I play regularly long games (60min each) with Droidfish/Stockfish the depth is always close around 21.
From time to time I overlook taktical flaws in my moves, obviously playing on worse positions against an engine makes no sense, so I take my move back. Technicaly the engine does the same, when it changes the evaluation.
That being said I most of the time end up in endgames that are drawn. With black I have trouble drawing the game but I eventualy will. With white I might have a edge, but the engine just always can hold a draw, somehow blockading the position to force a repetition.
I am a very positional player and i guess that is the reason I get these draws, because I mostly avoid taktical positions. NOTE: I am not going for totaly closed positions, I am playing normal positional chess.
I do not think I can beat the engine with black that would be asking for to much but I will try with white.
I play the Benko Opening wih white (1.g3).
If you are curious here is the last game I played with Droidfish:
[fen ""] 1. g3 d5 2. Nf3 Nf6 3. Bg2 c6 4. O-O Bf5 5. d4 g6 6. a4 Bg7 7. b3 O-O 8. Bb2 e6 9. Nbd2 Nbd7 10. c4 Re8 11. Rc1 Rc8 12. Nh4 Bf8 13. Nxf5 exf5 14. e3 Qa5 15. Nf3 Ne4 16. cxd5 cxd5 17. Ne5 Rxc1 18. Qxc1 Qd8 19. Nd3 Bd6 20. Ba3 Ndf6 21. Bxd6 Qxd6 22. Qc2 Qa3 23. Rc1 h5 24. Qb2 Qd6 25. Ne5 Kg7 26. b4 Re7 27. f3 Ng5 28. Kf2 Ne6 29. h4 Rc7 30. Rxc7 Qxc7 31. Bf1 Nd7 32. Nd3 Nf6 33. a5 Ne8 34. Qc1 Qxc1 35. Nxc1 Nd6 36. Nd3 Nc7 37. Ne5 Ne6 38. Nd7 Nf8 39. Nc5 Ne6 40. Bd3 b6 41. Nd7 bxa5 42. bxa5 Nb7 43. a6 Nbd8 44. Ke2 f6 45. Kd2 Kf7 46. Kc3 Ke7 47. Nc5 Nc7 48. Kb4 Nc6+ 49. Ka4 Nd8 50. Bb5 Nde6 51. Bf1 Kd6 52. Kb4 Nf8 53. Bd3 Nfe6 54. Bb5 Ng7 55. Nb7+ Ke7 56. Bd3 Nge6 57. Nc5 Kd6 58. Nb7+ Ke7
It went some moves on but ended in a repetition.
I am not really a fan of 1.e4 or sicilian type positions. I kinda got the opinion that you can not really beat the engine in a long positional game in contrast to human players because the engine makes very few inaccuracies. I guess the most chances are in a complex middle game. (I would still like them to be positional, maybe mixed with taktics)
I couldlnt really find any good (human vs engine) games where the engine was in trouble. I will take a look now at recent engine games stockfish lost maybe that will give me a clue how to beat an engine beast.
Maybe in the mean time you will have some usefull ideas, because that is what we are the best in (for now).