would elephantiasis predict about the imbalance?

[hgm]

This seems better for black than the other two positions I tested, but it still is not an easy win for QueeNy playing black against TQeeny playing white.

Well, it is quite a feat that QueeNy can win at all against an overwhelmingly superior opponent that agrees on what is good strategy. IMO that proves the situation must have an enormous advantage for the Knights.

The draws all ended with KNNK. The two games that QueeNy won got to the end game KQKNNNN. Is this endgame generally won for the knights?

Well, as I mentioned somewhere above, QueeNy is stupid and doesn't know that KNNK is draw. So it does not try to avoid a final Q for N+P trade, and is therefore an easy target for an engine that knows this brings a draw. It also does not protect its last Pawn, as decent engines would (e.g. reducing a Pawnless advantage at least by a factor 2). It would be intersting to see if there are positions before KNNK occurrsed that were a theoretical win for the Knights, or would be a win when TQueeny played them out against itself.

[petero2]

I have kind of lost track of what we are trying to prove here.

When I started these tests I didn't want to prove any particular points. I just wanted to better understand these types of unbalanced positions. From what I have seen so far, I believe the following is true:

1. There is a significant bonus for the knight side when many knights face a set of queens. In TQueeny I use this correction function:

Code: Select all

int correctionNvsK(int n, int q) {
    if (n <= q+1)
        return 0;
    int knightBonus = 0;
    if (q == 1)
        knightBonus = 70;
    else if (q == 2)
        knightBonus = 330;
    else if (q >= 3)
        knightBonus = 480;
    int corr = knightBonus * (n - q - 1);
    return corr;
}

So for 7N,3Q the correction is 480*(7-3-1)=1440 and for 5N,2Q the correction is 330*(5-2-1)=660. The basic knight value in my engine is 385 and the basic queen value 1244.

2. In 7Nvs3Q and 5Nvs2Q, an engine that knows about the bonus above can easily beat an engine that does not know about the bonus, even if that engine is normally several hundred elo points stronger.

3. In 7Nvs3Q and 5Nvs2Q, if both engines know about the bonus, the games are usually very tactical and not an easy win for either side.

I don't know which side generally has the advantage in 7Nvs3Q and 5Nvs2Q, but if I had to guess I would guess the knights have the advantage, based on self-play with TQueeny. However, it may also be the case that the queen side has some defence resource that is not covered by the evaluation function and too hard to find by search.

Do you know of any "fair" 7Nvs3Q positions that can easily be won by QueeNy against a tactically stronger opponent that knows about the bonus?

[Lyudmil Tsvetkov]

[d]2bqk3/pppppppp/8/8/8/8/PPPPPPPP/1N1QK3 w - - 0 1

But also, this one would be an interesting and mostly neutral position to test the validity of the claim that Q+N perform better than Q+B, as they complement better in a group.

We know that the bishop deserves some bonus for play on both wings, the knight might be favoured by the large number of pawns, and by possible arising blocked structures. That set apart, relying just on piece values, do Q+N complement better than Q+B? I would say yes, but it is not clear what tests should be conducted to ascertain that. Maybe a sample of games could hint at something, but who knows.

[Lyudmil Tsvetkov]

OK, so TQueeny is obviously much stronger than Queeny. (Which is no surprise, as Spartacus, from which QueeNy actually is an early, unfinished version, gets whipped by Texel each month in the on-line engine blitz.) Being stronger doesn't help you in a lost position, however. Even micro-Max can beat Houdini in KRK. An engine that only search 2 ply probaby couldn't. In a won position there is a certain minimum depth that is required to secure the win even against perfect play. At 40/7' apparenlt that level of play is not yet reached for QueeNy, as it seems to make unnecessary tactical blunders that TQueeNy can recognize. I will give it a try to see what happens at longer TC.

Lyudmil's strategy to draw is interesting. But IMO it cannot conclusively show that the initial position is well balanced. By stonewalling positions that otherwise would be very unbalanced can become dead draws. Like most Chess engines QueeNy is totally naive against this. Closing the position like this is furthermore only possible when each side has more than 5 Pawns.

I have kind of lost track of what we are trying to prove here. According to simple addition of any reasonable piece values the Queens should have an overwhelming advantage here, of more than two minors. Yet now it seems to be already considered an achievement if you can draw such a position in a small minority of the cases where there are so many Pawns that it can be closed against a weak engine that is completely naive in this respect. If we really want to get an idea of whether the Knights or Queens are stronger with this many Pawns, it should at least be tested with an engine that recognizes the danger of closing, and makes some attempt to resist it.

It is also not clear to me what the effect of the Pawn configuration 1s supposed to be. Is the consensus now that whether the position is won for Queens or Knights is critically dependent on the Pawn chain or on the initial positioning of the Knights? Why not test it with each side just 4 Pawns in the center? (To eliminate the danger of highly unbalanced games ending in draws by stonewalling.) If that would give an unfair advantage to the Knights because of a better King fortress (I don't see why, because the white King is behind those Pawns too), why not move the Kings into a corner then, keeping the Knights in the center?

