Bishop vs Knight

Question

I read in a book written by Fischer about piece values, and he said that a knight is worth 3 pawns, and a bishop is worth 3,25 pawns. I know that in closed positions knights are better, and I have also read in a Nimzovich book that a centralized knight and bishop have equal value.

So, while evaluating a position, how can I recognize when a bishop is better, or when a knight is better? I also saw that grandmasters like bishop pairs very much. What about knight pairs?

Do engines make this difference?

Does it depend on the number of the pawns in the center, or something like that? What factors establish which are better?

Answer 1

Basically, what it comes down to is mobility.

In closed positions bishops are often hemmed in by pawn chains everywhere, whereas knights can slowly maneuver to a good outpost. But it isn't the closedness of the position that makes knights better in this case. Some closed positions are so cramped that even knights cannot jump anywhere useful. It is only that knights usually are more mobile than bishops in closed positions.

[FEN ""]
[Event "USSR Championship"]
[Site "Leningrad (RUS)"]
[Date "1956"]
[EventDate "1956"]
[Round "?"]
[Result "1/2-1/2"]
[White "Yuri Averbakh"]
[Black "Boris Spassky"]
[ECO "E75"]
[PlyCount "145"]

1. c4 Nf6 2. Nc3 g6 3. e4 d6 4. d4 Bg7 5. Be2 O-O 6. Bg5 c5
7. d5 Qa5 8. Bd2 a6 9. a4 e5 10. g4 Ne8 11. h4 f5 12. h5 f4
13. g5 Qd8 14. Bg4 Nc7 15. Bxc8 Qxc8 16. Nf3 Nc6 17. dxc6 bxc6
18. Nh4 Qe8 19. hxg6 hxg6 20. Qg4 Rb8 21. Nd1 Ne6 22. Ra3 Nd4
23. Rah3 Qf7 24. Bc3 Rfe8 25. R3h2 Qxc4 26. Nxg6 Re6 27. Bxd4
Rxg6 28. Qf5 Qe6 29. Qxe6+ Rxe6 30. Bc3 d5 31. f3 Rb3 32. Rh3
c4 33. Kd2 Rg6 34. Rg1 d4 35. Ba5 Bf8 36. Rg4 Rd6 37. Kc2 Rd7
38. g6 Rdb7 39. Be1 c5 40. Rgh4 Bg7 41. Ba5 c3 42. bxc3 Ra3
43. cxd4 exd4 44. Rxf4 Ra2+ 45. Kd3 Rb1 46. Rh1 Rxa4 47. Kc2
Rb5 48. e5 d3+ 49. Kxd3 Rxf4 50. Bc3 Rxf3+ 51. Ke4 Rg3 52. Kf4
Rxg6 53. Ne3 Rb8 54. Nf5 Rf8 55. Rh5 Re8 56. Ke4 Rg1 57. Rh3
Bf8 58. Kd5 Rd1+ 59. Ke4 Rc1 60. Kd5 Rd1+ 61. Ke4 Rd7 62. Nh6+
Bxh6 63. Rxh6 Rh7 64. Rg6+ Kf7 65. Rf6+ Ke7 66. Rc6 Kd7
67. Rxc5 Rh6 68. Kd5 Rb6 69. Ba5 Rb5 70. Rxb5 axb5 71. e6+
Rxe6 72. Kc5 Re5+ 73. Kb6 1/2-1/2

Take this famous game. At move 16 the position is quite closed, but the black knights are pretty unhappy anyway. White is about to build a strong attack on the kingside and the black knights just don't have the space to create some counterplay. So Spassky take the rather shocking practical decision to ditch one of his immobile knights for more space and a chance of counterplay. Notice how a few moves later the remaining black knight lands on the perfect outpost on d4.

To be mobile knights have to be positioned close to the centre. But in the centre pieces are vulnerable to (pawn-) attacks. Therefore it is very important for knights to have save, central outposts.

In the endgame the bishops often get a lot stronger than knights, if there are pawns on both sides of the board. The knights on the other hand love local weaknesses.

Bishop pairs are strong because together they can control a lot of squares. Knights don't complement each other as well. Often they are even rivals for the same outpost. That's why the knight pair isn't a factor.

Answer 2

These answers are very comprehensive. As food for thought I would only add three points that I haven't seen mentioned about the transitory (changing) value of the pieces during a game, and a caution against relying on the number values.

