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My first instinct in this is that only black plays for the win here. There are no mating nets here for white, and his pawn is just too far away from becoming a queen. Black’s threats are more immediate- like checking from d1 and pushing a2-a1Q. White must concentrate on stopping the black pawns- either giving up the rook for both, or maybe giving up both pieces and try finding a drawing line with the c-pawn vs the rook.
With that in mind- how do you bring the pices back to bear down on the black pawns? White can check from h6 and then transfer the rook to the a or b-file. He can bring the knight back with Nc4 or Nd3. Let’s look at the Rh6+ first:
1. Rh6 Kg7
I have a reason for picking this move for black that I will come to in a moment. Continuing:
2. Rb6 a2 (cleaner than b2)
And white has a problem- black is going to check with his rook and queen the a-pawn. If white plays the rook to a6, black just pushes b2 and black will get a queen on the board. In fact, these pawn pushes are so deadly that it is clear the knight has to be the piece that comes back first. Let’s look at 1.Nc4.
1. Nc4
Visually, this move is clearly superior to Nd3 for a simple reason- Nc4 attacks the a3 pawn immediately. White is threatening to simply sacrifice at a3 and then liquidate the b-pawn with Kc3 and Rh3 to draw the game. Continuing:
1. …..a2
Pushing b2 won’t win: [1. …b2 2.Na3! Ra3 3.Rh6 Kanywhere 4.Rb6 draws at the very least for white]. Black can play Rd1 here, but will still have to play a2 on the following move, so I think it is transposition. Continuing:
2. Rh6!
This is almost certainly the only drawing move since black is now threatening Rd1 followed by a1Q. The white rook must go to the a-file to stop this threat. Continuing:
2. …..Ke7
3. Ra6 Rd1
I don’t see how any other move is better, though any rook move here should be equivalent. Continuing:
4. Kc3!
Certainly the only drawing move, so now black can win white’s rook, but his b-pawn is going to be lost, too:
4. …..a1(Q)
5. Ra1 Ra1
6. Kb3 and this is surely a draw since black will find a way to sacrifice the rook for the white pawn at some point.
The last loose thread was back in the first line I discussed. There white played 1.Rh6 and I chose Kg7 specifically. I chose this attack on the rook to force white’s hand. If black doesn’t attack the rook with the king, we can transpose into the 1. Nc4 line.
I am betting this is drawn with best play.
If Yancey Ward’s solution is published for the reason that it is wrong, this is of course helpful to know:-)
I like:
1. Nc4! a2
2. Nxa3!
This sack was mentioned by YW as a threat, why not use it?
2. … Rxa3
3. Rh6+ Ke7 (keeping an eye on the c-pawn)
4. Rb6
Those moves also mentioned by YW, but it’s after the Na3 sack that they are really helpful:-)
Black’s b-pawn being doomed, white is up with a pawn.
For now, I’m too lazy to dive deeper into the continuation:-)
I’m not good enough at endgames to sort this out, but I guess something along the lines:
1. Nc4 b2
2. Nxa2 Rxa2
3. Rh6+ Ke7
4. Rb6 Ra1 (Ra4+ Kd5)
5. Rxb2 Rd1+ (Rc1 Rb3 Ke6 Rc3)
6. Kc4 Rc1+
7. Kb5 Ke6
8. Re2+ Kd5
9. Rd2+
or perhaps:
4. … Ra8
5. Rxb2 Rd8+
6. Kc4 Ke6
7. Re2+ Kd7
8. Rd2+ Kc6
9. Rd6+
I can only find a draw here with a king, rook, king, knight ending.
pht,
Yes, having the comment published that quickly does suggest something was missed. Right now, I can’t see how anything other than Nc4 can be the first move for white, and I don’t have any further insights on my line, either.
1.Rf5+…
a)1…Kxf5 2.c6 b2 3.c7 b1Q 4.c8Q+
b)1…Kg7 2.Rf7+…/2…Kg8 3.c6 / 2…Kh6 3.Rf6+ Kg5 4.Rf5+ Kh4 5.Rf4+ Kg3 6.Rf3+
c)1…Ke7 2.Rf7+ Ke8( Kd8, Ke6 )3.c6
d)1…Ke6 2.c6
Yancey Ward:
I must admit that I hadn’t read your solution properly before I gave my suggestion.
I agreed with Nf4, but only considered the b2 continuation, didn’t look at a2, as you actually wrote.
Well, looking at it now, how to stop that a-pawn in another way than you suggest, is a mystery to me as well.