And above all, is the claim that it depends on the Pawn configuration not an admission that the position is close to equality, and thus that the Queens are very strongly devaluated?

It would be supressed, if the position is won for the knights.

Why not if it is draw? Surely a single Queen is worth 3 Knights, so that the Knights side seems to be two minors short of equality. Normally that would be well outside the draw margin, especially in the presence of Pawns.

A single queen trades for 2 knights for the simple reason that, if that is not done, in a reasonable amount of time the queen value would really be supressed to below 2 knights, however, the trade avoids precisely that. The knights would be strong, if they manage to cooperate well, only when abundantly defending each other, otherwise they would not. The queen exchange avoids precisely that. Say it that way: 7 well placed knights would suppress the value of 3Qs, but not 7 randomly placed knights. The knights would suppress the queen value, if they necessarily placed well, but there is no proof for that.
The trade is an attempt not to allow good coordination for the knights side, or good defence, an immaterial factor, that should be taken into account when calculating the piece values.

OK, so your position seems to be that it might be possible, but unproven, that the Queen value is suppressed if the Knights are placed well. In that case I wonder why we are focusing on positions where the Knights apparently are not placed well; it seems the first thing that should be done is prove that the suppression indeed occurs with well-placed Knights. Because that is really the claim made by the elephantiasis theory, that it is board control and mutual defense by the Knights that causes the depression. Obviously in a position where no such board control is exercised by the Knights, because they only attack squares already controlled by Pawns, the theory would predict there is no instantaneous suppression. If the Queens can use their undepressed value to strike a decisive blow while that situation exists, it doesn't prove much about elephantiasis.

I still think it should be kind of hard for the Queens to profit from this situation, though. The Knights are not trapped, and can safely move out to before their Pawns, after which they already start to attack a great many squares in the center. Black should not go hunting for Pawns, though, before having deployed most of its Knights.

OK, let us test this now:

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

What would elephantiasis predict about the imbalance?

Well, one thing is clear: elephantiasis does not work particularly well with bishops. First game, and, without any effort to seek a win, a drawn in 10 moves against Queeny by entirely blocking the game. You see, the theory that bishops suffer by blocked structures is not a myth, they are absolutely helpless there.

[pgn][Event "Computer chess game"]
[Site "OWNER-PC"]
[Date "2013.10.27"]
[Round "?"]
[White "owner"]
[Black "QN"]
[Result "*"]
[BlackElo "2000"]
[Time "20:42:46"]
[WhiteElo "2400"]
[TimeControl "300"]
[SetUp "1"]
[FEN "bbbbkbbb/pppppppp/8/8/8/8/PPPPPPPP/Q2QK2Q w - - 0 1"]
[Termination "unterminated"]
[PlyCount "22"]
[WhiteType "human"]
[BlackType "program"]

1. g4 c5 {(c7c5 d2d4 g7g6 c2c3 c5d4 c3d4 e7e5 d4d5 h8g7 e2e4 f8b4 e1e2 b8d6
f2f3) +4.73/14 6} 2. b3 e5 {(e7e5 e2e3 g7g5 f2f4 h8g7 f4f5 b8d6 d2d3 d8c7
e3e4 f7f6 c2c3 g8f7 d3d4 e5d4 c3d4 d6h2) +5.14/15 9} 3. c4 g5 {(g7g5 e2e4
h8g7 d2d3 b8d6 d1c1 f8e7 f2f3 d8b6 c1d1 f7f6 h2h4 h7h6 h4g5 h6g5) +5.33/14
5} 4. e4 b6 {(b7b6 d2d3 h8g7 d1c1 a8b7 f2f3 b8d6 a1b1 d8e7 c1a3 a7a6 e1e2
f7f6 h2h4 h7h6 h4g5 h6g5) +5.67/17 10} 5. d3 Bbd6 {(b8d6 d1c1 h8g7 f2f3
a8b7 h1g2 f8e7 g2h3 d8c7 h3h5 e8f8 c1a3 a7a6) +5.74/17 9} 6. f3 Bhg7 {(h8g7
d1c1 a8b7 a1b2 a7a6 a2a3 f8e7 b2d2 d8c7 a3a4 b7c6 a4a5 b6b5 c4b5 c6b5 d2c3)
+5.77/17 9} 7. a4 Bc6 {(a8c6 a4a5 b6a5 a1c3 f8e7 d1e2) +5.98/15 4} 8. h3
B8b7 {(c8b7 d1d2 d6c7 d2f2 f8d6 h1f1 d8e7 f2h2 a7a6 a4a5 b6b5 c4b5 c6b5)
+6.08/16 11} 9. Qc3 Bfe7 {(f8e7 c3a1 d8c7 d1b1 e8d8 b1a2 f7f6 h3h4 h7h6
h4g5 h6g5 a4a5) +6.14/16 6} 10. Qg2 B8c7 {(d8c7 c3b2 h7h6 b2a1 g8h7 d1e2
a7a5 a1a3 h7g6 g2g3 e8f8) +6.21/15 8} 11. Qdc1 f6 {(f7f6 h3h4 h7h6 c1a1
g8e6 a4a5 b6a5 g2h3 a5a4 b3a4 e6f7) +6.37/15 4} *
[/pgn]

[d]4k1b1/pbbpb1bp/1pbb1p2/2p1p1p1/P1P1P1P1/1PQP1P1P/6Q1/2Q1K3 w - - 0 12

Bishops hate blocked pawns.