First, some have already noted how bishops become more powerful in the ending when their better mobility really gets to shine, but in the opening, Andrew Soltis notes in Rethinking the Chess Pieces that:

"a knight is frequently more active, more threatening, in short, more significant than a bishop in the first ten or so moves of a game. That may sound trivial but it is more than a quarter of a 40-move game."

a few paragraphs later he added:

"GM Gennady Timoshchenko studied a database of 150,000 games and came to the conclusion that BxN often makes sense in the opening because a knight is simply the more useful piece then. "A well-written chess program should be aware of the fact that at the beginning of the game the knight is at the peak' of its strength relative to the bishop and its relative strength decreases" from then on, he wrote in the [CCA Journal, December 1993."

Conversely, and as alluded to in other replies, bishops increase in relative value as the game goes on.

Second, the value of minor pieces changes depending on captures, and on the presence of major pieces (and on pawn structure, as noted by others). Jose Capablanca wrote in A Primer of Chess that a knight becomes weaker as pieces are traded off (while rooks become stronger). Larry Kaufman added to this that the same holds true after pawn exchanges. GM Timoshchenko said a knight increases in value after a trade of rooks, and decreases in value after a trade of queens.

Another way of saying this is that the combination of Q+N and R+B are generally stronger in the endgame than Q+B and R+N. So in general in the ending having R+B > R+N, while Q+B < Q+N.

Finally, I would also caution against relying on the numbers too much in deciding which pieces are better. Expand your understanding of the position (and of chess) by using a more sophisticated approach endorsed by many chess teachers. Yusupov suggests using the following five factors to determine the relative value of pieces (relative to other pieces in an actual position):

1. Mobility
2. Activity
3. Coordination
4. Central location
5. Safety

Answer 3

Kasparov once said something like: "The number of positions in which a bishop is better a than knight is greater than the number of positions in which a knight is better than a bishop. That's why bishops are better than knights, in general".

As mentioned in other answers, general principle is that knights are usually superior in closed positions, where the advantage of being able to jump over pieces becomes more important than the long range bishops have.

Now, I am not a very good chess player, but I will give you my view on advantages and disadvantages of knights and bishops, and I will try to make it as concrete as possible. However "wrong" my views may seem to you (or objectively are), at least I hope it will be something for you to think about.

What I like about bishops:

• they can simultaneously play a defensive role and an attacking role;
• in an endgame (especially when there are only few pawns left, and not all on the same side of the board), bishop can be sacrificed "at the very last moment" meaning: you let your opponent spend a lot of moves to get her/his pawn(s) to the promotion square and then it disappears, all the while you use your bishop to nurse your pawn up the board; since knights are rather clumsy at stopping pawns alone, this is a significant factor around which one can make plans in an endgame; one of my favorite endgames ever is Fischer vs. Taimanov (excellently video-annotated here); the B vs N endgame appears on move 45;

[FEN ""]
[Event "Fischer - Taimanov Candidates Quarterfinal"]
[Site "Vancouver, Canada"]
[Date "1971.05.25"]
[EventDate "1971.05.16"]
[Round "4"]
[Result "1-0"]
[White "Robert James Fischer"]
[Black "Mark Taimanov"]
[ECO "B47"]
[WhiteElo "?"]
[BlackElo "?"]
[PlyCount "141"]

1. e4 c5 2. Nf3 Nc6 3. d4 cxd4 4. Nxd4 Qc7 5. Nc3 e6 6. g3 a6
7. Bg2 Nf6 8. O-O Nxd4 9. Qxd4 Bc5 10. Bf4 d6 11. Qd2 h6
12. Rad1 e5 13. Be3 Bg4 14. Bxc5 dxc5 15. f3 Be6 16. f4 Rd8
17. Nd5 Bxd5 18. exd5 e4 19. Rfe1 Rxd5 20. Rxe4+ Kd8 21. Qe2
Rxd1+ 22. Qxd1+ Qd7 23. Qxd7+ Kxd7 24. Re5 b6 25. Bf1 a5
26. Bc4 Rf8 27. Kg2 Kd6 28. Kf3 Nd7 29. Re3 Nb8 30. Rd3+ Kc7
31. c3 Nc6 32. Re3 Kd6 33. a4 Ne7 34. h3 Nc6 35. h4 h5
36. Rd3+ Kc7 37. Rd5 f5 38. Rd2 Rf6 39. Re2 Kd7 40. Re3 g6
41. Bb5 Rd6 42. Ke2 Kd8 43. Rd3 Kc7 44. Rxd6 Kxd6 45. Kd3 Ne7
46. Be8 Kd5 47. Bf7+ Kd6 48. Kc4 Kc6 49. Be8+ Kb7 50. Kb5 Nc8
51. Bc6+ Kc7 52. Bd5 Ne7 53. Bf7 Kb7 54. Bb3 Ka7 55. Bd1 Kb7
56. Bf3+ Kc7 57. Ka6 Nc8 58. Bd5 Ne7 59. Bc4 Nc6 60. Bf7 Ne7
61. Be8 Kd8 62. Bxg6 Nxg6 63. Kxb6 Kd7 64. Kxc5 Ne7 65. b4
axb4 66. cxb4 Nc8 67. a5 Nd6 68. b5 Ne4+ 69. Kb6 Kc8 70. Kc6
Kb8 71. b6 1-0

