White to move. Can white win this?
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simple answer: yes.
Breakthrough with 1 h5. Idea is that black’s knight can’t prevent both the a pawn and the breakthrough pawn on g or h files from both queening while white’s knight can hold off the black pawns.
1 h5 gxh5
2 g5 hxg5
3 h6 f4
4 h7 g4
5 h8Q etc.
3.h6!!??
Sorry, confused two lines in my head. This one should go
3.fxg5 f4
4 f6 etc.
1. h5 g5
2. fxg5 hxg5
3. h6 etc.
Sorry, confused two lines in my head. This one should go
3.fxg5 f4
4 f6 etc.
The other line goes:
1. h5 g5
2. fxg5 hxg5
3. h6 etc.
Karthik,
I wanted to wait until I had posted my two longer comments before coming back to your suggested start. Here is the problem with 1. h5- and don’t feel bad, it was my first thought for a bit this morning:
1. h5 gh5 (anything else for black loses quickly)
Now, here for white, you suggested 2.g5:
2. g5 hg5 (again, the only move for black)
3. fg5
However, black need not cooperate with f4 here- he can defend better with Ke5 to keep the g-pawn corralled well enough. Basically, white is move to the worse than he was in the lines I discussed below- basically speaking, his knight is on a worse square. Lets look at the obvious try with Nd2:
3. ………Ke5
4. Nd2 f4
5. Nf3 Kf5
And now the white knight is bound to the g-pawn. White can, of course, force the black knight to sacrifice for the a-pawn still, but black will eventually force the white knight to take at either h4 or h2 and win the g-pawn to force a draw.
I did look at several variations in this line, but I can’t convince myself they are any better than a draw. There are other lines starting with white’s second move here, but they all have the same problem- white can’t protect the last king side pawn long enough to win the black knight and transfer the king to the kingside.
how should white use his “a” P? should he try to drive away the N to queen the P or get the N in exchange for the P and win with K side pawns? But there is little hope on K side.
1.h5 looks like an obvious move but you need a tin of white paint to change the color of the P to get at Karthik’s solution. So i have tried the most improbable 1.g5
1.g5 h5 2.Kc5 Kxf4 3.Kc6 Kg4 4.Kc7 Na7 5.Kb7 Nb5 6.Ne3+ Kxh4 7.Nc4 f4 8.Kb6 Kg3 9.Kxb5 f3 10.a7 f2 11.Nd2
Probably black has got better defence with 1…. hxg5 2.fxg5 leaving unhindered path(unhindered by black K) for “f” pawn.
3rd move f take g5 or g take h7 ie h5 and g5 for white
Professor Bhat is correct- the only real winning chance here isl likely to be 1.g5, of which there are two main lines:
1. g5 h5 (will discuss hg5 in seperate comment)
2. Kc5 Kf4 (what is better?)
At this point, Bhat suggests 3.Kc6, and it is an “obvious” plan, but there is a hitch that is hard to see in knight and pawn endings unless you have had quite the experience in them as I have had- I could see the problem immediately, having played both sides multiple times over the years:
3. Kc6 Kf3 (same plan as white is pursuing)
4. Kb7 Nd6
If white tries 4.Kc7 to prevent Nd6+, black just plays Na7 instead to block the pawn, and then will play either Nc8 in response to Kb6, or play Nb5 in response to Kb7- then, after Kb6, the knight goes to d6, and the pawn can’t advance without allowing the fork from c8 allowing black to sacrifice his knight for the a-pawn. I really don’t think white has a solution after the hasty 2.Kc5/3.Kc6 Continuing from 4. …Nd6 above:
5. Kc7
Or, if 5.Kc6, the knight returns to c8:
5. …………..Nb5 (covering a7)
6. Kb6
Or, if 6.Kc6, then Na7:
6. ……………Nd6
Again threatening Nc8+ if white pushes with 7.a7, or returns the knight to either c8 or b5 if white moves the king. White has a problem winning this I think. A better idea is to take the time advantage white has in having already established an advanced passed pawn, and get the knight into a better position starting at move 2 or 3 (I think white can play 2.Kc5/3.Nd2 and 2.Nd2/Kc5 interchangeably, but could be wrong.
1. g5 h5 (again, I will discuss hg5 later)
2. Nd2 Kf4 (will have to think about Kd5 more later)
3. Kc5
As I wrote above, I think white can play these moves at 2 and 3 interchangeably, but I might be wrong- I simply haven’t taken the time to think it all through. With Kc5, white is now threatening the previous plan, but with the ability to take away d6 by playing Nc4. I don’t think black has a defense now. He can try Ke5 or Ke3, but white will check from c4 and then proceed with Kc6:
3. ……………Ke5
4. Nc4 Ke6
5. Kc6 f4 (what better now?)
6. Kb7
Here, white will also win with 6.Kc7, but this is left as an exercise for the curious. Continuing:
6. ……………Kd7 (what else?)
