I know that it is makes no sense to promote a pawn to a bishop or a rook as the queen can compensate for both but a knight is something different. However, the queen is still much more powerful. So what situations would provoke you into promoting your hard-labored pawn to just a knight rather than a queen?
White to move:
[FEN "8/q1P1k3/8/8/8/8/6PP/7K w - - 0 1"]
Since my example is rather contrived and artificial, I'll also say that the so-called Lasker trap in the Albin Countergambit gives a more realistic setting, and one where a knight promotion is the best option as early as move 7:
[FEN ""] 1.d4 d5 2.c4 e5 3.dxe5 d4 4.e3 $2 Bb4+ 5.Bd2 dxe3! 6.Bxb4 $4 exf2+ 7.Ke2 fxg1=N+ $1 8.Ke1 Qh4+ 9.Kd2 (9.g3 Qe4+) Nc6 $19
Oddly enough, I happened across that line for the first time just earlier today.
Oh, and there are situations where underpromotion to a bishop or rook is necessary in order to avoid a stalemate that a queen might create. For instance, in the sequence of moves coming from the Saavedra position, if white were to create a queen with
6. c8=Q, this would allow black to draw by stalemate, and so white must instead play
6. c8=R in order to win:
[FEN "8/8/1KP5/3r4/8/8/8/k7 w - - 0 1"] 1.c7 Rd6+ 2.Kb5 Rd5+ 3.Kb4 Rd4+ 4.Kb3 Rd3+ 5.Kc2 $1 Rd4 $1 6.c8=R $1 (6.c8=Q $2 Rc4+ $1 7.Qxc4 $10) 6...Ra4 7.Kb3 $18
During round 9 of the Istanbul 2012 Chess Olympiads, at the Nakamura-Kramnik table of the USA vs Russia match, we've witnessed another one of those promotions to knight at move 62 by white.
The relevant position (white to play):
[fen "8/2P1k3/8/8/5p2/5KbB/3pp3/3N4 w - - 1 62"] 1. c8=N+ (1. Kxe2? f3+ 2. Kxf3 Bxc7)
We can see here that if
62. ... f3+
and the bishop on
g3 will take the
c7 pawn next move resulting in a draw.
To avoid that, Nakamura promotes his pawn to a knight with check to save his advantage.
Here are 4 different commentaries of the game, pick your favorite one!
After answering this question, I was reminded of another important situation where underpromotion is necessary:
[FEN "8/8/8/8/8/2K5/1p5R/2k5 b - - 0 1"] 1... b1=N+! (1... b1=Q 2. Rh1++)
In this position,
1...b1=N+ is the only move to draw. Any other move will allow a quick mate, but after knighting the pawn, black sets up a drawing fortress.
While this is a slightly contrived example, it does come in handy sometimes. As an anecdote, I was playing a rook and pawn endgame where I was up a pawn. In one variation, my opponent could sacrifice his rook for my last pawn and reach this position:
[FEN "8/8/2K5/1p5R/2k5/8/8/8 b - - 0 1"] 1... b4 2.Rh4+ ( 2. Rc5+ Kd3 3. Kb5 b3 4. Ka4 b2 5. Rb5 Kc2 6. Rc5+ Kd2) Kc3 3.Kc5 b3 4.Rh3+ Kc2 5.Kc4 b2 6.Rh2+ Kc1 7.Kc3
I was able to recognize that this is actually a draw because black can play
1...b4 2.Rh4+ Kc3 3.Kc5 b3 4.Rh3+ Kc2 5.Kc4 b2 6.Rh2+ Kc1 7.Kc3 reaching the position above. Due to this, I went into another variation and won. Without knowing this idea, however, it would have been very hard to resist winning my opponent's rook.
There are even positions where one promotes R or B to save a draw by getting stalemated (rather than win by avoiding stalemate). One example is the Traxler-Dedrle setup:
[FEN "4rN1K/5qP1/8/8/8/8/k7/8 w - - 0 1"] 1. g8=B!! (1. g8=Q Rxf8 2. Qxf8 Qxf8) Rxf8
WTM loses with 1 g8Q? Rxf8 2 Qxf8 Qxf8+ but draws with 1 g8B!! when Rxf8 is stalemate (NB the g8B pins Qf7).