• in general one could say that bishops are more useful in endgame pawn races;
• the movement of the bishop is more natural (straight diagonal lines), and therefore easier to use and to visualize; this makes them also better team players; you may heard people saying "a rook and a bishop is better than a rook and a knight"; it is easier to coordinate rooks and bishops, bishops and bishops, and especially queens and bishops, than knights,
• bishops can dominate knights more easily than vice versa.

What I do not like about bishops:

• when not paired, they are limited to one color of the squares (obviously, this is not optimal)
• you cannot win an endgame with an a- or h- pawn, if you have the wrong-colored bishop.

What I like about knights:

• each square on the board can be controlled by a knight;

• they can be "eternal" (there is a notion of an "eternal knight", i.e. in a situation knight vs. bishop, there is often a possibility of establishing an outpost for the knight, where it is untouchable and this is often the beginning of a long positional domination of the side with the eternal knight); one of my favorite games demonstrating this is Fischer vs. Bolbochan (excellently commented here); the "eternal knight vs. bad bishop" situation appears after move 20;

[FEN ""]
[Event "Stockholm Interzonal"]
[Site "Stockholm, SWE"]
[Date "1962.03.03"]
[EventDate "1962.??.??"]
[Round "21"]
[Result "1-0"]
[White "Robert James Fischer"]
[Black "Julio Bolbochan"]
[ECO "B90"]
[WhiteElo "?"]
[BlackElo "?"]
[PlyCount "74"]

1.e4 {Notes by Bobby Fischer} c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6
5.Nc3 a6 6.h3 Nc6 7.g4 Nxd4 8.Qxd4 e5 9.Qd3 Be7 {More accurate
is 9...B-K3 immediately.--Fischer} 10.g5 Nd7 11.Be3 Nc5 12.Qd2
Be6 13.O-O-O O-O 14.f3 Rc8 15.Kb1 {Amateurs are often puzzled
by this apparent loss of time. Actually it is a handy
defensive move, getting out of the pin on the QB-file which
could become annoying after ...P-QN4-5. One never knows when
lightning will strike! -- Fischer} Nd7 16.h4 b5 17.Bh3 Bxh3
18.Rxh3 Nb6 19.Bxb6 Qxb6 20.Nd5 {White has a strategically won
game; his Knight cannot be dislodged. -- Fischer} Qd8 21.f4
exf4 22.Qxf4 Qd7 23.Qf5 Rcd8 24.Ra3 Qa7 25.Rc3 g6 26.Qg4 Qd7
27.Qf3 Qe6 28.Rc7 Rde8 29.Nf4 Qe5 30.Rd5 Qh8 31.a3 h6 32.gxh6
Qxh6 33.h5 Bg5 34.hxg6 fxg6 35.Qb3 {The coup de
grace.--Fischer} Rxf4 36.Re5+ Kf8 37.Rxe8+ {Black
resigns. After 37...KxR; 38 Q-K6+, K-B1; 39 Q-B8+
mates.--Fischer} 1-0

• they are more forcing pieces than bishops in the sense that you cannot block knights; if your king is in check from a knight, either you have to move your king, or take the knight, which reduces the number of resources for the defending king; you can see this theme especially in the games of the great champion Mikhail Tal;

• their unusual movement generally offers more room for creativity; it often helps in creating unusual and visually spectacular attacks (again, see Tal's games---I am no expert, but he sacrificed knights maybe more often than any other piece);

• white knights on the 6th rank (or black ones on the 3rd) are incredibly powerful; I assume you saw the 16th game of the 1985 WCC (Kasparov himself explains this game in his documentary---there is a portion of it on Youtube); while mere mortals can only dream of ever playing such a beautiful game, this is still good to have in mind as a potential threat; the mentioned situation appears after Black's 16th move; there the knight cuts off all of White's heavy pieces (such knight is popularly called an "octopus knight");

