A questionable position

[Hobacle]

If the first one was as easy as that, it wouldn't be any problem to keep the winning lines in hash at Backward.
Have a look at Spliffjiffer's line how long it takes, if Black's King doesn't choose h1 voluntarily to escape to but the opposite side of the board.

http://talkchess.com/forum3/viewtopic.p ... 04#p891804

I've seen that long ago. Why not 2. Bd1?

Edit: I was wrong. The first position is OK. Of course my fickle posts are boring, but to face such a complex theme, patience is necessary.

[peter]

Now I'm the one wanting to delete a posting of mine.
Not being able to do so anymore, I just replace it with this correction, sorry.

Just as for 2.Bd1 instead of Bd5 (or Be2), I have no idea at all, if one of these will be significantly shorter or longer, just becaus I don't think any of those or others can prevent Black's King from escaping towards a8 instead of the much more convenient h1- corner.

And nevermind about many postings to the same theme, it's fascinating to me anyhow, otherwise I wouldn't have had so much fuzz of my own with it

[Hobacle]

Now I'm the one wanting to delete a posting of mine.
Not being able to do so anymore, I just replace it with this correction, sorry.

Just as for 2.Bd1 instead of Bd5 (or Be2), I have no idea at all, if one of these will be significantly shorter or longer, just becaus I don't think any of those or others can prevent Black's King from escaping towards a8 instead of the much more convenient h1- corner.

And nevermind about many postings to the same theme, it's fascinating to me anyhow, otherwise I wouldn't have had so much fuzz of my own with it

Many times I know the key to my position but I'm not able to explain myself because I'm quite poor at English. Perhaps you've found it.

This theme is mainly about how KB force K to somewhere. Maybe as difficult as KBNvK, but more interesting. With two free Black Pawns it's much longer and more difficult(for both humans and engines) than KBNvK. In my opinion I can build a great puzzle around it if White can really win, and this puzzle will be much better than that one with three black coloured Black Bishops(and harder, maybe). I'd rather not compose puzzles with pieces created by promotion unless I have to!

[Hobacle]

I'll wait for Hobacle to decide for a certain starting- position and an according winning line of his now regards

I chose the first position because convenient to discuss. Here's a possible winning line.

[pgn][Event "?"]
[Site "?"]
[Date "2021.05.03"]
[Round "?"]
[White ""]
[Black ""]
[Result "1-0"]
[FEN "6bn/5pPq/5PpB/5pPp/5K2/5B2/8/6k1 w - - 0 1"]
[SetUp "1"]

1. Kg3 Kf1 2. Bc6 Ke2 3. Bg2 Ke3 4. Bf3 Kd2 5. Kf2 Kd3 6. Bg2 Kd4 7. Ke2 Kc3 8.
Ke3 Kc4 9. Bf3 Kc3 10. Be2 Kc2 11. Bf1 Kc3 12. Bd3 Kb3 13. Kd2 Kb4 14. Be2 Kb3
15. Bd1+ Kb4 16. Kd3 Kc5 17. Bb3 Kb4 18. Bd5 Kc5 19. Bc4 Kb6 20. Kd4 Ka5 21.
Kc5 Ka4 22. Bd5 Ka3 23. Kc4 Kb2 24. Kd3 Ka3 25. Kc3 Ka4 26. Bc6+ Ka5 27. Kc4
Kb6 28. Bb5 (28. Kd5) 28... Kc7 29. Kc5 Kb7 30. Bc6+ Kc7 31. Bf3 Kd7 32. Bd5
Kc7 33. Bc6 Kb8 (33... Kc8) 34. Kb6 Kc8 35. Bb5 h4 36. Kc6 Kb8 37. Kb6 Kc8 38.
Bc6 h3 39. Kc5 Kc7 40. Bh1 Kd7 41. Kd4 Kd6 42. Ke3 Ke5 43. Kf3 Kd4 44. Kg3 Ke3
45. Kxh3 Kf2 46. Bc6 Ke3 47. Kg3 Ke2 48. Bg2 Ke3 49. Bf3 Kd2 50. Kf2 Kd3 51.
Bg2 Kd4 52. Ke2 Kc3 53. Ke3 Kc4 54. Bf3 Kc3 55. Be2 Kc2 56. Bf1 Kc3 57. Bd3 Kb3
58. Kd2 Kb4 59. Be2 Kb3 60. Bd1+ Kb4 61. Kd3 Kc5 62. Bb3 Kb4 63. Bd5 Kc5 64.
Bc4 Kb6 65. Kd4 Ka5 66. Kc5 Ka4 67. Bd5 Ka3 68. Kc4 Kb2 69. Kd3 Ka3 70. Kc3 Ka4
71. Bc6+ Ka5 72. Kc4 Kb6 73. Bb5 (73. Kd5) 73... Kc7 74. Kc5 Kb7 75. Bc6+ Kc7
76. Bf3 Kd7 77. Bd5 Kc7 78. Bc6 {God of Chess:} 78... Kc8 79. Kb6 f4 80. Bg2 Kd7
81. Kc5 Kc7 82. Bf3 Kd7 83. Kd4 Kc7 84. Ke5 Kb6 85. Kxf4 Kb5 86. Ke3 Kc4 87.
Be4 Kc3 88. Bd3 Kb3 89. Kd2 Kb4 90. Ba6 90... Kc5 91.
Kd3 Kd5 92. Bb7+ Kc5 93. Kc3 Kb6 94. Bd5 Kc5 95. Bc4 Kb6 96. Kd4 Ka5 97. Kc5
Ka4 98. Bd5 Ka3 99. Kc4 Kb2 100. Kd3 Ka3 101. Kc3 Ka4 102. Bc6+ Ka5 103. Kc4
Kb6 104. Kd5 Qxg7 105. Bxg7 Bh7 106. Bf8 Bg8 107. Be7 Bh7 108. Bd8+ Ka6 109.
Kc5 Ka7 110. Bd5 Bg8 111. Bc7 Bh7 112. Kc6 Bg8 113. Bd6 Bh7 114. Bc4 Bg8 115.
Kc7 Ka8 116. Bc5 Bh7 117. Bd5# {#39/73} 1-0
[/pgn]

