lichess.org/training/LqAa3The server considers the only correct winning sequence: [39. Kc5 f5 40. f3...]
[40. a6] is considered a mistake, even though Stockfish estimates it at the same +6.6 pawns. Why? Maybe there is something I don't know or understand
with 40. a6 black can go Kb6 and stop the pawn and he will be winning because he is a few pawns up
[40. a6] allows [40. Kb6], which blunders the pawn and basically stops the white king from advancing.
Basically, at the end of the winning sequence, black's king is in zugzwang, and every move worsens his position. If [40. ... Kb7], then [41. Kb7, 41. Kd6, Ka6, 42. Kxc6, Kxa5, 43. Kxd5, Kb5, 44. c4+] where white takes the two black pawns in front as black takes white's a-pawn, and white advances the c-pawn. Also, [40. ... Kd7] follows to [41. Kb6] and white gives the threat of promoting the a-pawn. Finally, any attempts to stall, such as [40. ... g6] will let white do [41. a6], and a resulting line of [41. ... f4, 42. a7, Kb7, 43. a8=Q+, Kxa8, 44. Kxc6] results in white having a crushing advantage, while black's king is useless at the corner of the board.
I do not know why Stockfish reported [40. a6] as +6.6 (try checking it again), but this was a good question to ask.
Have a great day!
I don't mean [39. a6], I mean [39. Kc5 f5 40. a6]. Black can't play [40... Kb6], because there is white king on c5. Look at moves' number
What a great move.
I'm waiting for my laptop to reach 50 depth, which the python puzzle generator uses; it's not a 100% fair comparison but perhaps there is some way black can force a draw here (probably not great for a puzzle!) but at depth 45 it's rating the move at +48.6 advantage. I think you just broke the puzzle, unless it hits the 50 move rule soon...
I kind of wonder if it's related to this line from the puzzle generator README:
"the opponent should play human-like moves, not obscure stockfish lines"
I don't think it's a super obscure stockfish line, if anything it's probably easier to see as a strong chess player (not me) because it's more like there's a general feeling that the white king can't catch up with the black king gobbling all his pawns, but perhaps there's something in the code that specifically excludes long lines like this from consideration as potential solutions.