[hgm]

Well, one thing is clear: elephantiasis does not work particularly well with bishops.

Yes, I noticed that too. 7 Bishops lose to 3 Queens very easily. (Much unlike your initial conjecture that replacing Knights by Bishops would be an advantage to black, btw.) So closing the position is actually the last thing you would want to do: you give away an easy win.

I am not sure what the explanation is. Watching the games it seems the Bishops are in each others way quite a lot, strongly reducing their mobility / board control. (I guess they have to be if they want to protect each other.) So Bishops are actually much poorer in achieving board control than Knights, and the good performance of the Bishop pair is really an exception to this. As soon as you have more than two, it becomes very difficult to deploy them in such a way that you control many squares, and keep them protected.

Earlier in the thread I conjectured that multiple Bishops on the same color should get an 'anti-pair penalty', and the number of anti-pairs obviously grows with the square of the number of Bishops. Bishops are intrinsically un-cooperative pieces, and two on the same color are worth a lot less than twice a single one. In the opening values you don't notice this too much, as there is enough material around (opponent Bishops or Knights) that you can trade it for. So the effective value is what you can trade it for, even though the intrinsic value is lower. I have never tried an engine that would use trade-avoiding strategy against like Bishops (because I did not have an engine that could do that), to see if you could prevent the opponent from getting rid of his anti-pair, so he would be stuck with it.

[Lyudmil Tsvetkov]

Well, one thing is clear: elephantiasis does not work particularly well with bishops.

Yes, I noticed that too. 7 Bishops lose to 3 Queens very easily. (Much unlike your initial conjecture that replacing Knights by Bishops would be an advantage to black, btw.) So closing the position is actually the last thing you would want to do: you give away an easy win.

I am not sure what the explanation is. Watching the games it seems the Bishops are in each others way quite a lot, strongly reducing their mobility / board control. (I guess they have to be if they want to protect each other.) So Bishops are actually much poorer in achieving board control than Knights, and the good performance of the Bishop pair is really an exception to this. As soon as you have more than two, it becomes very difficult to deploy them in such a way that you control many squares, and keep them protected.

Earlier in the thread I conjectured that multiple Bishops on the same color should get an 'anti-pair penalty', and the number of anti-pairs obviously grows with the square of the number of Bishops. Bishops are intrinsically un-cooperative pieces, and two on the same color are worth a lot less than twice a single one. In the opening values you don't notice this too much, as there is enough material around (opponent Bishops or Knights) that you can trade it for. So the effective value is what you can trade it for, even though the intrinsic value is lower. I have never tried an engine that would use trade-avoiding strategy against like Bishops (because I did not have an engine that could do that), to see if you could prevent the opponent from getting rid of his anti-pair, so he would be stuck with it.

But now I think you are wrong.
It looks possible to draw games for the queen side by closing entirely the game, however, it might be that just weaker engines would allow full closure and that it is not at all possible, I do not know. Whenever I do not try to very quickly close the game, it seems that the 3Qs, in distinction to the 7 knights imbalance, have an extremely hard time, so hard that I would suppose if full closure is not possible, the 7Bs easily clinch the win.
There is nothing of the redundancy you were talking about: the 7 bishops not only still excellently defend each other, but, in big distinction to the knights, excellently complement each other. At the same time they control squares from a distance, so no urgent need to centralise them, construct great diagonal batteries to exercise bigger attacking pressure, are a relatively good cover for the king (although admittedly worse than the knights), etc. It seems impossible even to apply the strategy for exchanging queen for 2 bishops, as it is difficult even to attack them.

My conjecture, after playing a couple of games (and I play this imbalance for the first time), is that the 7Bs are better than the 7Ns by at least some 1.5-2 pawns, and that is a measurable growth. Possibly you just dispense 3 full bishops pair bonus points. But this would be true only with this particular imbalance, I do not know what happens if there are rooks, to which bishops would be more vulnerable.

Maybe someone could test further this position, but I suppose that, as engines do not know how to close the game, all wins will go to the bishops side. So here we have extremely good defence (elephantiasis), which could hold the game somewhere in the balance, plus very efficient complementarity, that already wins. So that complementarity matters. I would be surprised if in a match of equally strong engines the Q side wins even a single game, again, in sharp disticntion to the knight imbalance.

I also noticed that Queeny does not make any difference between 7 Ns and 7Bs in terms of evaluation.