Still not sure whether.
And, what will happen if Black moves the free f Pawn earlier than moving the h Pawn?
I think it's probably impossible to get the correct DTM easily even if we've been sure White can win. Some questionable moves are marked in my PGN above.

[Hobacle]

Have corrected some mistakes.

[pgn][Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[FEN "6bn/5pPq/5PpB/5pPp/5K2/5B2/8/6k1 w - - 0 1"]
[SetUp "1"]

1. Kg3 Kf1 2. Bc6 Ke2 3. Bg2 Ke3 4. Bf3 Kd2 5. Kf2 Kd3 6. Bg2 Kd4 7. Ke2 Kc3 8.
Ke3 Kc4 9. Bf3 Kc3 10. Be2 Kc2 11. Bf1 Kc3 12. Bd3 Kb3 13. Kd2 Kb4 14. Be2 Kb3
15. Bd1+ Kb4 16. Kd3 Kc5 17. Bb3 Kb4 18. Bd5 Kc5 19. Bc4 Kb6 20. Kd4 Ka5 21.
Kc5 Ka4 22. Bd5 Ka3 23. Kc4 Kb2 24. Kd3 Ka3 25. Kc3 Ka4 26. Bc6+ Ka5 27. Kc4
Kb6 28. Bb5 Kc7 29. Kc5 Kb7 30. Bc6+ Kc7 31. Bf3 Kd7 32. Bd5 Kc7 33. Bc6 h4
(33... Kb8 $2 34. Kb6 Kc8 35. Bb5 h4 36. Bc6 h3 37. Bb5 h2 38. Bc6 Kd8 39. Kb7
h1=Q 40. Bxh1 Kd7 41. Kb6 Kd6 42. Kb5 Ke5 43. Kc4) (33... Kc8 $2 34. Kb6 h4 35.
Ba4 $1 35... h3 36. Bb5) (33... f4 $5) 34. Bf3 Kd7 35. Bd5 Kc7 36. Bc6 h3 37.
Bh1 Kd7 38. Kd5 Kc7 39. Ke5 Kb6 (39... Kd7 $5) 40. Kf4 Kc5 41. Kg3 Kd4 42. Kxh3
Ke3 43. Kg3 Ke2 44. Bg2 Ke3 45. Bf3 Kd2 46. Kf2 Kd3 47. Bg2 Kd4 48. Ke2 Kc3 49.
Ke3 Kc4 50. Bf3 Kc3 51. Be2 Kc2 52. Bf1 Kc3 53. Bd3 Kb3 54. Kd2 Kb4 55. Be2 Kb3
56. Bd1+ Kb4 57. Kd3 Kc5 58. Bb3 Kb4 59. Bd5 Kc5 60. Bc4 Kb6 61. Kd4 Ka5 62.
Kc5 Ka4 63. Bd5 Ka3 64. Kc4 Kb2 65. Kd3 Ka3 66. Kc3 Ka4 67. Bc6+ Ka5 68. Kc4
Kb6 69. Bb5 Kc7 70. Kc5 Kb7 71. Bc6+ Kc7 72. Bf3 Kd7 73. Bd5 Kc7 74. Bc6 {God of Chess:} 74... Kc8
75. Kb6 f4 76. Bg2 Kd7 77. Kc5 Kc7 78. Bf3 Kd7 79. Kd4 Kc7 80. Ke5 Kb6 81. Kxf4
Kb5 82. Ke3 Kc4 83. Be4 Kc3 84. Bd3 Kb3 85. Kd2 Kb4 86. Ba6 Kc5 87. Kd3 Kd5 88.
Bb7+ Kc5 89. Kc3 Kb6 90. Bd5 Kc5 91. Bc4 Kb6 92. Kd4 Ka5 93. Kc5 Ka4 94. Bd5
Ka3 95. Kc4 Kb2 96. Kd3 Ka3 97. Kc3 Ka4 98. Bc6+ Ka5 99. Kc4 Kb6 100. Kd5 Qxg7
101. Bxg7 Bh7 102. Bf8 Bg8 103. Be7 Bh7 104. Bd8+ Ka6 105. Kc5 Ka7 106. Bd5 Bg8
107. Bc7 Bh7 108. Kc6 Bg8 109. Bc4 Bh7 110. Bd6 Bg8 111. Kc7 Ka8 112. Bc5 Bh7
113. Bd5# {#39/73} 1-0
[/pgn]

Then it's up to you to check it.