[FEN ""]
[Event "Wch Moscow i 40/202; YB 4/91"]
[Site "16"]
[Date "1985.10.15"]
[EventDate "?"]
[Round "16"]
[Result "0-1"]
[White "Anatoly Karpov"]
[Black "Garry Kasparov"]
[ECO "B44"]
[WhiteElo "?"]
[BlackElo "?"]
[PlyCount "80"]

1.e4 c5 2.Nf3 e6 3.d4 cxd4 4.Nxd4 Nc6 5.Nb5 d6 6.c4 Nf6 7.N1c3
a6 8.Na3 d5 9.cxd5 exd5 10.exd5 Nb4 11.Be2 Bc5 12.O-O O-O
13.Bf3 Bf5 14.Bg5 Re8 15.Qd2 b5 16.Rad1 Nd3 17.Nab1 h6 18.Bh4
b4 19.Na4 Bd6 20.Bg3 Rc8 21.b3 g5 22.Bxd6 Qxd6 23.g3 Nd7
24.Bg2 Qf6 25.a3 a5 26.axb4 axb4 27.Qa2 Bg6 28.d6 g4 29.Qd2
Kg7 30.f3 Qxd6 31.fxg4 Qd4+ 32.Kh1 Nf6 33.Rf4 Ne4 34.Qxd3 Nf2+
35.Rxf2 Bxd3 36.Rfd2 Qe3 37.Rxd3 Rc1 38.Nb2 Qf2 39.Nd2 Rxd1+
40.Nxd1 Re1+ 0-1

• from White's point of view, getting a knight on f5 is a pretty good accomplishment; this is a good square because the knight is difficult to evict without creating serious weaknesses, and it is ready to sacrifice itself at any moment, so your opponent has to worry about it constantly (a good lecture about this can be found at the YouTube channel of Chess Club and Scholastic Center of Saint Louis)

  What I do not like about knights:

• I guess they are in general worse pieces than bishops; they are more difficult to manoeuvre, as they are slower than bishops, they also get stuck more easily than bishops (there are no "bishop on a rim..." sayings in chess)

• pinning a knight is usually easier than pinning a bishop, and one has to look after knight pins, especially in certain openings, so you have to be more careful with knights, than with bishops in that respect.

That's it for now. I hope it will help. I just listed things as they came to my mind. It's neither meant to be comprehensive, not objectively correct. It's a list of subjective views. The question itself is quite general, so it's hard to give a concrete and objective answer.

But I do want to say that while it is good to have basic guidelines in chess for bishops, knights, and everything else, it is also important to think about them and try to evaluate them for yourself before accepting (or rejecting) them. Good luck!

Answer 4

There are many good positional books that cover this topic in depth, such as Silman's "Reassess Your Chess." For a lighter answer, there are several good guidelines (many of which are well-known):

Middlegame guidelines

• Is the position open or closed?
  • Open positions favor bishops; closed positions favor knights.
• Does the knight have advanced outposts on which it can do something?
  • Powerful knights that cannot be driven away are valuable.
• Does the bishop have an active function?
  • Bad bishops (blocked by own pawns) and ghost bishops (the battle is being fought on the opposite color) can be useless.
• Does one side have the bishop-pair?
  • GM Larry Kaufman, with the aid of non-subjective silicon, says the bishop-pair is worth 1/2 pawn. However, if the position is closed, this 1/2 pawn can be more than offset by the ineffectiveness of bishops in the position.
• Is there a weak square complex, especially around the king?
  • If so, a bishop of that color is more valuable for both sides, unless the bishop is trapped.
• Bishops of opposite colors favors the attacker in the middlegame.

Endgame guidelines

• Are all pawns on one side, or are there pawns on both flanks?
  • One side favors knight due to its ability to cover both colors
  • Both flanks favors bishop due to its long-distance range
• Is there a rook-pawn?
  • Rook-pawn + bishop of wrong color is a draw if the opposing king is well placed.
  • Rook-pawn + knight is a win even if the opposing king is well placed, unless the pawn is (or is forced to go to) the 7th rank.
• Are there no pawns?
  • 2 bishops mate is easy, bishop + knight mate is hard, and 2 knights mate cannot be forced
• Is one side up in pawns?
  • Bishops of opposite colors tends to be drawish when there are no other pieces (excl. pawns).
• The endgame tends to be open, so keep that in mind.

