5

If one side captures everything and promotes all pawns (including the opponent's re-placed pawns) to a queen, it is possible to achieve 206 points of material difference 18 queens, 4 rooks/knights/4 bishops).

Here is an example solution.

[FEN "8/4k3/8/8/RNBQ1BNR/RNBQKBNR/QQQQQQQQ/QQQQQQQQ b - - 36 137"]

What is the theoretical minimum amount of moves for achieving this material difference, and how would one implement it?

4

This solution finishes with White's 54th move. Every White move other than the early e-pawn moves is one of the following:

  1. A promotion

  2. A pawn capture by a Queen moving from the eighth rank

  3. Placing a piece

  4. Placing a pawn on the seventh rank

    [FEN ""]
    
    [Variant "Crazyhouse"]
    
    1. e4 d5 2. exd5 c6 3. dxc6 a5 4. p@c7 Ra6 5. cxb7 Rb6 6. p@a7 Rxb2 7. axb8=Q Rxa2 8. bxc8=Q Rxc2 9. p@a7 p@b2 10. Qxb2 Rxd2 11. a8=Q e5 12. Qxa5 Rxf2 13. p@b7 Ke7 14. b8=Q p@b3 15. Q8xb3 Kf6 16. p@b7 Rxg2 17. b8=Q p@b5 18. Q8xb5 Rxh2 19. p@a7 p@a6 20. a8=Q Rd2 21. Qa8xa6+ Kg5 22. N@c3 Kf4 23. p@e7 Kg3 24. exf8=Q f6 25. p@f7 g6 26. fxg8=Q p@a7 27. N@g5 p@a3 28. Qfxa3 p@c5 29. B@h3 Rd7 30. cxd8=Q Re7 31. p@g7 Re8 32. gxh8=Q Rf8 33. Qhxh7 Re8 34. B@h6 Re7 35. p@f7 Rb7 36. f8=Q e4 37. Qfxf6 e3 38. Qgxg6 e2 39. p@e7 Rb8 40. e8=Q Rb6 41. p@b7 Rc6 42. b8=Q+ Rd6 43. Qbxa7 Rd7 44. Qcxc5 Rf7 45. Qexe2 Rf8 46. p@g7 Kh4 47. gxf8=Q Kg3 48. p@g7 Kh4 49. g8=Q Kg3 50. p@e7 Kh4 51. e8=Q Kg3 52. R@h8 Kh4 53. R@f7 Kg3 54. Q@g7
    
0
2

Reference solution in 58 moves by /u/CratylusG on reddit.com - missing last three placements: https://lichess.org/fP8zuniL

[fen ""]

1. a4 b5 2. axb5 a6 3. bxa6 Bb7 4. axb7 Ra2 5. e4 f5 6. exf5 g6 7. fxg6 Rxb2 8. gxh7 Rxc2 9. hxg8=Q Rxd2 10. P@g7 Rxf2 11. gxh8=Q P@b2 12. Qxb2 Rxg2 13. P@h7 c5 14. h8=Q P@c3 15. Qhxc3 c4 16. Qgxc4 Rxh2 17. P@h7 P@d4 18. h8=Q d5 19. Qhxd4 P@g3 20. P@a7 Bh6 21. axb8=Q Kf7 22. Qbxg3 Bf4 23. b8=Q Ke6 24. Qbxf4 Qb8 25. N@f5 Kf7 26. P@c7 Rh8 27. cxb8=Q e5 28. Qbxe5 Rb8 29. P@c7 P@b3 30. cxb8=Q P@d6 31. Q8xb3 Kf8 32. B@d8 Kf7 33. P@b7 Kf8 34. b8=Q Kf7 35. N@e7 Kf8 36. Qbxd6 Kf7 37. P@b7 Kf8 38. b8=Q Kf7 39. Q8b4 Kf8 40. P@b7 Kf7 41. b8=Q Kf8 42. Q8b5 Kf7 43. P@a7 Kf8 44. P@b7 Kf7 45. P@c7 Kf8 46. a8=Q Kf7 47. b8=Q Kf8 48. c8=Q Kf7 49. R@e6 Kf8 50. Qaxd5 Kf7 51. P@a7 Kf8 52. a8=Q Kf7 53. P@a7 Kf8 54. Qac6 Kf7 55. a8=Q *

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