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Pretty much has to be a knight move of some kind, though I think white can get some winning chances even with the prosaic fxg3:
1. fg3 dc5 (Kc5?? 2.Rb5!)
2. e4 Kd6
3. Rd8 and black will likely have to play very carefully to avoid losing, but this is quite complex and I don’t really have a firm grasp on it with just a casual glance.
So, let’s go back to looking at the knight moves. I really can only imagine that it has to be Ne4 or Nb3 since other knight moves take the knight further away from the first rank, or lose him altogether:
1. Ne4 gf2
This is clearly forced since playing g2 will allow Rb5 followed by Rxg5 covering the g1 square. Even 2.Rb1 should win almost as easily. Continuing:
2. Rb5
I don’t see how any other move is better, and other moves are likely transpositions, too. Continuing:
2. …..Kc6 (Ke6?? 3.Ng5+-)
3. Nf2 Rf2
4. Rg5 Rh2
And I don’t really think this can be won by either side, though I am far from certain in this belief. Both sides’ weak pawns make it difficult to envision a plan for winning. So, let’s see if 1.Nb3 is any different:
1. Nb3 gf2 (alternatives later)
2. Rb5
Took me a while to find this move, and the ones that follow:
2. …..Kc6 (Ke6 3.Nd4 Ke7 4.Rb7)
3. Na5! Kd7
4. Rb7 Ke6
5. Rf7 Kf7
6. Ke2 and this should be a winning endgame, even with the scattered pawns. White will mop up f2 and has time to guard h5- the black king will be badly overtaxed.
So, let’s see about black’s alternatives at move 1:
1. Nb3 g2
2. Rb5 Ke6 (Kc6 no better)
3. Nd4
I think 3.Rg5 will win, but it is not nearly as accurate. Continuing:
3. …..Ke7
4. Rg5 Rf2 (what else now?)
5. Ne2 Kf6
6. Rg3 Ke5
7. e4 and white will eventually win the g2 pawn, though the ending still requires some skill and care.
Or, at move 1:
1. Nb3 Rf2
2. Rb5 Ke6
3. Rg5 g2
4. Nd4 Kf6
5. Rg4 Ra2 (what else?)
6. Ne2 Ra1
7. h6
And this, too, should be a won ending for white, though not trivially.
The g3 pawn is difficult to stop, having both gxf2 and g2.
I couldn’t find an alternative to starting with dropping the knight.
I closed out both 1. fxg3 (giving black a strong c-pawn and an active rook), and 1. e4+ followed by fxg3 (giving black Rf3+), and so I found the idea:
1. f4! (closing f-file) dxc5 (Kxc5? Rb5+)
2. Rg8
The best move I could find.
This is a complicated battle, but I have the feeling that white could get an edge here?
I must have been rather blind here.
I closed out 1. fxg3, but that must be wrong!
1. fxg3! dxc5 (Kxc5 Rb5+)
2. e4+! Ke5
3. Re8+!
or
2. … Kc6
3. Ke3!
The position is equalized, but white looks more active here.
This is all I can find that actually looks natural….
So, I was stuck with the “prosaic” 1. fxg3.
I simply overlooked the chances with the knight, should of course have seen that a knight move can’t be answered with:
1. … g2?
2. Rb5+ …
3. Rxg5
1.Rb5…
a)1…gxf2 2.Ne4+…( 2…Ke6 3.Nxg5+ Kf6 4.Ke2/+-/ ) 2…Kc6 3.Nxf2 Rxf2 4.Rxg5
b)1…g2 2.Ne4+…( 2…Ke6 3.Nxg5+ Kf6 4.Nh3/+-/ ) Kc6 3.Rxg5 /+-/
c)1…dxc5 2.e4+ Kd5 3.fxg3 Rf3+ 4.Kc4 Rxg3 5.Rxc5