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Black to move. Are they winning?
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According to my humble opinion:
Black is clearly winning.
And this is why:
Whites Bishops and Knight on g2, g1 and h1 are crippled. White is not able to free them without sacrificing a lot of material. Also the 'free' Knight is pretty blocked in.
How do you do it?
Blacks rook should be used to remove the g-pawn that is ready to promote. After that the Bishop should be used to block the promotion of the a-pawn. You then sacrifice your Queen so the pawn on d4 can promote. In that progress the white Knight is lost. And the White King is just to slow to free up the remaining pieces.
Therefore this is the solution:
1. ... - Rxg7 (eliminate the g-pawn!)
2. Nb3+ - Kb2 (this in-between check is required for white as it prevents the direct loss of the Knight after Kxg7)
3. Kxg7 - Bb6 (important to block the a-pawn! + White has no way to continue without losing something)
4. Kf6 - Qxc4 (and now d4 is ready to promote)
5. dxc4 - Kxb3 (two pieces for a Q, not so bad since the route to promotion is clear)
6. Kg5 - d3
7. Kxg4 - d2
8. Kxh3 - d1D
From here on it's a clear win for black. White has three pieces and its King crowded around the A1 corner. White can try to play for promotion with its g-pawn but that can easily be blocked by black whilest gobbling up all the c and d pawns.
After blocking the g pawn (if advanced) black can go ahead and promote a second pawn to a Q.
Engines will probably see a mate in 37 there but let's not go into that :-)
I propose 1. Qxd2!!
If 2. g8=Q Re5. The threat here is to go Qh6+ so black has to respond with either 3. Qg7 or 3. Qg6 either way we stop the a pawn with 3. Bb6. The king can never leave f6 because it would allow Qf5 or Rf5 so Black has no options but to continue endlessly shuffling the queen between g7 and g6. Qxg4 is the only line I have no response for, but it is 3am where I live so I will edit this answer when I have a solution for this tomorrow. For now I assume this is somehow ok
Here one might be tempted to play Rh5 when the queen is on g7 but this is premature since Qxg4 will allow white to push the g pawn and free their pieces. Now we have unlimited tempi, we slowly move our king all the way to capture the knight on h1 and then move it back to g2. Now we wait for white's queen to be back on g7 (either by triangulating the king on d1, c1, c2 or Ba7 both should be fine) then play Rh5 with the threat of Rh6. Now white's king must move back, regardless where to you can jump in with Qg5, and white has no choice but to trade the queens to avoid checkmate.
After this exchange Black's king will be at either e6 e7 or f7. The easy case is if the king is on f7 you will simply put your rook on e5 then e1 and trade it for the two bishops and queen the h pawn. If the king goes from e6/e7 to d7 with the idea of a7 Bxa7 Kxc7 simple continue with Re5 to Re1 and trade, even if white queens first you will have an extra rook or queen and should win
If 2. Kxe7 3. Qg5+ white must protect their pawn on the 7th so they must move towards the pawn, black can eventually force the white king to g8 with just the queen (see https://youtu.be/qO0xH2khBrI?t=675 for reference). When this happens you have a tempo to play Bb6 stopping the a pawn. Repeating this process every time white's king tries to move out of the way of the pawn, you can obtain infinite tempi. With this your king will travel all the way to capture the knight on h1 then all the way back to a5. Then black will eventually play Ba7, Bb8, Kb6, Ka7, Ka8, Ba7 and get your king in from the 8th rank to eventually capture the pawn on g7 and checkmate white.
This maneuver is cool and all but what if anytime during this white tries to sacrifice the white bishop by maneuvering to d1 and capturing on f3. If the bishop ever reaches d1, we play the explosive c4 which will guarantee one of our pawn's promotion even after Bb3. This sacrifice is also why it's important to capture the knight on h1 before going to assist the queen otherwise c4 may no longer works since the knight is able to jump to f2 in some lines to prevent promotion
I'm sure I'm missing a few lines here and there but it's getting extremely late where I live so I might come back and make some revisions tomorrow. I think I got the main idea at the very least.
My thought is
Yes he is
My reasoning - First
If white gets a queen he's at least equal and probably winning because of blacks weak pawns
black must prevent the immediate g8. If he sacs the Rook, 1... Qb8 2. Kxe7, he doesn't have quite enough time to mobilize the bishop to help, 2... Bxd2 3. Kf7. That leaves 1... Re8.
2. Nb6+ (2.a7 Qe1 -/+) Kb2 3. Kf7 Qb8 -/+ or 3. a7 Qe1 -/+