Capablanca's Theorem Q+N > Q+B

[Lyudmil Tsvetkov]

Likewise the queen + knight tend to work better than queen + bishop in the endgame because the queen + bishop duo can sometimes be redundant.

This might be true but it doesn't hold against two rooks: QN vs RR is a general draw while QB vs RR is a general win. The rook pair's main resource is the third rank defence which can be broken only by the Q+B duo. The key to success seems to be the bishop's ability to attack the first rank. An example:

[D]8/8/8/8/6kb/R4R2/3q4/5K2 b - -

The shortest win is 1...Bf2! -+

fully correct, chess is at times paradoxical.

[Lyudmil Tsvetkov]

It's common knowledge that rook + bishop work better than rook + knight. Likewise the queen + knight tend to work better than queen + bishop in the endgame because the queen + bishop duo can sometimes be redundant.

The knight is unique compared to the bishop.

‘A bishop and a rook are also stronger than a knight and a rook, but a queen and a knight may be stronger than a queen and a bishop.’

Even when it's proven some people don't agree for some reasons.

‘... I don’t necessarily agree with the clichéd adage that “the queen and knight duo are superior”.

Statistically QN vs QB scores 55-57% on average against QB. That percentage is found by chessbase statistics.

What is your say?

http://www.chesshistory.com/winter/winter50.html

Where does that 55-57% figure come from? I just checked it out for myself and found that the QB scores almost 51%. Of course, you have to check for both colors, since White comes out ahead overall with either side of this configuration. The exact results will depend on your database, your threshold rating, your requirement for "persistence" (I use 3 plies), and your requirements regarding other material (I required no other pieces to be on the board, but any number of pawns as long as they are equal). Perhaps your requirements were very different?

My opinion is that in general bishops are better than knights, but with just a queen to assist each this advantage is much reduced though not completely eliminated.

Larry, did not you quote somewhere, probably in the past, a statistical advantage for QN over QB?

problem is, what criteria you choose for masking the configuration.

maybe all stats are just a random noise, unless you also check for score being 0.0, or at least within a small drawish margin.

[Lyudmil Tsvetkov]

Where does that 55-57% figure come from?

Chessbase 14's Similar Endgames search.

Searching this position with symmetrical structure (colors is not ignored) from master class rated 2200 up to 2800s

[d]3qk1n1/pp3ppp/8/8/8/8/PP3PPP/3QKB2 w - - 0 0







My question to Kaufman: Is Q+N tandem eligible for material bonus for Komodo?

Yes, in majority of cases the bishop is most of the times the best minor piece. Capablanca's Theorem is the exception when combined with the queen in endgame.

there are different factors to be taken into account too, like availability of pawns on both wings, blocked structures, available center pawns, etc., so it is very difficult indeed, if not altogether impossible, to assess the imbalance in a pure setting.

maybe, playing 10 000 games with all pawns on their home ranks and only QB vs QN?
probably with a small or larger book.

[Nordlandia]

Lyudmil: Q+N scores better in most search settings i've done.

I have always been taught that Q+N is stronger than Q+B, because Q and N are complementary, while Q and B are slightly "redundant.

Maybe for computers the advantage on average narrowed further?

https://www.reddit.com/r/chess/comments ... nd_bishop/

[hgm]

Well, Arpad already falsified this: Q+B is better than Q+N against 2R.

[abulmo2]

Your forgot to give us the interval of confidence of your data:
Q+B vs Q+N:
1-0: 114 +/- 15
0-1: 129 +/-15

So, on a statistical point of view, you cannot conclude that Q+B > Q+N. Your data show no conclusive difference.

[Arpad Rusz]

If you take a random tablebase position with WTM you have the following chances:

QN vs. QB
37.47% White wins
5.90% Black wins
56.63% Draw

QB vs. QN
45.32% White wins
3.35% Black wins
51.33% Draw

This also demonstrates the slight edge of QB over QN.

[Nordlandia]

Capablanca's Theorem with engine games.

6P Q and B vs 6P Q and N.

White:


Black:


http://www.amateurschach.de/

[JJJ]

In the meantime a test is launched here :

http://tests.stockfishchess.org/tests/v ... 16ff64aff4

[Lyudmil Tsvetkov]

If you take a random tablebase position with WTM you have the following chances:

QN vs. QB
37.47% White wins
5.90% Black wins
56.63% Draw

QB vs. QN
45.32% White wins
3.35% Black wins
51.33% Draw

This also demonstrates the slight edge of QB over QN.

this is not representative.

tablebases mostly feature a pawn-empty board, so this is extremely specific: bishops, as long-range pieces, tend to perform much better the lower the number of pawns that don't restrict their movements.

there is absolutely no doubt for me that in the general case Q+N performs better than Q+B, and that was also demonstrated by the successful bonus in Komodo, going to QN rather than QB.

it has to be highlighted though, that the Q+N bonus is a general one, and not implicit only in the case of QN vs QB.

actually, Q+N bonus seems to be the least efficient vs Q+B.

QN are much more performing vs QR(QN side having some pawns), and even more so in the case of QN vs RR + pawns.

so, it is a general bonus.