Queens vs Knights

[Evert]

Not sure why I'm bothering with this, because I don't find KQQQKNNNNNNN all that interesting as an ending, but anyway. I played some short (~10 games) fast (~40/0:10) games to get an impression for these. So there's quite a bit of noise on these results. With those caveats, what I get is:

[d]1nn5/nkn5/nnn5/8/8/8/6QQ/6QK w - - 0 1
Dead draw (10/10). White trades down very quickly and efficiently.

[d]2nnknn1/3nnn2/8/8/8/8/8/2QQKQ2 w - - 0 1
Dead draw (10/10). White trades down even quicker than in the previous one.

[d]3nkn2/3n1n2/3nnn2/8/8/8/8/2QQKQ2 w - - 0 1
More interesting. White cannot trade down very effectively and it often ends up in KQKNNNN. Which Nightfish then fails to convert to a win in 5/10 cases; I suspect that's the time control being counter productive.

Tentative conclusion from this on KQQQKNNNNNNN:
1. If the knights can work together effectively, they win.
2. If they cannot, the queens can exchange down to KQQKNNNNN and then KQKNNN, which can be trivially drawn by the Queen side.

Whether a starting position where the Knights can coordinate is fairer than one where they cannot seems to me a pointless debate and up to personal preference. To answer the question on whether such positions are "generally" won/lost/drawn you need to know the proportion of positions in which the Knights can coordinate and the positions where they cannot. That requires building a tablebase for this ending, which... seems unlikely, even with an efficient indexing scheme.

[Evert]

it is written Schnarnagl, and not Scharnagle.

Hilarious. Even on simple matters like spelling you do not manage to say something that is correct even a single time.

Yeah, but of course he's half right in this case. Scharnagl is just a really complicated name.

[Lyudmil Tsvetkov]

I tried playing a single game with the pure-setting imbalance, seemingly the queens have a forced trading line, but I am not certain about it, as the imbalance on an empty board simply makes me giddy.

[pgn][Event "Blitz 1m"]
[Site "Microsoft"]
[Date "2017.07.20"]
[Round "?"]
[White "myself, owner"]
[Black "Stockfish 8 64 POPCNT"]
[Result "1/2-1/2"]
[Annotator "owner"]
[SetUp "1"]
[FEN "2nnknn1/3nnn2/8/8/8/8/8/2QQKQ2 w - - 0 1"]
[PlyCount "6"]
[TimeControl "60"]

{512MB, OWNER-PC} 1. Qa6 {0} Ngf6 {6.83/16 3} 2. Qaxc8 {10} Nxc8 {3.34/17 1} 3.
Qxc8 {2} Nfe6 {3.33/20 1} 1/2-1/2

[/pgn]

obviously, just 3 moves were needed to draw standard SF, but I don't see how black avoids one exchange of Q for 2Ns after Qa6:

[d]2nnknn1/3nnn2/Q7/8/8/8/8/2QQK3 b - - 0 1

black has only move that does not allow a quick trade on c8, Ndb6.

Ncb6 is met by Qe3, threatening Qb6 capture, and Nd5 fails to Qd5, of course.

after Ndb6, white plays Qc7:

[d]2nnknn1/2Q1nn2/Qn6/8/8/8/8/3QK3 b - - 0 2

again, black has only move which does not allow a trade, Nfd7.

Ned5 obviously fails to Qd5 Nd5 Qc8.

[d]2nnk1n1/2Qnnn2/Qn6/8/8/8/4Q3/4K3 b - - 0 3

almost not a single black knight is able to move without allowing a trade.

for example, if Nd7 moves, queen captures on b6, e5 square is protected by queen twice, no landing there, the e7 knight is pinned, so Nc6 also impossible, if the c8 knight moves, the b6 knight is left undefended, etc., etc.

so, possibly only black move again is Ngf6.

[d]2nnk3/2Qnnn2/Qn3n2/8/8/8/4Q3/4K3 w - - 0 4

but I stop the analysis here, as my head simply gets too giddy with this unusual position.