[peter]

Have corrected some mistakes.

[pgn][Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[FEN "6bn/5pPq/5PpB/5pPp/5K2/5B2/8/6k1 w - - 0 1"]
[SetUp "1"]

1. Kg3 Kf1 2. Bc6 Ke2 3. Bg2 Ke3 4. Bf3 Kd2 5. Kf2 Kd3 6. Bg2 Kd4 7. Ke2 Kc3 8.
Ke3 Kc4 9. Bf3 Kc3 10. Be2 Kc2 11. Bf1 Kc3 12. Bd3 Kb3 13. Kd2 Kb4 14. Be2 Kb3
15. Bd1+ Kb4 16. Kd3 Kc5 17. Bb3 Kb4 18. Bd5 Kc5 19. Bc4 Kb6 20. Kd4 Ka5 21.
Kc5 Ka4 22. Bd5 Ka3 23. Kc4 Kb2 24. Kd3 Ka3 25. Kc3 Ka4 26. Bc6+ Ka5 27. Kc4
Kb6 28. Bb5 Kc7 29. Kc5 Kb7 30. Bc6+ Kc7 31. Bf3 Kd7 32. Bd5 Kc7 33. Bc6 h4
(33... Kb8 $2 34. Kb6 Kc8 35. Bb5 h4 36. Bc6 h3 37. Bb5 h2 38. Bc6 Kd8 39. Kb7
h1=Q 40. Bxh1 Kd7 41. Kb6 Kd6 42. Kb5 Ke5 43. Kc4) (33... Kc8 $2 34. Kb6 h4 35.
Ba4 $1 35... h3 36. Bb5) (33... f4 $5) 34. Bf3 Kd7 35. Bd5 Kc7 36. Bc6 h3 37.
Bh1 Kd7 38. Kd5 Kc7 39. Ke5 Kb6 (39... Kd7 $5) 40. Kf4 Kc5 41. Kg3 Kd4 42. Kxh3
Ke3 43. Kg3 Ke2 44. Bg2 Ke3 45. Bf3 Kd2 46. Kf2 Kd3 47. Bg2 Kd4 48. Ke2 Kc3 49.
Ke3 Kc4 50. Bf3 Kc3 51. Be2 Kc2 52. Bf1 Kc3 53. Bd3 Kb3 54. Kd2 Kb4 55. Be2 Kb3
56. Bd1+ Kb4 57. Kd3 Kc5 58. Bb3 Kb4 59. Bd5 Kc5 60. Bc4 Kb6 61. Kd4 Ka5 62.
Kc5 Ka4 63. Bd5 Ka3 64. Kc4 Kb2 65. Kd3 Ka3 66. Kc3 Ka4 67. Bc6+ Ka5 68. Kc4
Kb6 69. Bb5 Kc7 70. Kc5 Kb7 71. Bc6+ Kc7 72. Bf3 Kd7 73. Bd5 Kc7 74. Bc6 {God of Chess:} 74... Kc8
75. Kb6 f4 76. Bg2 Kd7 77. Kc5 Kc7 78. Bf3 Kd7 79. Kd4 Kc7 80. Ke5 Kb6 81. Kxf4
Kb5 82. Ke3 Kc4 83. Be4 Kc3 84. Bd3 Kb3 85. Kd2 Kb4 86. Ba6 Kc5 87. Kd3 Kd5 88.
Bb7+ Kc5 89. Kc3 Kb6 90. Bd5 Kc5 91. Bc4 Kb6 92. Kd4 Ka5 93. Kc5 Ka4 94. Bd5
Ka3 95. Kc4 Kb2 96. Kd3 Ka3 97. Kc3 Ka4 98. Bc6+ Ka5 99. Kc4 Kb6 100. Kd5 Qxg7
101. Bxg7 Bh7 102. Bf8 Bg8 103. Be7 Bh7 104. Bd8+ Ka6 105. Kc5 Ka7 106. Bd5 Bg8
107. Bc7 Bh7 108. Kc6 Bg8 109. Bc4 Bh7 110. Bd6 Bg8 111. Kc7 Ka8 112. Bc5 Bh7
113. Bd5# {#39/73} 1-0
[/pgn]

Then it's up to you to check it.

