From this question, the couple queen + knight is strong in attacking the opponent's king.
I searched why the knight combines better than the bishop with a queen, and all I could find, from this article, is:
"Knights cooperate better than bishops with the queen, as the two pieces complement each other and will control the position better."
Can you explain why?
It is a fairly short and simple explanation:
They can combine to attack any square, not just squares on one color. As part of that they can also shift the attack better from one square to another.
One of the ways I teach kids how knights move is to put the queen and the knight on the same square. The knight can go to the nearest squares that the queen can't go to.
It is this unique complimentary nature of the two pieces which means that they form such a potent combination. With queen plus any other piece this is missing and there is a duplication of function.
As an aside, something similar applies to the two bishops, although they obviously are always on different coloured squares. This explains why two bishops are generally worth more than 2 x one bishop.
John Watson's "Secrets of Modern Chess Strategy" contains a section titled "Folklore or Reality? Queens and Knights" John lists some folks that say Queen and Knight are better
And refers to Steve Meyer's book "Bishop vs Knights" which also says the Queen + Knight is better.
I am currently playing through "Karpov move by move" which has
..it is well established that queen and knight can create threats more efficiently than queen and bishop
John makes a few points. I will simplify his points here.
John concludes
...the idea of the advantage of queen and knight over queen and bishop seems to be one of those folkloric bits of wisdom/mythology of at most extremely limited validity, and quite possibly none whatsoever.
I cannot do justice to John's analysis in this post. If you like statistical analysis and questioning of accepted wisdom I recommend this book. I especially enjoyed the section on the two bishops.
A knight and queen complement each other because they each do what the other can't. The queen can move like a rook and bishop combined, but it can't move in L-shapes and jump over other pieces. The logic here is that a bishop or rook can't help the queen so much since a queen can already move like them, but the knight has something the queen doesn't.
However, it's a big generalization to say a knight is always better than a queen for working with a bishop. In close quarters combat (say when being close to the enemy king), a knight is indeed better with the queen. But in an open game in general, a bishop can be better simply by being worth slightly more than a knight in general. The point is that Queen + Knight can be better when trying to accomplish a short-term attacking goal, where range isn't an issue.
I feel that many people before me have already answered the question, but I just want to add another dimension to the entire scenario. If you had to choose pieces which would be the trickiest and most difficult to calculate variations for it would probably by the queen and the knight. This isn't an objective answer, but it is just a point to take into consideration.
Steve Meyer, in his book Bishop v Knight, concludes the final chapter of the book, "Capablanca's Theorem – ♕+♘ is better than ♕+♗ in the Ending", as follows:
Verdict: Capablanca's intuitive insight into the advantage of queen and knight vs queen and bishop in the ending is correct. While general positional methods of evaluation are still important, the attacking force of the queen and knight can be very fierce, particularly in blocked positions or those featuring fewer pawns.
But John Watson, in his book "Secrets of Modern Chess Strategy", chapter "Minor-Piece Issues" claims that the examples are one-sided. He continues:
My own view, just from looking at a lot of examples, is as follows:
a) an unusually large proportion of ♕+♘ vs ♕+♗ games are drawn;
b) most games which are won by either side, as in the examples mentioned above, are characterized by that side having one or more rather obvious other advantages
Finally, and this might make the theorem a kind of self-fulfilling prophecy, he notes:
One proviso I have already noted above is that the side with the queen and knight (in the pure ♕+♘ vs ♕+♗ case) tended to be a bit stronger, for whatever reason. That alone might account for the small statistical edge for the ♕+♘. Moreover, as explained in the Introduction to this book, a perception of the superiority of queen and knight may well lead players who are in already advantageous but complex positions to convert them into what they view as a safer ♕+♘ vs ♕+♗ advantage. This would skew the percentages in favour of the ♕+♘.
The problem for the knight in the endgame is that it cannot protect a pawn that is protecting it, like the bishop can. So while Knight + Queen is better than Bishop + Queen, often the fact that a number of pawns will be present can tip the balance back to the bishop. This is especially true if the player with the bishop forces an exchange of queens.
One thing Q + B can do that Q + N cannot is to threaten remote squares. They can also, among other things, completely control two adjacent diagonals, which is a lot of territory. I vote Q + B.
One way to look at it is this:
Knights are harder to defend by pawns. In the rare events that you are attacking an open K, Q+B is equally lethal as Q+N. However two connected pawns can hold Q+B for a few turns or until new attackers come while Q+N has a higher chance to penetrate on their own.
Here are some stats from the Syzygy tablebase, of win and loss percentages of various material balances. This tablebase is of positions of up to 7 units, so where White has KQB or KQN, Black can't have more than 4 units.
First, let's pit the balances KQB and KQN against each other. Here, in KQB v KQN, KQB wins 25.0% & loses 21.0% of positions.
Next, for various choices of Black's balance, I tabulated White's win and loss percentages when White has KQB and KQN respectively.
By x+y% I mean x% if we presume that game ends in a draw as soon as a 50-move draw claim would be upheld, plus an additional y% if 50-move draws didn't exist.
Where each side has a bishop, Syzygy's stats relate to the whole tablebase of positions with the stated material regardless of whether the bishops are on opposite or the same coloured squares.
| Win percentages | Loss percentages |
Black | KQB win | KQN win | KQB loss | KQN loss |
------+----------+----------+----------+----------+
KQR | 20.3% | 18.0% | 47.3% | 51.4% |
KQPP | 24.2% | 20.9% | 31.9% | 36.3% |
KRR | 62.8+0.1 | 48.0+3.9 | 19.5% | 23.0% |
KRBB | 52.4+4.2 | 52.5+0.8 | 22.8% | 25.6+0.8 |
KRBN | 58.1% | 55.1+6.5 | 21.4% | 23.2% |
KRNN | 58.9% | 53.7% | 18.7% | 20.1% |
KRBP | 68.1% | 65.6% | 20.8% | 23.2% |
KRNP | 70.9% | 68.7% | 19.2% | 21.3% |
KRPP | 74.4% | 72.0% | 17.9% | 20.0% |
So, against the black material balances shown, KQN loses more than KQB loses. KQB wins more than KQN wins, with few exceptions.
The bishop is in general, a weak end game piece.
In some end games the bishop is more valuable than a knight, but this is only if the bishop is your only piece that can move an arbitrary distance in a single move. That's an important end game function for being able to snatch pawns while still providing pressure from a distance.
As long as this "spooky action at a distance" function is covered by some other piece, the knight is generally stronger, which is why it pairs better with a queen.