There's a famous study by Rusinek where White must promotes both R and B (as well as N) to guarantee a draw; see the position shown in Rusinek's Wikipedia page https://en.wikipedia.org/wiki/Jan_Rusinek.
Here is a fun tactic, involving underpromotion, to finish off the game if you are two connected pawns up in a rook endgame. I saw this in an endgame manual a long time ago, but cannot find the source anymore. The tactic is totally unnecessary as white has other ways to win. Still, it's quite impressive.
[FEN "r6k/8/6PP/5RK1/8/8/8/8 w - - 0 1"] 1.Rf8+ Rxf8 2.g7+ Kh7 (2...Kg8 3.Kg6) 3.gxf8=N+!(3.gxf8=B!)(3.gxf8=Q??)(3.gxf8=R??)
1.Rf8+ Rxf8 2.g7+ black doesn't play
2...Kg8 because of
3.Kg6 and mate next move (
4.h7#). Instead black plays
2...Kh7 hoping for stalemate. Then
3.gxf8=B! both win, while
3.gxf8=R?? lead to immediate draw.
[FEN "8/2P5/8/8/3r4/8/2K5/k7 w - - 0 1"] 1. c8=Q? (1. c8=R!) Rc4+ 2. Qxc4
When you said it made no sense to promote to a Rook or Bishop, it brought this position to mind. Here, if White promotes to a Queen, the game is drawn, but if White promotes to a rook, White wins.
on 1. c8/Q Black would answer 1 ... Rc4+ 2, Qxc4 stalemate. But on 1. c8/R 2. Rc4+ White can capture the rook without fear of stalemate.
Sometimes the queen is not the most powerful piece available. Every position is different, and the extra move possibilities of the Queen can work against you sometimes. Whenever you promote, think. Most of the time, yes, a Queen is the best choice; but not always. Look around and see if a different piece would be better, or if there is a danger of stalemate posed by the queen's extra moves.
Here, 29. ... Ba3+!! and promoting to knight could've save the game!
[Date "2012.05.12"] [Result "1-0"] [FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"] [White "Ni Hua"] [StartPly "57"] [WhiteElo "2673"] [Black "Le Quang Liem"] [BlackElo "2703"] [Event "Asian Continental Open Championship"] [Site "Ho Chi Minh City"] [Round "8"] [ECO "B84"] 1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 a6 6.Be3 e6 7.Be2 Qc7 8.g4 b5 9.g5 Nfd7 10.a3 Bb7 11.Qd2 Nc6 12.Nxc6 Bxc6 13.f4 Nc5 14.Bf3 Qb7 15.Qd4 e5 16.fxe5 Ne6 17.Qd2 dxe5 18.Nd5 Bd6 19.O-O-O O-O 20.h4 a5 21.h5 b4 22.h6 bxa3 23.b3 Rfc8 24.Nb6 Bb4 25.Qh2 Bxe4 26.hxg7 a2 27.Kb2 a4 28.c4 axb3 29.g6 Ba3+!! 30.Kxb3 a1=N+!! 31.Rxa1 ( 31.Kc3 Rxc4+!! ( 31...Bb4+! 32.Kxb4 Ra4+!! 33.Kc3 ( 33.Kxa4 Nc5+ 34.Bxc5 Qc6+ 35.Ka3 Qxc5+ 36.Ka2 Qa5+ 37.Kb2 Qxb6+ 38.Kxa1 Qa5+ 39.Qa2 Qc3+ 40.Qb2 Ra8# ) 33...Rcxc4+!! 34.Kd2 ( 34.Nxc4 Qb4# ) 34...Ra2+ 35.Ke1 Rxh2 ) 32.Kd2 ( 32.Nxc4 Qb4# ) ( 32.Kxc4 Qc6+ 33.Bc5 Qxc5# ) 32...Rc2+ 33.Ke1 Rxh2 ) 31...Qxb6+!! 32.Bxb6 Nd4+!! 33.Kc3 ( 33.Bxd4 Rcb8+ 34.Kc3 ( 34.Ka2 Bc5# ) 34...Bb4+ 35.Kb2 Bd2+ 36.Bb6 Rxb6# ) 33...Rxc4+!! 34.Kxc4 ( 34.Kd2 Nxf3+ 35.Kd1 Nxh2 36.Rxh2 fxg6 ) 34...Rc8+ 35.Bc5 Rxc5# 0-1
Sometimes the reason to promote to a knight is not because is avoids stalemate, forks, skewers, or saves a game, but because it is simply the strongest move in the position.