Sorry, too much work.
I started from Ke3 always, which doesn't make any difference problably, and it can but need not transpose to any other of the many possible variations even without any detour or shortcut.
So trying to copy and paste lines like yours into an existing .pgn like the one of mine doesn't work, whenever positions are reached that transpose, the rest of the pasted lines are cut.
So one can only restart the other one's lines from scratch again and make full new Backward to look for better moves.
My primary line looks like this:

[pgn][Event "?"]
[Site "?"]
[Date "2021.05.01"]
[Round "?"]
[White "Hobacle, Can"]
[Black "White, Win?"]
[Result "1-0"]
[SetUp "1"]
[FEN "6bn/5pPq/5PpB/5pPp/5K2/5B2/8/6k1 w - - 0 1"]
[PlyCount "195"]

1. Ke3 Kf1 2. Bd5 Ke1 3. Bg2 Kd1 4. Bf1 Kc2 5. Ba6 Kc3 6. Bd3 Kb3 7. Kd2 Kb4 8.
Ba6 Kc5 9. Kd3 Kd5 10. Bb7+ Kc5 11. Kc3 Kb5 12. Bd5 Kc5 13. Bc4 Kb6 14. Kd4 Ka5
15. Kc5 Ka4 16. Bd5 Ka3 17. Kc4 Kb2 18. Kd3 Ka3 19. Kc3 Ka4 20. Bc6+ Ka5 21.
Be8 Kb6 22. Kb4 Ka6 23. Kc5 Ka7 24. Ba4 Ka6 25. Bc6 Ka5 26. Bb5 h4 27. Bf1 Ka4
28. Kd4 Kb4 29. Ke3 Kc5 30. Kf2 Kd4 31. Ba6 Ke4 32. Bb7+ Ke5 33. Kg2 Kd4 34.
Kh3 Ke5 35. Bg2 Kf4 36. Bc6 Ke5 37. Bb5 Kd4 38. Bf1 Ke3 39. Bc4 Kd4 40. Ba2 Kc5
41. Kxh4 Kb5 42. Bd5 Kc5 43. Bh1 Kb4 44. Kg3 Kc5 45. Bg2 Kc4 46. Kf4 Kd4 47.
Bf1 Kd5 48. Ke3 Kc5 49. Bd3 Kd5 50. Bb1 Kc4 51. Kd2 Kc5 52. Kd3 Kd5 53. Kc3 Ke5
54. Kc4 Kd6 55. Kd4 Kc6 56. Bd3 Kd6 57. Bb5 Ke6 58. Bc6 Kd6 59. Bd5 Kc7 60. Kc5
Kd7 61. Bb3 Kc7 62. Bc4 Kd7 63. Bd5 Kc7 64. Bc6 Kc8 65. Kb6 f4 66. Kc5 Kc7 67.
Bf3 Kd7 68. Kd5 Kc7 69. Ke5 Kb6 70. Kxf4 Kb5 71. Be2+ Kb4 72. Ke3 Kc3 73. Bd3
Kb2 74. Kd4 Kb3 75. Be4 Kb4 76. Bd5 Kb5 77. Bb3 Kb4 78. Bc4 Ka5 79. Kc5 Ka4 80.
Bd5 Ka3 81. Kc4 Kb2 82. Kd3 Ka3 83. Kc3 Ka4 84. Bc6+ Ka5 85. Be8 Kb6 86. Kb4
Ka6 87. Kc5 Ka7 88. Ba4 Ka6 89. Bc6 Ka7 90. Kb5 Kb8 91. Kb6 Kc8 92. Bb5 Kb8 93.
Ba4 Kc8 94. Bc6 Kb8 95. Bb7 Qxg7 96. Bxg7 Bh7 97. Bf8 Bg8 98. Bd6# 1-0[/pgn]

Guess I yet could have some shortcut(s) still but there could be detour(s) as well. Mating score cannot be kept in hash at Backward further then to about 30th with my hardware and reasonable computing time.

But one blunder I found in your latest .pgn for sure, letting the h-Pawn come so far doesn't work, with 40...Qxh6! instead of ...Kc5? Black escapes:

1. Kg3 Kf1 2. Bc6 Ke2 3. Bg2 Ke3 4. Bf3 Kd2 5. Kf2 Kd3 6. Bg2 Kd4 7. Ke2 Kc3 8.
Ke3 Kc4 9. Bf3 Kc3 10. Be2 Kc2 11. Bf1 Kc3 12. Bd3 Kb3 13. Kd2 Kb4 14. Be2 Kb3
15. Bd1+ Kb4 16. Kd3 Kc5 17. Bb3 Kb4 18. Bd5 Kc5 19. Bc4 Kb6 20. Kd4 Ka5 21.
Kc5 Ka4 22. Bd5 Ka3 23. Kc4 Kb2 24. Kd3 Ka3 25. Kc3 Ka4 26. Bc6+ Ka5 27. Kc4
Kb6 28. Bb5 Kc7 29. Kc5 Kb7 30. Bc6+ Kc7 31. Bf3 Kd7 32. Bd5 Kc7 33. Bc6 h4 34.
Bf3 Kd7 35. Bd5? Kc7 36. Bc6 h3 37. Bh1 Kd7 38. Kd5 Kc7 39. Ke5 Kb6 40. Kf4 Kc5?

