Brunetti wrote: ↑Mon Nov 11, 2024 8:19 pm
I think 1...Bc3 is a better try, but even in your variation, black has Bb2-Bc1-Bc3 moves

they are not in a zugzwang.
They are or will get into it. That's the one of the two reasons for engines with too much nullmove pruning here not to find the solution easily, zugzwang arises not until some moves along the lines, yet it's there later on. The other one tricky point of course is that White has to sacrifice the Queen at a very special moment, that first has to be reached by using Black's zugzwang to force it to get there.
see my analysis
I did, but I won't bother to deny all your many lines one by one, SF would do so for you, if you'd finally take the time to have a Backward with Huntsman, SF 11 or Sting (best to solve without Backward but not if you want to see DTM- output most quickly too to be sure of the shortest winning line too). With full hash from main line of the original study or one of the many winning outputs of Huntsman, SF 11 and Sting (going far enough into main line of study you can even take SlowChess 2.9 as shown above too) I gave already, at least as far as necessary to having "seen" the Queen- sac, they'll keep it in hash (if big enough and hardware isn't too weak) till 1.(3. in original study) Ba3, from there you can see other trials of Black's, as well losing as in main line, together with DTM- score of e.g. Huntsman or SF 11 too.
As for the main line of your analysis- pgn
[d]6k1/1p3p1p/1Pb1pPpP/1pPpP1P1/1P1P4/8/3b1K2/2B2Q2 w - - 0 1
1. Ba3 Bc3 2. Ke3 Ba1 3. Qd3 Bc3 4. Qe2 Bb2 5. Qc2?
4.Qe2 is still ok as for winning, just makes DTM longer for 2 moves, 4.Qc2 instead was #32 (without the 2 cut off of original study), but after your 5.Qc2? you let the crucial ...Bxa3! happen (at once or after next one move or after 6.Kf3 as in your .pgn), that blunders the win.
Output of Huntsman after 5.Qc2? and the moves up to there in main line of your .pgn:
[d]6k1/1p3p1p/1Pb1pPpP/1pPpP1P1/1P1P4/B3K3/1bQ5/8 b - - 0 1
Analysis by The Huntsman 1:
5...Lxa3 6.Dd1 Kf8 7.Kf2 Ke8 8.Kg2 Lc1 9.Db3 Kd8 10.Dd3 Kd7 11.Kh3 Ke8 12.Kg4 Kd8 13.Db1 La3 14.Da1 Kd7 15.Kf3 Kd8 16.Da2 Kd7 17.Kg3 Kd8 18.Kh4 Kd7 19.Db1 Kd8 20.De1 Kd7 21.Kh3 Kd8 22.Dd2 Ke8 23.Kg3 Kd8 24.Da2 Kd7 25.Kh2 Kc8 26.Kg1 Kd7 27.Da1 Kd8 28.Dxa3 Kd7 29.Kh2 Kd8 30.Kh3 Kd7 31.Kg3 Kc8 32.Da7 Kd7 33.Kf3 Kc8 34.Da8+ Kd7 35.Da3 Kd8 36.Dd3 Ke8 37.Db3 Kd7 38.Kf2 Ke8 39.Dc2 Kd7 40.Dc1 Kd8
Tiefe: 70/82 00:00:16 1344MN
+/= (0.65)
1 ply backward 5.Qd3! instead is shown by Huntsman here, like that Queen- sac is to be reached and is winning later on (9th in output below, following that line with Huntsman till there latest will show you DTM and keep it in hash backwards then again):
(1. Ba3 Bc3 2. Ke3 Ba1 3. Qd3 Bc3 4. Qe2 Bb2)
[d]6k1/1p3p1p/1Pb1pPpP/1pPpP1P1/1P1P4/B3K3/1b2Q3/8 w - - 0 1
Analysis by The Huntsman 1:
5.Dd3 Lc3 6.Dc2 Lb2 7.Db3 Lc1+ 8.Kf2 Kf8 9.Da4 Le3+ 10.Kf3 bxa4 11.b5 Lxd4 12.bxc6 bxc6 13.Lc1 Lxc5 14.La3 Ke8 15.Lxc5 Kd8 16.Ke2 Kc8 17.Kd2 Kb7 18.Kc3 a3 19.Kb3 a2 20.Kxa2 Kc8 21.Ka3 Kb7 22.Kb4 Kc8 23.Ka5 Kb7 24.Ld4 c5 25.Lxc5 d4 26.Kb5 d3 27.Lb4 d2 28.Lxd2 Ka8 29.Kc6 Kb8 30.b7 Ka7 31.La5 Kb8 32.Lc7+ Ka7 33.b8D+ Ka6 34.Db6#
Tiefe: 100/60 00:00:08 442MN
Weiß setzt Matt.
+- (#30)
Of course after 5.Qd3 Bxa3? isn't possible anymore, losing by #4 then, 6.Dxa3 Le8 7.Da8 Kf8 8.Dd8 Kg8 9.Dxe8#
Shortest way to mate you get as said with 4.Qd1 or Qc2 (minor dual, not relevant in side line of original study, that's even two moves longer) instead of Qe2!? in your main line after 1...Bc3.
Before 4th move of White in this one main line in your .pgn)
1. Ba3 Bc3 2. Ke3 Ba1 3. Qd3 Bc3
[d]6k1/1p3p1p/1Pb1pPpP/1pPpP1P1/1P1P4/B1bQK3/8/8 w - - 0 1
Analysis by The Huntsman 1:
4.Dc2 Lb2 5.Db3 Lc1+ 6.Kf2 Kf8 7.Da4 Le3+ 8.Kf3 bxa4 9.b5 Lxd4 10.bxc6 bxc6 11.Lc1 Lxc5 12.La3 Ke8 13.Lxc5 Kd8 14.Ke3 Kc8 15.Kd4 Kb7 16.Kc3 a3 17.Kb3 a2 18.Kxa2 Kc8 19.Ld4 Kb7 20.Ka3 Kb8 21.Kb4 Kc8 22.Kc5 Kb7 23.Kd6 Ka6 24.Kxc6 Ka5 25.Kc5 Ka6 26.Kb4 Kb7 27.Kb5 Kb8 28.Kc6 Kc8 29.b7+ Kb8 30.Lc5 d4 31.Kb6 d3 32.Ld6#
Tiefe: 97/58 00:00:38 1933MN
Weiß setzt Matt.
+- (#29)
So just 2 moves shorter DTM.
If you don't get Huntsman or SF 11 or Sting to show you the other one traps and theirs solutions along the lines, you have one more main line free to chose and show here, more than that I won't find the time to help, I won't paste Huntsman- outpout into each and every side line of your .pgn, that would be too much work even to me, that's what we have engines for nowadays, engines and engines' branches

Peter.