[FEN ""] [startply "91"] 1. e4 c5 2. Nf3 e6 3. d4 cxd4 4. Nxd4 a6 5. Bd3 Qc7 6. O-O Nf6 7. Qe2 d6 8. f4 Nbd7 9. Kh1 Be7 10. c4 b6 11. Nc3 Bb7 12. Bd2 O-O 13. Rae1 Rad8 14. Bb1 Rfe8 15. f5 exf5 16. Nxf5 Bf8 17. Bg5 Rc8 18. Nh6+ gxh6 19. Bxf6 Nxf6 20. Rxf6 Bg7 21. Qg4 Re5 22. Rxh6 Qe7 23. Nd5 Qg5 24. Qxg5 Rxg5 25. Ne7+ Kf8 26. Nxc8 Bxh6 27. Nxd6 Bc6 28. Rf1 Be8 29. Nf5 Bg7 30. Nxg7 Kxg7 31. Kg1 Rc5 32. Bd3 Bd7 33. Kf2 Be6 34. b4 Rc7 35. Rc1 Kf6 36. Ke3 Ke5 37. a3 f6 38. c5 b5 39. a4 bxa4 40. Bxa6 a3 41. b5 a2 42. b6 Rg7 43. b7 Rg8 44. c6 Kd6 45. c7 a1=Q 46. c8=N+ Rxc8 47. bxc8=N+
What important here is that Krabbe states that those knight promotions were the strongest moves in that position. This is another possible reason to underpromomote a pawn to a knight.
What’s interesting is that Stockfish 8 seems to agree with Tim Krabbe. I played black’s last move in the position before white’s promotion, and Stockfish made a promotion to a knight, as White did on move 46. I followed with the rook capture that black did in the real life game. And the computer again played what White did; the second horse bounced along.
Another good reason is that it comes with checkmate
[Title "Wiede-Alphonse Goetz, Strasbourg, 1880, 0-1"] [FEN ""] [startply "14"] 1. e4 e5 2. f4 exf4 3. b3 Qh4+ 4. g3 fxg3 5. h3 g2+ 6. Ke2 Qxe4+ 7. Kf2 gxh1=N#
Or maybe your Hikaru Nakamuru and you want to have fun.