40...Qxh6!
41. gxh6 g5+!

There are too many unnessesary Bishop- moves latest starting with 35.Bd5?, at least togehter with then 36.Bc6, 37.Bh1 38.Bd5.
35.Kd4 at this point repairs it again for sure as for the outcome in full point, if I'll find the time to, I'll try to get a new DTM from there but better from earlier deviation to be found anywhere anyhow.

Here's some output at position after 35.Kd4:

6bn/3k1pPq/5PpB/5pP1/3K3p/5B2/8/8 b - - 0 1

Analysis by Stockfish-MOJO 020521:

35...Kd6 36.Ke3 Ke6 37.Kf2 Ke5 38.Ba8 Kf4 39.Bb7 Kg4 40.Kg2 Kf4 41.Bd5 Ke5 42.Ba8 f4 43.Kf2 Kd6 44.Kf3 Ke5 45.Bb7 Kd4 46.Kg4 Ke5 47.Bg2 Kd6 48.Be4 Ke5 49.Bb1 Qxg7 50.Bxg7 Bh7 51.Bc2 f3 52.Kxf3 h3 53.Kg3 Bg8 54.Bh6 h2 55.Kxh2 Kf4 56.Bb1 Bh7 57.Kh3 Kf3
+- (9.83) Depth: 40/55 00:00:41 1258MN

Seriously, too much work for me, especially as long as the starting position is interesting and fascinating but for my personal pov. too far away from a study with the claim of somewhat singular moves at least as for the very first one(s).

Good luck with the study you're going to compose out of this, I'll be glad to see such and jump in then at once again, if you think the piece is getting somewhat more forced regards

[Hobacle]

Have corrected some mistakes.

[pgn][Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[FEN "6bn/5pPq/5PpB/5pPp/5K2/5B2/8/6k1 w - - 0 1"]
[SetUp "1"]

1. Kg3 Kf1 2. Bc6 Ke2 3. Bg2 Ke3 4. Bf3 Kd2 5. Kf2 Kd3 6. Bg2 Kd4 7. Ke2 Kc3 8.
Ke3 Kc4 9. Bf3 Kc3 10. Be2 Kc2 11. Bf1 Kc3 12. Bd3 Kb3 13. Kd2 Kb4 14. Be2 Kb3
15. Bd1+ Kb4 16. Kd3 Kc5 17. Bb3 Kb4 18. Bd5 Kc5 19. Bc4 Kb6 20. Kd4 Ka5 21.
Kc5 Ka4 22. Bd5 Ka3 23. Kc4 Kb2 24. Kd3 Ka3 25. Kc3 Ka4 26. Bc6+ Ka5 27. Kc4
Kb6 28. Bb5 Kc7 29. Kc5 Kb7 30. Bc6+ Kc7 31. Bf3 Kd7 32. Bd5 Kc7 33. Bc6 h4
(33... Kb8 $2 34. Kb6 Kc8 35. Bb5 h4 36. Bc6 h3 37. Bb5 h2 38. Bc6 Kd8 39. Kb7
h1=Q 40. Bxh1 Kd7 41. Kb6 Kd6 42. Kb5 Ke5 43. Kc4) (33... Kc8 $2 34. Kb6 h4 35.
Ba4 $1 35... h3 36. Bb5) (33... f4 $5) 34. Bf3 Kd7 35. Bd5 Kc7 36. Bc6 h3 37.
Bh1 Kd7 38. Kd5 Kc7 39. Ke5 Kb6 (39... Kd7 $5) 40. Kf4 Kc5 41. Kg3 Kd4 42. Kxh3
Ke3 43. Kg3 Ke2 44. Bg2 Ke3 45. Bf3 Kd2 46. Kf2 Kd3 47. Bg2 Kd4 48. Ke2 Kc3 49.
Ke3 Kc4 50. Bf3 Kc3 51. Be2 Kc2 52. Bf1 Kc3 53. Bd3 Kb3 54. Kd2 Kb4 55. Be2 Kb3
56. Bd1+ Kb4 57. Kd3 Kc5 58. Bb3 Kb4 59. Bd5 Kc5 60. Bc4 Kb6 61. Kd4 Ka5 62.
Kc5 Ka4 63. Bd5 Ka3 64. Kc4 Kb2 65. Kd3 Ka3 66. Kc3 Ka4 67. Bc6+ Ka5 68. Kc4
Kb6 69. Bb5 Kc7 70. Kc5 Kb7 71. Bc6+ Kc7 72. Bf3 Kd7 73. Bd5 Kc7 74. Bc6 {God of Chess:} 74... Kc8
75. Kb6 f4 76. Bg2 Kd7 77. Kc5 Kc7 78. Bf3 Kd7 79. Kd4 Kc7 80. Ke5 Kb6 81. Kxf4
Kb5 82. Ke3 Kc4 83. Be4 Kc3 84. Bd3 Kb3 85. Kd2 Kb4 86. Ba6 Kc5 87. Kd3 Kd5 88.
Bb7+ Kc5 89. Kc3 Kb6 90. Bd5 Kc5 91. Bc4 Kb6 92. Kd4 Ka5 93. Kc5 Ka4 94. Bd5
Ka3 95. Kc4 Kb2 96. Kd3 Ka3 97. Kc3 Ka4 98. Bc6+ Ka5 99. Kc4 Kb6 100. Kd5 Qxg7
101. Bxg7 Bh7 102. Bf8 Bg8 103. Be7 Bh7 104. Bd8+ Ka6 105. Kc5 Ka7 106. Bd5 Bg8
107. Bc7 Bh7 108. Kc6 Bg8 109. Bc4 Bh7 110. Bd6 Bg8 111. Kc7 Ka8 112. Bc5 Bh7
113. Bd5# {#39/73} 1-0
[/pgn]

