Section B1 – Min Win
Firstly we see that the wP, which is crucial for White to win, is under attack, so White has to save it.
1.Bg8+
And Black needs not only to stop the wP from promoting, but also to keep the attack on the wP. Otherwise, the wB will be free so that White can win easily.
1…Kf6
By Ke6-f6-g7, Black uses only his King to reach both of his 2 goals and his Bishop remains free! Prefect!
2.h7 Kg7
Now the wB has to protect the wP so that it cannot move.
3.Kg2!
For the win, the wP must try to promote, and obviously, only the wN can help it. However, the wN’s movement is so limited due to the threat of promotion of the bP, and h8 is so far from the wN, that if the wN goes to help the wP, the bP will promote before the wP. Note that the bK can only stay on g7 or h8 due to the 2 goals, and Black won’t play Kh8 on his own otherwise it will be possible for White to play Kg6 to free his Bishop and even checkmate. So White’s plan is to move the wN to check the bK on g7, which is near enough from the wN, to at least win necessary tempi for the wN to help the wP promote. But that plan has a hole so White must move his King to h5 before.
3…Be5 4.Kf3 Bf6
Black moves away his Bishop early to set a trap!
5.Ke4!
Zigzag I: the wK attacks the bPc5 to win tempi.
5…c4
Otherwise, White will stop the bP from c3 and execute his plan with no hole. But if Black played this move early, White would play the same maneuver with a more obvious purpose which was to chase the bB.
6.Kf5 Bd4 7.Kg5!
Just in time!
( 7.Nb4? Kh6! The hole of White’s plan: Black can stop the wP from promoting with not only his King, but also his Bishop! 8.Nc2 Bh8! 9.Ne3 c3 10.Ng4+ Kg7 11.Ne3 Kh6 Check is still possible but the wN cannot help the wP promote safely. That also explains why White cannot use his King to stop the bP and free his Knight to help the wP, e.g. 12.Ke4 Kg6 13.Kd3 Kh6 14.Nf5+ Kg6 15.Nd6 Bg7 16.Nf7 Bf6 17.Ke3 Bg7 18.h8=Q Bxh8 19.Nxh8+ Kg7 )
( 7.Ke6? This is so early that d4 is still a safe square for the bB. 7…c3! Then White cannot stop Black playing Kg6/Kh6 to utilize the hole. )
7…Bf6+ 8.Kh5
The wK returns to edge of the board. Now Black’s Kg6/Kh6 is impossible so that he cannot hold h8 with his Bishop while keeping the attack on the wP, and White can continue his plan.
8…c3
But Black turns to another defense!
9.Nb4 Be7 10.Nc2 Bc5
Now the bB guards both e3 and d4 so White cannot complete his plan immediately. However, that implies lack of protection of the bP…
11.Kg4!?
To avoid an annoying check.
( 11.Kg5?! Be7+ 12.Kf5?! Bf6 13.Ke6
( 13.Na1 Bd8 14.Kg4!? Bf6 15.Kh5!? Be7 16.Nc2!? Bc5 Waste of time. )
13…Bd8 14.Ke5!? Bg5 15.Ke4!? Bh4 16.Kf4!? Bd8 17.Kg4 Bb6 Waste of time. )
11…Bb6
( The bB doesn’t have enough time to turn back and hold h8: 11…Be7 12.Ne3 Bf6 13.Kh5 Bd4 14.Nf5+ White executes his plan successfully. )
12.Kf5
The wK returns to f5.
12…Bf2
( 12…Bd8 13.Nd4 Bf6 14.Ne6+ White executes his plan successfully. )
13.Ke5!
Zigzag II: the wK attacks the bPc3 to force a zugzwang position with Black to move.
( 13.Ke6?! Bh4 14.Ne3 Bf6 With White to move. 15.Kf5
( 15.Nf5+? A 15…Kg6 a )
( 15.Bf7? B 15…Bg5 b )
15…Bd4 16.Nc2 Bf2 Waste of time. )
13…Bb6
( 13…Bh4?! 14.Ne3 Bf6+ 15.Ke6 Back to main but with 1 move quicker. )
14.Kd5 Bd8
Now it has to turn back, otherwise 15.Kc4 will decide.
15.Ne3 Bf6 16.Ke6
Zugzwang. The hole is still there, but Black has no safe move to utilize it!
16…Bg5
b
( 16…Kg6 a 17.Bf7+ B. Now the wB is free so that White can win easily. )
17.Nf5+
A. White executes his plan successfully. Now White wins necessary tempi for the wN to help the wP promote, e.g. 17…Kh8 18.Nd6 c2 19.Nf7+ Kg7 20.h8Q+. Black cannot do anything but lose.
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