The article by GM Larry Kaufman also somewhat addresses this topic.

Note that bishop pairs are not redundant, and knight "pairs" are, so the bishop pair is better than 2 knights.

Mobility is important for bishops (beware of ghost bishops). Knights, if they are well placed and invulnerable, bypass the mobility consideration because the very purpose of mobility is activity, and well placed knights do not need to be mobile in order to be active (think knight blockade, or an attacking outposted knight).

Answer 5

In the endgame a Knight is usually better than a bishop. Two bishops are almost always better than a bishop and a knight.

However, you need to play at Master level for this to become important. There are many more factors more important in the position, including material. If you have a good bishop against a bad knight but you are the Queen down, it is not going to help you.

Answer 6

Is a Knight inferior to a Bishop? A perfect reply is, I think an impossibility.

Well the superiority of Knight over Bishop (or vice versa) is position dependent. I believe as a general guideline (but not a rule) that a Knight is only slightly superior to a Bishop, though several exceptions can be demonstrated.

Some people believe that a Knight is inferior to a Bishop in endings. It is worth noting that in about 55% of masters' games (single Bishop vs. single Knight) the Knight dominates the opposing Bishop. It is again often the case that Queen + Knight combination is better than a Queen + Bishop combination because the Knight is unique in its movement and thus supplements its friendly Queen. So is a R + N combination a little superior to a R + B team.

Some also believe that a Knight is pretty useless on an empty board, which can be a wrong notion. What finally becomes important is whether the piece (the Knight or the Bishop) watches crucial squares and does the 'job' well.

What about pairs of pieces? A Bishop pair is usually much worth compared to a Knight pair! The Bishop pair can win 80% or so of chess endings when they confront pair of Knights. What I like about chess is that it 'disproves' Mathematics in this context!

Answer 7

In endgames, especially when knight or bishop is against pawns, the knight has another advantage. It is that knights can reach and attack pawns on dark squares as well as light squares. Also for many players it is harder in the endgame to see knight moves than bishop moves.

Answer 8

No one has answered about engines yet, so I'll write about Stockfish, the strongest engine in the world at this moment with NNUE. It has gone through a lot of tweaking through fishtest which includes the relative piece values. These values actually change from middlegame to endgame as pawns become substantially more valuable.

https://github.com/official-stockfish/Stockfish/blob/9f6bcb38c032a18c8b1aec318d5c7255827f9c7b/src/types.h#L189

  PawnValueMg   = 126,   PawnValueEg   = 208,
  KnightValueMg = 781,   KnightValueEg = 854,
  BishopValueMg = 825,   BishopValueEg = 915,
  RookValueMg   = 1276,  RookValueEg   = 1380,
  QueenValueMg  = 2538,  QueenValueEg  = 2682,

Using these values at face value, Stockfish considers bishops to be slightly better than knights. However, note that these values are only one in a whole bunch and Stockfish searches much deeper than a human can.

Some interesting discussion https://www.reddit.com/r/chess/comments/e57lqz/stockfish_doesnt_use_the_traditional_piece_values/

Comment from Stockfish dev: https://www.reddit.com/r/chess/comments/e57lqz/stockfish_doesnt_use_the_traditional_piece_values/f9idquq/ (here is the referenced PSQT)

This is not really correct. https://github.com/official-stockfish/Stockfish/blob/master/src/types.h#L182 As you can see there in middlegame values are even more off (like bishop is worth 6.5 pawns, etc). I think this is needed for stockfish to understand positional pawn sacs in midgame/opening. Pawns become more valuable into endgame, but still bishop is worth like 4.5 pawns. But you should understand smth :

1. stockfish eval is actually worse than human eval. It's needed to guide search. It thinks completely differently from how human do it that's why not all human concepts are good for sf eval and vice versa;
2. eval isn't pure piece values at all. For example, each piece is assigned bonuses with PSQT and everything but pawns and king is used in calculation of mobility. This bonuses are actually not 0-centered, so it can be somewhat compensating;
3. for human players it's much harder to win smth like B + R + P vs R + 4p than it is for stockfish, so for human players bigger material eval of pawn is more logical;
4. stockfish has a lot of bonuses for passers, so it's kinda balanced around it. This means that if pawn becomes a passer it becomes worth a ton so probably low material value of pawn is a subproduct of this.

Further statistics of analysis of games are at chess programming wiki https://www.chessprogramming.org/Bishop_versus_Knight which also brings up that a bishop pair is stronger than a knight and a bishop or two knights