Then it's up to you to check it.

Sorry, too much work.
I started from Ke3 always, which doesn't make any difference problably, and it can but need not transpose to any other of the many possible variations even without any detour or shortcut.
So trying to copy and paste lines like yours into an existing .pgn like the one of mine doesn't work, whenever positions are reached that transpose, the rest of the pasted lines are cut.
So one can only restart the other one's lines from scratch again and make full new Backward to look for better moves.
My primary line looks like this:

[pgn][Event "?"]
[Site "?"]
[Date "2021.05.01"]
[Round "?"]
[White "Hobacle, Can"]
[Black "White, Win?"]
[Result "1-0"]
[SetUp "1"]
[FEN "6bn/5pPq/5PpB/5pPp/5K2/5B2/8/6k1 w - - 0 1"]
[PlyCount "195"]

1. Ke3 Kf1 2. Bd5 Ke1 3. Bg2 Kd1 4. Bf1 Kc2 5. Ba6 Kc3 6. Bd3 Kb3 7. Kd2 Kb4 8.
Ba6 Kc5 9. Kd3 Kd5 10. Bb7+ Kc5 11. Kc3 Kb5 12. Bd5 Kc5 13. Bc4 Kb6 14. Kd4 Ka5
15. Kc5 Ka4 16. Bd5 Ka3 17. Kc4 Kb2 18. Kd3 Ka3 19. Kc3 Ka4 20. Bc6+ Ka5 21.
Be8 Kb6 22. Kb4 Ka6 23. Kc5 Ka7 24. Ba4 Ka6 25. Bc6 Ka5 26. Bb5 h4 27. Bf1 Ka4
28. Kd4 Kb4 29. Ke3 Kc5 30. Kf2 Kd4 31. Ba6 Ke4 32. Bb7+ Ke5 33. Kg2 Kd4 34.
Kh3 Ke5 35. Bg2 Kf4 36. Bc6 Ke5 37. Bb5 Kd4 38. Bf1 Ke3 39. Bc4 Kd4 40. Ba2 Kc5
41. Kxh4 Kb5 42. Bd5 Kc5 43. Bh1 Kb4 44. Kg3 Kc5 45. Bg2 Kc4 46. Kf4 Kd4 47.
Bf1 Kd5 48. Ke3 Kc5 49. Bd3 Kd5 50. Bb1 Kc4 51. Kd2 Kc5 52. Kd3 Kd5 53. Kc3 Ke5
54. Kc4 Kd6 55. Kd4 Kc6 56. Bd3 Kd6 57. Bb5 Ke6 58. Bc6 Kd6 59. Bd5 Kc7 60. Kc5
Kd7 61. Bb3 Kc7 62. Bc4 Kd7 63. Bd5 Kc7 64. Bc6 Kc8 65. Kb6 f4 66. Kc5 Kc7 67.
Bf3 Kd7 68. Kd5 Kc7 69. Ke5 Kb6 70. Kxf4 Kb5 71. Be2+ Kb4 72. Ke3 Kc3 73. Bd3
Kb2 74. Kd4 Kb3 75. Be4 Kb4 76. Bd5 Kb5 77. Bb3 Kb4 78. Bc4 Ka5 79. Kc5 Ka4 80.
Bd5 Ka3 81. Kc4 Kb2 82. Kd3 Ka3 83. Kc3 Ka4 84. Bc6+ Ka5 85. Be8 Kb6 86. Kb4
Ka6 87. Kc5 Ka7 88. Ba4 Ka6 89. Bc6 Ka7 90. Kb5 Kb8 91. Kb6 Kc8 92. Bb5 Kb8 93.
Ba4 Kc8 94. Bc6 Kb8 95. Bb7 Qxg7 96. Bxg7 Bh7 97. Bf8 Bg8 98. Bd6# 1-0[/pgn]

Guess I yet could have some shortcut(s) still but there could be detour(s) as well. Mating score cannot be kept in hash at Backward further then to about 30th with my hardware and reasonable computing time.

