It’s easily calculated that black is going to take white’s pawn next. After that, white must have a winnig Q+N attack. How? I see no other playable move than:
1. Kd4! Qxb5 (e.g. Qg1+ Kd5 and white king is steering towards a safe place, keeping the pawn) 2. Ne5+
Opening a diagonal for queen. Now white queen has all possibilities to check next, the Q+N attack is very strong.
But I’m too lazy to try and calculate all variations here.
I don’t think I can do an exhaustive analysis on this one, but I think white can win with Kd4:
1. Kd4 Qb5
Other moves (queen checks) are probably longer surviving here, but I chose this line to analyze because I believe the others are clearly lost since they allow the white king to reach the b-pawn to retain it. Once the white king reaches the b-pawn, white will win by queening it, though the ending is still not trivial. So, let’s see why Kd4 prevents Qxb5:
2. Ne5
I think this is the only winning move, but am not 100% sure of that. Ne5 seems to gain a critical tempo for activating the white pieces by checking the black king. Continuing:
2. …..Kf5 (alternatives later) 3. Qf8
I think white can win with Qc8+, too, and in the same number of moves, but this line is clearer to me:
3. …..Ke6
Or if Kg5, then 4.Qg7 will be followed by a mate with Qg4 no matter where the black king goes. Continuing:
4. Qf7
Surely the only winning move. Continuing:
4. …..Kd6 5. Nc4
Again, this can be the only win. Continuing:
5. …..Kc6 6. Qe8 wins the black queen since the knight prevents the black king from playing to b6 to protect the lady.
Now, back at move 2, black had alternatives to Kf5, but they all look to be shorter mates since the black king can’t even reach the black queen in those. From the top:
1. Kd4 Qb5 2. Ne5 Kf4 3. Qf8
Here, Qe4 wins, too. Continuing:
3. …..Kg3 (Kg5 4.Qg7 as earlier) 4. Qf3 Kh2 (Kh4 5.Qg4#) 5. Ng4 Kg1 6. Qf2 with 7.Qh2# to follow.
Or:
2. …..Kh4 3. Qe4
I think this is the only winning move. If white checks from d8 or h8 with the queen, the black king will reach g3 and I don’t see how the white queen can close the distance on the black king quickly enough to prevent him from escaping through f2, but maybe I am just not seeing a more lengthy line that wins. Continuing:
3. …..Kg3
Here, 3. …Kh3 loses as shown in the previous line; 3. …Kh5 loses to 4.Qf5 followed by mate; 3. …Kg5 loses to Qg6 followed by 4.Qg4#. Continuing:
4. Qf3 Kh2 5. Ng4 with the same mate we saw earlier.
Or:
2. …..Kg3 3. Qf3 with the same mates seen above to follow.
Or:
2. …..Kh3 3. Qf3 and mate will follow as above.
Or, finally:
2. …..Kh5 3. Qh8 Kg5 4. Qg7 and we have seen this already loses above.
The holes in this, of course, are the lines where black doesn’t take at b5 at move 1. I will just assume they are lost due to the extra white pawn. But I could spend all day and tomorrow trying to prove them each out.
It’s easily calculated that black is going to take white’s pawn next. After that, white must have a winnig Q+N attack. How? I see no other playable move than:
1. Kd4! Qxb5 (e.g. Qg1+ Kd5 and white king is steering towards a safe place, keeping the pawn)
2. Ne5+
Opening a diagonal for queen. Now white queen has all possibilities to check next, the Q+N attack is very strong.
But I’m too lazy to try and calculate all variations here.
I don’t think I can do an exhaustive analysis on this one, but I think white can win with Kd4:
1. Kd4 Qb5
Other moves (queen checks) are probably longer surviving here, but I chose this line to analyze because I believe the others are clearly lost since they allow the white king to reach the b-pawn to retain it. Once the white king reaches the b-pawn, white will win by queening it, though the ending is still not trivial. So, let’s see why Kd4 prevents Qxb5:
2. Ne5
I think this is the only winning move, but am not 100% sure of that. Ne5 seems to gain a critical tempo for activating the white pieces by checking the black king. Continuing:
2. …..Kf5 (alternatives later)
3. Qf8
I think white can win with Qc8+, too, and in the same number of moves, but this line is clearer to me:
3. …..Ke6
Or if Kg5, then 4.Qg7 will be followed by a mate with Qg4 no matter where the black king goes. Continuing:
4. Qf7
Surely the only winning move. Continuing:
4. …..Kd6
5. Nc4
Again, this can be the only win. Continuing:
5. …..Kc6
6. Qe8 wins the black queen since the knight prevents the black king from playing to b6 to protect the lady.
Now, back at move 2, black had alternatives to Kf5, but they all look to be shorter mates since the black king can’t even reach the black queen in those. From the top:
1. Kd4 Qb5
2. Ne5 Kf4
3. Qf8
Here, Qe4 wins, too. Continuing:
3. …..Kg3 (Kg5 4.Qg7 as earlier)
4. Qf3 Kh2 (Kh4 5.Qg4#)
5. Ng4 Kg1
6. Qf2 with 7.Qh2# to follow.
Or:
2. …..Kh4
3. Qe4
I think this is the only winning move. If white checks from d8 or h8 with the queen, the black king will reach g3 and I don’t see how the white queen can close the distance on the black king quickly enough to prevent him from escaping through f2, but maybe I am just not seeing a more lengthy line that wins. Continuing:
3. …..Kg3
Here, 3. …Kh3 loses as shown in the previous line; 3. …Kh5 loses to 4.Qf5 followed by mate; 3. …Kg5 loses to Qg6 followed by 4.Qg4#. Continuing:
4. Qf3 Kh2
5. Ng4 with the same mate we saw earlier.
Or:
2. …..Kg3
3. Qf3 with the same mates seen above to follow.
Or:
2. …..Kh3
3. Qf3 and mate will follow as above.
Or, finally:
2. …..Kh5
3. Qh8 Kg5
4. Qg7 and we have seen this already loses above.
The holes in this, of course, are the lines where black doesn’t take at b5 at move 1. I will just assume they are lost due to the extra white pawn. But I could spend all day and tomorrow trying to prove them each out.