I don't believe black can in any way avoid a forced 1st trade of Q for 2Ns, after which it is easy.

as seen, black has only moves; you can not hold long with only moves.

so, I thik my belief is pretty much justified and this is a simple draw.

btw., when testing, one should bear in mind that it will all depend on the engine used and its knowledge + search.

for example, we might know how some engine with imbalance knowledge performs here, but we don't know what will happen if we increase or decrease the imbalance parameter, what would be the consequences in terms of game play then?

also, it would be best to use an engine with an optimised search for such positions, for example SF with search prioritised to look for captures/captures of lower-value pieces, instead of just the plain standard SF search. that might have a tremendous bearing on results.

so that, we simply don't know what happens with perfect play.

maybe someone could try different imbalance term values in their engines, it would be best that we accomodate SF for this, as it is very strong, but it will still have unmodified search, so we should modify that too.

at present, I think it is best to play a lot of games with modified SF with different imbalance settings from this position, but, strangely enough, when Evert could really be of help, he simply refuses to comment.

maybe the queens get the trade rather easy, after all?

[Lyudmil Tsvetkov]

btw., I am certain SF + knowledge and modified search will handle tactically this position much better than me, engines excel at tactics, so chances for spotting a forced trade should only increase.

[hgm]

Whether a starting position where the Knights can coordinate is fairer than one where they cannot seems to me a pointless debate and up to personal preference. To answer the question on whether such positions are "generally" won/lost/drawn you need to know the proportion of positions in which the Knights can coordinate and the positions where they cannot. That requires building a tablebase for this ending, which... seems unlikely, even with an efficient indexing scheme.

EGT always contain a very large fraction of positions that are not tactically quiet, but lead to a quick forced loss of material for one side. These are not considered as belonging to that end-game, but to the end-game they convert to. In Lyudmils position many Knights are singly protected, which is no protection against Q-2N trades. So they are in fact 'hanging piece pairs', and because there are so many, these can be easily forked. As Lyudmils analysis shows. But this merely proves the position is not 3Q-7N but instead a disguised 2Q-5N, and thus totally irrelevant. It would be just as silly to make any claims about 3Q-7N based on this position, as it would be to claim KQKNNN is won based on a position with all 4 Knights in a different corner. Or claiming 3Q-6N is lost based on this position:

[d]8/2nkn3/3n4/1n1n1n2/8/Q1Q1Q1K1/8/8 w - - 0 1

Note that end-games generally are reached by conversion from an end-game with more pieces, where both sides have been engaged in battle organizing their troops already for a long time. They don't fall from the sky, with randomly placed pieces. So statistics based on counting all positions with equal weight is pretty meaningless. In end-games with many pieces, a generally losing side will usually score draw or win in more than 50% of the cases when he has the move, as with many pieces, most board squares will be attacked, and pieces of the strong side starting there will be immediately gobbled up to spoil his winning chances. E.g. K+Q together cover ~40% of the board, so in KQRKQ the R has 40% probability for being attacked, and ~60% probability for being unprotected. So 24% of the positions will draw by 1.QxR. And K+R cover only 30% of the board on average, so the chances that the Q is unprotected is even 70%, so that 28% of the positions start with 1.QxQ (unprotected), for a KQKR win. So KQRKQ is mostly not won for the Q+R side, and yet we consider Q+R a certain win over Q.