But one blunder I found in your latest .pgn for sure, letting the h-Pawn come so far doesn't work, with 40...Qxh6! instead of ...Kc5? Black escapes:

1. Kg3 Kf1 2. Bc6 Ke2 3. Bg2 Ke3 4. Bf3 Kd2 5. Kf2 Kd3 6. Bg2 Kd4 7. Ke2 Kc3 8.
Ke3 Kc4 9. Bf3 Kc3 10. Be2 Kc2 11. Bf1 Kc3 12. Bd3 Kb3 13. Kd2 Kb4 14. Be2 Kb3
15. Bd1+ Kb4 16. Kd3 Kc5 17. Bb3 Kb4 18. Bd5 Kc5 19. Bc4 Kb6 20. Kd4 Ka5 21.
Kc5 Ka4 22. Bd5 Ka3 23. Kc4 Kb2 24. Kd3 Ka3 25. Kc3 Ka4 26. Bc6+ Ka5 27. Kc4
Kb6 28. Bb5 Kc7 29. Kc5 Kb7 30. Bc6+ Kc7 31. Bf3 Kd7 32. Bd5 Kc7 33. Bc6 h4 34.
Bf3 Kd7 35. Bd5? Kc7 36. Bc6 h3 37. Bh1 Kd7 38. Kd5 Kc7 39. Ke5 Kb6 40. Kf4 Kc5?

40...Qxh6!
41. gxh6 g5+!

There are too many unnessesary Bishop- moves latest starting with 35.Bd5?, at least togehter with then 36.Bc6, 37.Bh1 38.Bd5.
35.Kd4 at this point repairs it again for sure as for the outcome in full point, if I'll find the time to, I'll try to get a new DTM from there but better from earlier deviation to be found anywhere anyhow.

Here's some output at position after 35.Kd4:

6bn/3k1pPq/5PpB/5pP1/3K3p/5B2/8/8 b - - 0 1

Analysis by Stockfish-MOJO 020521:

35...Kd6 36.Ke3 Ke6 37.Kf2 Ke5 38.Ba8 Kf4 39.Bb7 Kg4 40.Kg2 Kf4 41.Bd5 Ke5 42.Ba8 f4 43.Kf2 Kd6 44.Kf3 Ke5 45.Bb7 Kd4 46.Kg4 Ke5 47.Bg2 Kd6 48.Be4 Ke5 49.Bb1 Qxg7 50.Bxg7 Bh7 51.Bc2 f3 52.Kxf3 h3 53.Kg3 Bg8 54.Bh6 h2 55.Kxh2 Kf4 56.Bb1 Bh7 57.Kh3 Kf3
+- (9.83) Depth: 40/55 00:00:41 1258MN

Seriously, too much work for me, especially as long as the starting position is interesting and fascinating but for my personal pov. too far away from a study with the claim of somewhat singular moves at least as for the very first one(s).

Good luck with the study you're going to compose out of this, I'll be glad to see such and jump in then at once again, if you think the piece is getting somewhat more forced regards

1. Ke3 looks significantly better than 1. Kg3.
38. Kd5 and then Kd5-e5-f4 was my mistake. At first I realized Qxh6, but forgot it when making my last one. But I still don't think 35. Kd4 is better than 35. Bd5 because White has to put the free Bishop in a specific place such as e8 to get the Black Pawn at h4 to prevent Qxh6. I take another variation to avoid uncertainty. Here's my new line:

[pgn][Event "?"]
[Site "?"]
[Date "2021.05.05"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[FEN "6bn/5pPq/5PpB/5pPp/5K2/5B2/8/6k1 w - - 0 1"]
[SetUp "1"]