[Title "Crafty (Computer-Hikaru Nakamura, ICC Blitz, 2007, 0-1"] [FEN ""] [startply "310"] 1. Nc3 g6 2. e4 Bg7 3. Bc4 e6 4. Nf3 Ne7 5. O-O d6 6. d4 O-O 7. Bg5 h6 8. Be3 b6 9. Qd2 Kh7 10. d5 e5 11. Ne1 f5 12. f3 f4 13. Bf2 g5 14. Nd3 h5 15. Rae1 Ng6 16. Re2 Bh6 17. Ne1 g4 18. Qd3 a6 19. a4 Nd7 20. Kh1 Nf6 21. b4 Rf7 22. Rg1 g3 23. hxg3 fxg3 24. Bxg3 h4 25. Bxh4 Nxh4 26. g3 Ng6 27. Rh2 Kg7 28. Kg2 Rf8 29. Nd1 Rh8 30. Rgh1 Bg5 31. Rxh8 Nxh8 32. Nf2 Ng6 33. c3 Qe8 34. b5 a5 35. Nc2 Ne7 36. Nh3 Bxh3+ 37. Rxh3 Qg6 38. Kf2 Rh8 39. Rxh8 Kxh8 40. Ba2 Nd7 41. Ne1 Nc5 42. Qc2 Qh6 43. Ng2 Ng6 44. Bc4 Qh2 45. Bf1 Kg7 46. Qa2 Nf8 47. Bc4 Nh7 48. Kf1 Qh1+ 49. Kf2 Qc1 50. Be2 Nf6 51. Qc4 Bd2 52. g4 Qxc3 53. Qxc3 Bxc3 54. Bd1 Bd2 55. Nh4 Ng8 56. Ke2 Bg5 57. Nf5+ Kf7 58. Bc2 Ne7 59. Ng3 Nd7 60. Kd3 Ng6 61. Nf5 Kf6 62. Kc3 Nh4 63. Nxh4 Bxh4 64. Kd2 Kg5 65. Bd1 Kf4 66. Ke2 Nf6 67. Kf1 Nh7 68. Kg2 Be1 69. Kf1 Bg3 70. Be2 Ng5 71. Kg1 Nxf3+ 72. Kg2 Ne1+ 73. Kf1 Nc2 74. Kg2 Ne3+ 75. Kh3 Be1 76. g5 Kxg5 77. Kh2 Kf4 78. Bd3 Ng4+ 79. Kg2 Nf2 80. Bc2 Nxe4 81. Bb3 Nc5 82. Kf1 Nxb3 83. Kxe1 Nc5 84. Ke2 Nxa4 85. Ke1 Nc5 86. Kf2 Ke4 87. Kg2 Kxd5 88. Kg3 Kc4 89. Kg4 Kxb5 90. Kg3 a4 91. Kf3 a3 92. Ke3 a2 93. Kf2 a1=N 94. Ke3 Kc6 95. Kf3 Nab3 96. Kg4 Nd4 97. Kg5 Nde6+ 98. Kf5 Kd7 99. Kg4 b5 100. Kf3 b4 101. Kg3 b3 102. Kf3 b2 103. Kg4 b1=N 104. Kf5 Na3 105. Kg4 Nb7 106. Kf5 Nf8 107. Ke4 Nd8 108. Kd3 Nb5 109. Kc4 Na7 110. Kd3 Nc8 111. Ke4 Ke6 112. Ke3 d5 113. Kd2 c5 114. Kd1 e4 115. Kc2 d4 116. Kb2 Kd5 117. Kc1 c4 118. Kd2 e3+ 119. Ke1 Ke4 120. Kf1 d3 121. Ke1 c3 122. Kd1 c2+ 123. Kc1 e2 124. Kd2 Kd4 125. Ke1 c1=N 126. Kd2 Nb3+ 127. Ke1 Kc3 128. Kf2 Nc5 129. Ke1 Nce6 130. Kf2 Nc7 131. Kf3 e1=N+ 132. Kf2 Nc2 133. Kf1 Ne8 134. Kg2 Nfe6 135. Kf2 Nf6 136. Kf3 Nd6 137. Kg3 Nc6 138. Kg2 N2d4 139. Kh3 N4f5 140. Kg2 Nfe7 141. Kf2 Ng6 142. Ke1 Kc2 143. Kf2 d2 144. Kg2 d1=N 145. Kf1 Nc3 146. Kf2 Ncd5 147. Kg2 Nce5 148. Kg1 Nde4 149. Kg2 Nd4 150. Kg1 Ngf4 151. Kh1 Nfg4152. Kg1 Nde3 153. Kh1 Ndf5 154. Kg1 Nf3+ 155. Kh1 Nfg3# 0-1
In some cases the knight's ability to attack in L-shaped directions is more useful than a queen's straight line attack vectors. Delivering an immediate mate with a knight would be an example.
Also, promoting to a rook/bishop can be preferable to a queen since it could avoid a stalemate. The same logic can also be applied to a knight.