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The fastest way to get to 18 queens is known. But what are the shortest possible games with a) 20 Bishops, b) 20 Knights, and c) 20 Rooks?

Here are my own attempts. Can anybody find/create a faster way?

[Title "20 Rooks-104 Ply, me, chess.stackexchange.com 3/31/2019, Non-Unique Proof Game In 52.0 Moves"]
[FEN ""]
[startply "104"]

1. b4 d5 2. g4 e5 3. h4 f5 4. a4 c5 5. c4 d4 6. f4 e4 7. Nf3 exf3 8. Nc3 dxc3 9. d4 a5 10. e4 h5 11. b5 Na6 12. g5 Nh6 13. bxa6 b5 14. gxh6 g5 15. d5 b4 16. e5 g4 17. Bd3 Bd7 18. Be4 Bb5 19. Qd4 Qg5 20. axb5 fxe4 21. hxg5 cxd4 22. g6 h4 23. g7 h3 24. f5 g3 25. f6 g2 26. Kf2 Kf7 27. Kg3 Kg6 28. Rh2 Rh7 29. g8=R+ Rg7 30. h7 g1=R+ 31. Rg2 h2 32. f7 f2 33. e6 e3 34. e7 e2 35. exf8=R h1=R 36. Re8 f1=R 37. f8=R e1=R 38. h8=R b3 39. b6 b2 40. b7 Ra7 41. Ra2 bxc1=R 42. b8=R Rb1 43. Rab2 Rab7 44. a7 d3 45. d6 d2 46. c5 c2 47. c6 a4 48. c7 a3 49. d7 a2 50. a8=R a1=R 51. c8=R c1=R 52. d8=R d1=R

 [Title "20 Bishops-104 Ply, me, chess.stackexchange.com 3/31/2019, Non-Unique Proof Game In 52.0 Moves"]
 [FEN ""]
[startply "104"]

1. g4 h5 2. g5 Rh6 3. gxh6 g5 4. h4 g4 5. b4 e5 6. f4 e4 7. Nf3 exf3 8. e4 f5 9. e5 Qg5 10. Nc3 a5 11. Ne4 fxe4 12. c4 a4 13.Qb3 axb3 14. a4 b5 15. a5 d5 16. c5 Ra6 17. hxg5 Rd6 18. cxd6 c5 19. Ra4 c4 20. d4 Na6 21. Be3 Nc5 22. dxc5 bxa4 23. g6 g3 24. h7 h4 25. g7 h3 26. b5 g2 27. Kf2 Kf7 28. f5 c3 29. f6 Kg6 30. Kg3 gxh1=B 31. a6 a3 32. a7 a2 33. b6 b2 34. b7 c2 35. c6 d4 36. c7 f2 37. Ba6 f1=B 38. Bf2 e3 39. a8=B Bhg2 40. b8=B h2 41. hxg8=B d3 42. Bb3 d2 43. g8=B Bh6 44. f7 e2 45. d7 a1=B 46. f8=B b1=B 47. d8=B Be6 48. c8=B Bf7 49. e6 c1=B 50. e7 d1=B 51. e8=B e1=B 52. Ba2 h1=B

[Title "20 Knights-104 Ply, me, chess.stackexchange.com 3/31/2019, Non-Unique Proof Game In 52.0 Moves"]
[FEN ""]
[startply "104"]

1. d4 c5 2. f4 e5 3. f5 d5 4. Bf4 Be6 5. fxe6 exf4 6. e4 f5 7. e5 c4 8. Bd3 Bc5 9. dxc5 cxd3 10. c4 a5 11. b4 a4 12. Qb3 axb3 13. a4 b5 14. a5 h5 15. g4 Rh6 16. g5 d4 17. gxh6 g5 18. h4 g4 19. Ra4 Qg5 20. hxg5 bxa4 21. Kf2 d2 22. e7 f3 23. g6 d3 24. g7 Kf7 25. Ke3 Kg6 26. Kd4 f4 27. e6 h4 28. h7 b2 29. a6 a3 30. b5 a2 31. b6 f2 32. c6 f3 33. c7 g3 34. a7 g2 35. b7 h3 36. c5 h2 37. c6 Kf5 38. Nh3 Na6 39. Na3 Nh6 40. bxa8=N gxh1=N 41. c8=N d1=N 42. e8=N f1=N 43. g8=N b1=N 44. h8=N a1=N 45. c7 d2 46. e7 f2 47. Nef6 Nb2 48. Ncb6 Nfg3 49. c8=N f1=N 50. e8=N d1=N 51. Nac7 Nhf2 52. a8=N h1=N
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  • 1
    Just a comment: Finding a faster 16-passed-pawn-game is not necessarily going to be optimal. For instance, it might be faster overall to promote pawns 1 or 2 at a time, thus at no point will there be 16 passed pawns on the board at once.
    – Remellion
    Apr 4 '19 at 8:10
0

Addendum 1/9/2021: In a Computer Chess Club archives page that I came across today, I found some holy grails! The thread author Eduard Nemeth posted four proof games, all from 1997 and by Zoltan Blazsik, for 18 queens and 20 rook, bishops, and knights.