1. Ke3 (1. Kg3 $2 1... Kf1 2. Bd5 Ke2 3. Bg2 Ke3 4. Bf3 Kd2 5. Kf2 Kd3 6. Bc6
Kd2 7. Bb5 Kc3 8. Ke3 Kc2 9. Be2 Kc3 10. Bd3) 1... Kf1 2. Bc6 Ke1 3. Bb5 Kd1 4.
Bc4 Kc1 5. Ke2 Kc2 6. Bd3+ Kc3 7. Ke3 Kb3 8. Kd2 Kb4 9. Ba6 Kc5 10. Kd3 Kd5 11.
Bb7+ Kc5 12. Kc3 Kb5 13. Bd5 Kc5 14. Bc4 Kb6 15. Kd4 Ka5 16. Kc5 Ka4 17. Bd5
Ka3 18. Kc4 Kb2 19. Kd3 Ka3 20. Kc3 Ka4 21. Bc6+ Ka5 22. Be8 Ka6 23. Kc4 Kb6
24. Kb4 Kb7 (24... Kc7 $5 25. Kc5 Kb7 26. Bb5 Kc7 27. Bc6) 25. Kc5 Ka6 26. Bc6
Ka5 27. Bb5 h4 (27... f4 $5) 28. Be8 Ka6 29. Kd4 Kb6 30. Ke3 Kc7 31. Kf3 Kd8
32. Ba4 Kc7 33. Kg2 Kd6 34. Kh3 Ke5 35. Be8 Kf4 36. Kxh4 Kf3 37. Bc6+ Kf2 38.
Kh3 Ke3 39. Kg3 Ke2 40. Kf4 Kd2 41. Kf3 Kd3 42. Kf2 (42. Bb5+ $5 42... Kd4)
42... Kd4 43. Bb5 Kc3 (43... Ke4 $2 44. Ke2 Kd4 45. Bd3 Ke5 (45... Kd5 46. Ke3
Kc5 47. Ba6 Kd5 (47... Kb4 48. Kd3) (47... Kb6 48. Bc4) 48. Kd3 Kc5 (48... Ke5
49. Bb7) 49. Bc4) 46. Ke3 Kd5 47. Be2 Kc5 48. Kd3 Kd5 49. Bf3+ Kc5 50. Kc3 Kb5
51. Bd5) 44. Ke3 Kc2 45. Be2 Kc3 46. Bd3 Kb2 (46... Kb3 $2 47. Kd4) 47. Kd2 Kb3
48. Be2 Kb4 49. Kd3 Kc5 50. Bf3 Kb4 51. Bd5 Kb5 52. Kc3 Kc5 53. Bc4 Kb6 54. Kd4
Ka5 55. Kc5 Ka4 56. Bd5 Ka3 57. Kc4 Kb2 58. Kd3 Ka3 59. Kc3 Ka4 60. Bc6+ Ka5
61. Be8 Ka6 62. Kc4 Kb6 63. Kb4 Kc7 64. Kc5 Kb7 65. Bb5 Kc7 66. Bc6 Kc8 67. Kb6
f4 68. Kc5 Kc7 69. Bf3 Kd7 70. Kd5 Kc7 71. Ke4 Kb6 72. Kxf4 Kb5 73. Be2+ Kb4
74. Ke3 Kc3 75. Bd3 Kb2 (75... Kb3 $2 76. Kd4 Kb2 77. Kc4 Kc1 78. Kc3 Kd1 79.
Bc4 Ke1 80. Kd3 Kf2 81. Bd5 Ke1 82. Ke3 Kd1 83. Bb3+ Ke1 84. Bc2 Kf1 85. Bd3+
Kg2 86. Be2 Kg3 87. Bf3 Kh2 88. Kf2 Kh3 89. Be2 Kh4 90. Kg2 Qxh6 91. gxh6 Kg5
92. gxh8=Q Bh7 93. Qxh7 Kf4 94. Qxf7 Ke4 95. Qc4+ Ke3 96. f7 Kd2 97. f8=Q g5
98. Qd8+ Ke3 99. Qxg5#) 76. Kd4 Kb3 77. Be4 Kb4 78. Bd5 Kb5 79. Bb3 Kb4 80. Bc4
Ka5 81. Kc5 Ka4 82. Bd5 Ka3 83. Kc4 Kb2 84. Kd3 Ka3 85. Kc3 Ka4 86. Bc6+ Ka5
87. Be8 Ka6 88. Kb4 Kb6 89. Ba4 Kc7 90. Kc5 Kb7 91. Bb5 Kc7 92. Bc6 Kb8 93. Kb6
Kc8 94. Bb5 Kb8 95. Bd7 Ka8 96. Bc6+ Kb8 97. Bb7 Qxg7 98. Bxg7 Bh7 99. Bf8 Bg8
100. Bd6# 1-0

[/pgn]

Has been becoming shorter and shorter

But I've found that spending to much time getting the correct DTM was probably a mistake. It should be the work for computers, not for humans. The most important thing for us is to make sure White can win here, isn't it?
After listing quite a few variations, I find no way for Black to escape. What about you?

[peter]

But I've found that spending to much time getting the correct DTM was probably a mistake. It should be the work for computers, not for humans. The most important thing for us is to make sure White can win here, isn't it?
After listing quite a few variations, I find no way for Black to escape. What about you?

Don't know why for sure, but have relavently shorter DTM with 1.Ke3 than with 1.Kg3 too and no, I don't see any way for Black to escape neither.

And I agree with you, that the provably exact DTM doesn't matter here much, as long as it isn't a ready to be judged study. Even for such, if it it isn't a mate in x problem, thematic way of solving is of much more importance than the length of the single lines, the main and the ones of allurement.

So I'd say making the possible starting moves distinctable as for their thematic meaning was the main problem now, there should be at least a single one best move to start with. Having 1.Kg3 as a maybe 15 moves longer DTM- solution than the best one 1.Ke3, brings back the DTM as a criterion that it shouldn't be.
Again good luck to build a study around this endgame. That's what I'm very weak in, composing on my own, I'm much better in cooking and finding holes

[Hobacle]

there should be at least a single one best move to start with.

What do you think of this?
[d]5Nbn/K2P1pPq/2k2PpB/5pPp/8/8/8/1B1r4 w - - 0 1

[peter]

there should be at least a single one best move to start with.

What do you think of this?
[d]5Nbn/K2P1pPq/2k2PpB/5pPp/8/8/8/1B1r4 w - - 0 1

Well now 1.Kb8 looks thematically a little better than e.g. Ka8, Ka6 or Ba2, but still the difference is a little hard to prove, isn't it?