# Why does a knight combine better with the queen than a bishop does?

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?

• Because they aren't stuck on a single colour. Jan 5 '20 at 10:36

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.

• This is also true of Q+B. So how does this make Q+N better? Jan 4 '20 at 10:24
• @RosieF That is not true. If you have a dark-squared bishop and a queen, you can only attack g7 with two pieces, for example. You can never attack h7 with two pieces. If you reposition the knight, you can. It is that you can attack every square on the board with two pieces, obviously, after some maneuvering. Jan 4 '20 at 10:27
• Ah -- did you mean they can both attack any square? Sorry, I misunderstood your words "to attack any square" and didn't see that you meant both pieces. Jan 4 '20 at 10:52

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.

• well, except that in an actual game, they'll never be on the same square so it's not immediately obvious how that applies :) Jan 5 '20 at 10:41
• @ilkkachu it also means that the knight can defend the queen without obstructing her movement.
Jan 6 '20 at 8:49
• @JAD, that, while it's just the reverse of the above, seems to make for a much better point. Jan 6 '20 at 13:03
• Well, it works both ways. Knight can protect queen without getting in its way. This is important when you make some close-range attacks on king. For attacking the opponent's king, the other direction is not so important except for some positions involving a good number of pawns. Jun 26 '20 at 6:35

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

• Capablanca
• Shirov
• Silman

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.

• examples of the superiority of queen + knight over queen + bishop are usually examples of a better knight and a bad bishop.
• Statistical analysis shows a very slight superiority of the queen + knight which can be explained by the stronger side choosing queen + knight in the belief that queen + knight is superior. that is, the queen + knight side was already winning.

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.

• I have seen Watson's opinion on this before, but as the old saying says: "there are lies, damned lies, and statistics". I have seen more World Champions (the most recent was Karpov in "The Karpov Method" videos), who believe that the Q+N is superior to the Q+B, so I will take their opinion over Watson, who I like a lot. Their judgment is far superior. Jan 4 '20 at 19:50
• It happens sometimes that human judgement fails to reach a truth that can be supplied by statistics/logic. The supremacy of chess computers hints that this may be true in chess. But chess is not a game of pure reason when people play it. My own experience is that Queen + Knight is superior. I can feel that is true. If I am making a practical decision in a actual game, or evaluating a position or gauging the strength of a speculative attack what will most likely lead to the best practical result? Thinking about statistics or going with how I feel? I'll take the Queen + Knight. Jan 5 '20 at 0:20
• but even with Watson's opinion, there seems to be a lot of his opinion in there still, the stats aside. For example, his opinion about whether positions are already better. Maybe they are, maybe not, and even if they are, it does not prove that it still did not make that much more difference. The difference could also be simply practical: The positions are just harder to defend for humans. Again, I will still stick with the world champions' opinions. Jan 5 '20 at 1:26
• Sometimes, “well established” means someone respected made a guess and hundreds of people repeated it as fact. Jan 5 '20 at 2:18
• Before 1900, the champions said that the knights were better than the bishops. Before AlphaZero, lots of things were assumed to be correct. In every game that I played against masters, I've always won when I had a knight versus their bishop. My experience goes against today's general principles. Jan 5 '20 at 18:49

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 agree. The queen-bishop spear stabbing into the h7 pawn with a ruinous check comes to mind. Jan 7 '20 at 13:41
• @StianYttervik Exactly, a queen and bishop can form a battery to attack from a distance. Jan 7 '20 at 20:05

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 ♕+♘.

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.

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.

• Good point. If Q & B are on opposite colours, they have the power of the 2 bishops, which are widely regarded as more powerful than B & N. As you say, they can command 2 adjacent diagonals. If Q & B are on the same colour, they can defend each other, which Q & N can't. Defended by a B on a line, the Q can move along that line, still defended; this is possible with Q & N but only to a limited extent. May 20 at 11:08

One way to look at it is this:

• If you add bishops to a queen, you are adding to an ability that she already possesses, which is attacking on diagonals (which is a 45 deg attack).
• Bishops practice their abilities each over its own color.
• Bishops cannot protect one another directly.
• If one bishop is captured, then the "union" of the bishops and queen is damaged greatly, since now the minor piece can only assist on one color.
• If you add knights to a queen, you are adding an ability that she does not possess, the L attack (which is attacking at about 60 or 30 deg).
• Knights practice their abilities on both colors, attacking one color at a time.
• Knights can protect one another.
• If one knight is captured, the minor piece can still assist on both colors.

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.