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There are challenges for the longest sequence of moves in which white's available moves increase or decrease. This challenge is for the longest sequence of moves (from the opening position) in which white's available moves stays at 20, without repeating any moves* or positions. (The fact that a given move can't be played for the purpose of the challenge doesn't prevent it being scored as an "available move").

For instance, after 1. b4 b5, white still has 20 moves available. The pawn has lost two moves, while the dark-squared bishop has gained two moves.

* "repeating a move" means moving the same exact piece from the same square to the same target square, and whether it is a capture: "the knight that started at b1 moving from c3 to e4, not capturing". Other considerations like check do not stop it being the same move. (The rule is to avoid situations where a number of interchangeable moves are played semi-repetitively without changing the board meaningfully).

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Hundreds of moves...

We can shuffle pieces for very long, the main constraint being not to play twice the same move (per OP's definition). Here is an example line with 25 moves, that can easily be prolongated (I may do it when I get some time...):

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1. g4 g5 2. f3 h5 3. c4 h4 4. a3 d5 5. Ra2 Qd6 6. b3 Nf6 7. Bh3 Bf5 8. Kf1 Qb6 9. Qe1 Bg6 10. Rc2 Bg7 11. Rc3 Qa6 12. Re3 e5 13. Qf2 Nc6 14. Bg2 O-O-O 15. Qe1 Nd4 16. Kf2 Nc2 17. a4 d4 18. Na3 Kb8 19. d3 Nb4 20. a5 Qc6 21. a6 h3 22. Kg3 Rd7 23.c5 Nfd5 24. Nc2 Nc3 25.Bd2 Re8

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