With a wall of Pawns both sides have the opportunity to 'develop', i.e. organize their pieces in a close-to-optimal way, before they engage in battle, as it takes time to break through the Pawn barrier. By the time the Pawns are gone, the pieces will be coordinated. Take away the Pawns, and you will lose that. To make a meaningful statement in that case, you have to start from very quiet positions.
Note that in Chess the value of a piece during virtually the entire game is mostly determined by how well it supports its own Pawns to promotion, and how efficiently it stops the opponent Pawns. Not by how efficiently it checkmates the King or catches other pieces. There is some correlation between teh two, but it is not perfect. So determining piece values under piece-only conditions is quite unnatural, and can possibly lead to wrong values. E.g. a non-royal King ('Commoner' M) draws a Queen: KQKM is a fortress draw. While KQKR is a loss. You cannot conclude that M is stronger than R from that. (It isn't; it is nearly as weak as a Knight.) And of course KQKM only draws when K and M are not far apart, so that the unprotected M is immediately captured through a fork. As the would be in a small minority of all positions, but virtually always in any position that would occur in the course of a game. (As otherwise the M would have been gobbled up long before you converted to KQKM; you would never let a slow piece like that stroll around the board unprotected when Queens are around, just like you would not walk your King to the center in that case.)

And something completely different: the drawing chances of the Queens seem to be present only because of the inability of even a pair of Knights to force checkmate on a bare King. Which is quite accidental. It means the Queens can hardly claim they equalled the power of the Knights, when they draw. They were just very lucky that a quite large excess power of the Knights still gives them a draw. On slightly different boards, they would not be so lucky. E.g. with 'wizard squares' like on the Omega Chess board, two Knights can force checkmate. Or the rules could have been such that stalemate is a win. Neither of that would measurably affect the normal Knight value, but it might greatly change the 3Q-7N results.

[Evert]

27% is not small at all, as you need only another 23% for perfect equality concerning the outcome of the game.

No you don't. We're talking 27% draws, 73% losses here. Raising that to 50% draws still gets you 50% losses.

you understand pretty well I am talking equality of win/draw chances.

that is sufficient for me for Harm's claim to be disclaimed.

I understand nothing of the sort. "Perfect equality concerning the outcome of the game" implies both sides have equal winning chances (which includes the game being a plain draw). That's not the case here.

[Evert]

[...]
[d]2nnk3/2Qnnn2/Qn3n2/8/8/8/4Q3/4K3 w - - 0 4

but I stop the analysis here, as my head simply gets too giddy with this unusual position.

I don't believe black can in any way avoid a forced 1st trade of Q for 2Ns, after which it is easy.

as seen, black has only moves; you can not hold long with only moves.

so, I thik my belief is pretty much justified and this is a simple draw.

Pretty sure I said that - for that particular position.

btw., when testing, one should bear in mind that it will all depend on the engine used and its knowledge + search.

for example, we might know how some engine with imbalance knowledge performs here, but we don't know what will happen if we increase or decrease the imbalance parameter, what would be the consequences in terms of game play then?

If the tuning for the material score is reasonable, then play and the outcome of the game is dominated by other evaluation terms because the engine will already avoid bad trades/seek out good trades.

also, it would be best to use an engine with an optimised search for such positions, for example SF with search prioritised to look for captures/captures of lower-value pieces, instead of just the plain standard SF search. that might have a tremendous bearing on results.

Changes to the search, in principle, do not change engine play in tactical positions, only in quiet positions where there are multiple (nearly) equivalent moves. They do change the efficiency of the search, but not the outcome.
This is not a rigorous statement if you use speculative pruning techniques, but it's a reasonable starting point. In short, changes to the search will not have a major effect on the outcome of the analysis of these positions.

maybe someone could try different imbalance term values in their engines, it would be best that we accomodate SF for this, as it is very strong, but it will still have unmodified search, so we should modify that too.

at present, I think it is best to play a lot of games with modified SF with different imbalance settings from this position, but, strangely enough, when Evert could really be of help, he simply refuses to comment.

Not sure what you're getting at. My life doesn't revolve around hanging around these forums, you know.
Anyway, the modified sources are posted upthread (and the changes are minor anyway) so if you can get someone to make a Windows compile for you you can play around with that to your heart's content.

maybe the queens get the trade rather easy, after all?

Depends on the position.