The bishop and knight games are faster than mine-new records! However, my 104 ply for 20 rooks remains untouched.

[Title "20 Knights-100 Ply, Zoltan Blazsik, 1997, Non-Unique Proof Game In 50.0 Moves"]
[FEN ""]
[startply "100"]

1. h4 g5 2. h5 g4 3. h6 Bg7 4. Rh3 gxh3 5. hxg7 h5 6. b4 a5 7. b5 Ra6 8. bxa6 a4 9. a7 a3 10. Bb2 axb2 11. a4 h2 12. g4 e5 13. f4 d5 14. e4 Be6 15. f5 h4 16. fxe6 f5 17. g5 h3 18. c4 Qd6 19. c5 f4 20. cxd6 c5 21. Bc4 dxc4 22. d4 c3 23. d5 c4 24. Qd4 exd4 25. a5 bxa1=N 26. a8=N c2 27. a6 c1=N 28. a7 c3 29. gxh8=N b5 30. Nb6 b4 31. a8=N b3 32. Na3 b2 33. e5 b1=N 34. g6 Na2 35. g7 Nh6 36. g8=N c2 37. d7+ Kf8 38. d8=N c1=N 39. e7+ Kg7 40. d6 h1=N 41. d7 h2 42. Nb7 d3 43. d8=N d2+ 44. Kf1 f3 45. e8=N+ Kh7 46. e6 f2 47. Kg2 d1=N 48. Nec7 f1=N 49. e7 Nhf2 50. e8=N h1=N

[Title "20 Bishops-100 Ply, Zoltan Blazsik, 1997, Non-Unique Proof Game In 50.0 Moves"]
[FEN ""]
[startply "100"]

1. a4 b5 2. a5 c5 3. Ra3 b4 4. d4 Qb6 5. axb6 a5 6. d5 Nc6 7. dxc6 bxa3 8. b4 a4 9. b5 c4 10. Nd2 c3 11. e4 f5 12. e5 Nf6 13. exf6 f4 14. g4 h5 15. g5 Rh6 16. gxh6 g5 17. h7 g4 18. h4 g3 19. Qg4 hxg4 20. h5 g2 21. h6 gxh1=B 22. Ne2 f3 23. h8=B fxe2 24. f4 g3 25. b7 g2 26. f5 e5 27. bxa8=B cxd2+ 28. Kf2 a2 29. c4 a1=B 30. b6 d5 31. b7 d4 32. c7 g1=B+ 33. Kg3 a3 34. c5 a2 35. b8=B Ba6 36. c8=B Bb2 37. c6 a1=B 38. Bcb7 d1=B 39. c7 Bb3 40. c8=B d3 41. f7+ Kd8 42. f6 Bb4 43. f8=B d2 44. Bc5 e1=B+ 45. Bf2 d1=B 46. f7 e4 47. h7 e3 48. Bg7 e2 49. h8=B Bed2 50. f8=B e1=B

Thanks to Remellion's comment that getting 16 passed pawns first isn't necessary, I shaved 2 plies off 20 knights.

Addendum 11/29/2020-With a Black king maneuver, another ply is gone.

[Title "20 Knights-101 Ply, me, chess.stackexchange.com 11/29/2020, Non-Unique Proof Game In 50.5 Moves"]
[FEN ""]
[startply "101"]

1. h4 a5 2. h5 a4 3. b4 g5 4. h6 a3 5. Bb2 Bg7 6. hxg7 axb2 7. a4 h5 8. Rh4 Ra5 9. bxa5 gxh4 10. g4 b5 11. g5 b4 12. g6 b3 13. c4 f5 14. c5 f4 15. c6 f3 16. Bg2 Bb7 17. cxb7 fxg2 18. gxh8=N bxa1=N 19. f4 c5 20. f5 c4 21. f6 c3 22. g7 b2 23. a6 h3 24. a7 h2 25. a8=N h1=N 26. a5 h4 27. a6 h3 28. a7 h2 29. e4 d5 30. d4 e5 31. Qf3 Qc7 32. Qf4 Qc5 33. dxc5 exf4 34. e5 d4 35. e6 d3 36. c6 d2+ 37. Ke2 f3+ 38. Ke3 f2 39. c7 c2 40. c8=N c1=N 41. e7 f1=N+ 42. Kd4 Na6 43. f7+ Kd7 44. e8=N Nh6 45. Nh3 g1=N 46. Na3 b1=N 47. Nac7 Nhg3 48. a8=N d1=N 49. b8=N+ Kd8 50. f8=N h1=N 51. g8=N
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