On lichess.com, partial 8-piece tablebases generated by Marc Bourzutschky were made available both for probing and downloading. The restriction is that at least one pair of opposing pawns must be on the board (e.g., wPe4/bPe6). There could be other (unopposed) pawns present, or even passed pawns.
The tablebases use a DTC metric (Depth to Conversion), i.e. the distance to checkmate, a winning capture or pawn promotion. The longest win for the 3P v 3P endgame, which can be also seen as a study, features the following ideas of Tattersall and Grigoriev:
1. Kc2 Ke5 2. Kd1! Kd5 3. Ke2 Kd4 4. Kd2 Ke5 5. Ke3 Kd5 6. d4 Kc4 7. Ke4 Kxb4 8. d5 Kc5 9. Ke5 b4 10. d6 b3 11. d7 b2 12. d8=Q b1=Q 13. Qc7+ Kb5 14. Qb7+ Kc5 15. Qxb1 +-
1. Kc2! 1. d4? Ke4 2. Kc3 Kf5! 3. Kd3 Kf4 = 1... Kf4 2. Kb2! Kf3 3. Kb3! Kf4 4. Kc2 Ke5 4... Kf3 5. Kd2 Kf4 6. Ke2 +-; 4... Ke3 5. Kc3 +- 5. Kd1! etc.
This is the longest win:
https://op1-tables.info/?fen=8/4p1p1/6p1/8/k3P3/8/2P3P1/K7_w_-_-_0_1,
but for a study, I prefer the following starting position:
1. c3 Kc4 2. Kd2 Kb3 3. Kd3 e5 White would like to reach the same position with BTM.
4. Kd2! 4. g3? g5 5. g4 g6 6. Kd2 Kc4 7. Kc2 Kb5! 8. Kb3 Kc5 9. c4 Kd4 10. Kb4 Kxe4 11. c5 Kf3 12. c6 e4 13. c7 e3 14. c8=Q e2 15. Qc1 Kf2 16. Qd2 Kf1 and draw because it is forbidden for the queen to use the f4 square. 4... Ka4! 4... Kc4 5. Kc2 +-; 4... Ka3 5. Kc2 +- 5. Ke2(3)! Grigoriev's triangulation 5... Ka3 6. Ke3(2)! Ka4 7. Kd2 Kb5 7... Kb3 8. Kd3 and white has managed to lose a tempo reaching the same position with BTM. 8... g5 9. Kd2 Ka4 10. Ke2 Ka3 11. Ke3 Ka4 12. Kd2 Kb3 13. Kd3 and so on.
8. Kc1! Tattersall's triangulation 8. Kc2?! Kc4 9. Kd2 Kb5 loss of time 8... Kc5 9. Kb2 Kc4 10. Kc2 g5 11. Kd2 Kb5 11... Kb3 12. Kd3 +- 12. Kc1! Kc5 13. Kb2 Kc4 14. Kc2 g4 15. Kd2 Kb5 16. Kc1! Kc5 17. Kb2 Kc4 18. Kc2 g3 19. Kd2 Kb5 20. Kc1! Kc5 21. Kb2 Kc4 22. Kc2 g6 23. Kd2 Kb5 24. Kc1! Kc5 25. Kb2 Kc4 26. Kc2 g5 27. Kd2 Kb5 28. Kc1! Kc5 29. Kb2 Kc4 30. Kc2 g4 31. Kd2 Kb5 32. Kc1! Kc5 33. Kb2 Kc4 34. Kc2
34... Kb5 35. Kb3 Kc5 36. c4 Kd4 37. Kb4 Kxe4 38. c5 Kd5 39. Kb5 e4 40. c6 Kd6 41. Kb6 e3 42. c7 e2 43. c8=Q e1=Q 44. Qd8+ Ke6 45. Qe8+ +-






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