[Evert]

EGT always contain a very large fraction of positions that are not tactically quiet, but lead to a quick forced loss of material for one side. These are not considered as belonging to that end-game, but to the end-game they convert to. In Lyudmils position many Knights are singly protected, which is no protection against Q-2N trades. So they are in fact 'hanging piece pairs', and because there are so many, these can be easily forked. As Lyudmils analysis shows. But this merely proves the position is not 3Q-7N but instead a disguised 2Q-5N, and thus totally irrelevant. It would be just as silly to make any claims about 3Q-7N based on this position, as it would be to claim KQKNNN is won based on a position with all 4 Knights in a different corner.

Sure.
My point is just that any claims on whether the K3QK7N ending (without pawns, as opposed to the general imbalance that includes pawns on both sides) is generally won or not cannot be made on the basis of a few individual positions, some of which are easy draws and some of which aren't.

Note that end-games generally are reached by conversion from an end-game with more pieces, where both sides have been engaged in battle organizing their troops already for a long time. They don't fall from the sky, with randomly placed pieces. So statistics based on counting all positions with equal weight is pretty meaningless.

Sure.
I do note that we've transitioned from talking about the K3QK7N imbalance to talking about the K3QK7N pawn-less ending, but then again I perceive a shift in the arguments of certain parties from K3QK7N being won for the Queens to K3QK7N being "at most" a draw for the Knights, to the Queens having a plan to draw the game.

And something completely different: the drawing chances of the Queens seem to be present only because of the inability of even a pair of Knights to force checkmate on a bare King. Which is quite accidental. It means the Queens can hardly claim they equalled the power of the Knights, when they draw. They were just very lucky that a quite large excess power of the Knights still gives them a draw. On slightly different boards, they would not be so lucky. E.g. with 'wizard squares' like on the Omega Chess board, two Knights can force checkmate. Or the rules could have been such that stalemate is a win. Neither of that would measurably affect the normal Knight value, but it might greatly change the 3Q-7N results.

Oh, NN being a defective pair has a big impact here. I think that's the whole point of "Troitzky Chess", which is FIDE Chess on a board with clipped corners where NN have mate potential.

Unrelated, Stockfish' play in KNNK is hilarious. Of course it (almost) doesn't matter what you do since (nearly) all positions are drawn, but giving away a piece or not grabbing a Knight when you can looks retarded. Sure it's just cosmetic, but I'm not a fan, personally.

[hgm]

Unrelated, Stockfish' play in KNNK is hilarious. Of course it (almost) doesn't matter what you do since (nearly) all positions are drawn, but giving away a piece or not grabbing a Knight when you can looks retarded. Sure it's just cosmetic, but I'm not a fan, personally.

Indeed, that is the problem of evaluating theoretical draws as a hard zero. I prefer a method where you just reduce the naive score by a very large factor (e.g. 32, so that the +650 advantage would reduce to +0.20, which should be low enough to not prefer it over any other position that does have significant winning chances).

[Adam Hair]

You are wrong. When there are no pawns such as the position above, modified Rodent as Black will not allow Q for 2N trades. At least not when the time control is 5' + 3". It wins against everybody, including against itself.

The only positions where 7N (modified Rodent) consistently loses against 3Q (Komodo) are those with disconnected pawns and large pawn spans. The greater mobility of the queens allows pressure to quickly swing from one side to the other side. This allows Komodo to eventually promote a pawn to a queen and gain the edge.

Problem is that for this particular type of positions (3Q vs 7N) engines are obviously not properly tuned. And it would require quite some time to get it tuned.
It is enough just to reduce the QueenValue in SF and it destroys normal SF or Queeny in every single game black or white from any single 3Q vs 7N starting position. I don't have modified Rodent or newest Komodo to try, but I believe it would beat them also with ease both playing white or black.
I believe these type of positions (3Q vs. 7N) are pretty balanced (some of them maybe slightly favour 7N side) but it is almost impossible to claim it for sure, before you manage to properly tune the strongest existing engine (SF) for them.

I believe that you are right.