7. Ne5! Kd8 (what else?)
8. Kb8!
A pretty example of zugzwang- black can move the f-pawn and lose it to the knight, move the king and lose the knight, or move the knight:
8. …………..Nb6 (Nd6 or Ne7 is met by a7 and the pawn will queen)
9. a7 Na8 (still in zugzwang- try anything)
10. Ka8 Kc7 (just for demonstration purposes)
11. Ng6 f3
12. Nf4 f2
13. Nd5 and the knight will hold up the f-pawn from e3 and advance the g-pawn instead, and had black played 10. …Kc8 just to prevent the check from d5 in this line, white would still have taken at g6 and maneuvered with Ne7+ and Nf5 to reach e3 (or g3 in that case.
In my next comment, I will consider the other defense black had at move 2.
In my previous comment, I showed how white might win with Bhat’s suggested 1.g5. Black had two options at move 1- take the pawn at g5, or pass it by with h5. So, let’s now discuss 1. ….hg5:
1. g5 hg5
2. fg5!
I don’t know for sure if 2.hg5 just draws or not, but after 2. …Kf4, I can’t see how white now wins- in the previous line, white needed his kingside pawns, but will lose them all within the first 3 moves. Maybe I am overlooking something, but I have concrete plan for the white h-pawn. Of course, the structure has one other big difference- black need not take the time to take the white f-pawn and clear the way for his own f-pawn. He can now play a move like 2. ….Kd5:
2. ……………Kd5 (Ke5 considered below)
3. h5 gh5 (any better move?)
4. Ne3
I think white can transpose moves 3 and 4- can’t make a good argument against it. Continuing:
4. …………..Ke5 (or Ke6 white still plays Ng2)
5. Ng2
An important juncture. I am getting into deep weeds here, so bear with me:
5. ………….f4 (will talk about alternatives later)
6. Nf4
This is the place I have spent 90% of my time this morning in analyzing this problem. The previous line, I banged out in about 10 minutes of actual work since the themes were familiar to me- the problem white had in preventing black from sacrificing the knight for the a-pawn which rested on the fact that the white pawns on the kingside were blocked and could not be protected long enough for the white king to come to his knight’s aid. In this line, white has forced a passer in the g-pawn which changes the balance in how black can defend on the queen side. I think white’s options here are either transpositions, or similar structures. What white needs is a stable arrangement on the king side with a pawn protected from behind by the knight- preferably blocking the h-pawn, too. Let’s continue from 6.Nf4 above:
6. ……………Kf5
Here, clearly black can’t take the knight- white just pushes the g-pawn to a queen (or the a-pawn if black plays Ne7 to stop the g-pawn). If black plays h4 at move 6, we will end up in the same place that follows- white will respond with 7.Nh3 and then force black to give up the knight for the a-pawn and easily win the resulting ending. Continuing from 6. …..Kf5 above:
7. Nh3
And this should be won now. If black plays h4, white just plays Kc5-Kc6-Kc7 etc, and forces the liquidation of the black knight and a-pawn and then brings the white king to the king side and wins the black h-pawn and queens the g-pawn. So, now let’s work backwards through the line above starting with black’s 6th move:
6. …………….Kd6 (to stop the advance of the white king)
7. g6
Here, 7.Kb5 should win, too. Continuing:
7. …………….Ke7 (if Ne7, white just plays a7)
8. Nh5 Kf8
9. g7 Kg8
10.Kc5 and white will win with ease from here by forcing the black knight to immolate itself for the a-pawn and win with the g-pawn instead. So, we can now move back up the move 5 in the following line:
1. g5 hg5
2. fg5 Kd5
3. h5 gh5
4. Ne3 Ke5
5. Ng2
So, previously, I had black playing f4. What about 5. ….h4?
5. …………..h4
6. Nh4 f4 (what better now?)
7. Kc5
Here, white is planning to blockade the black f-pawn with Nf4 which protects the g-pawn from behind and force the black knight to sacrifice for the a-pawn. All black can do is try to support the knight, but we already know this is hopeless:
7. …………..Ke6
8. Kc6 and it is over.
So, now let’s back up to move 5 again in this line and consider what happens if black doesn’t give up either remaining pawn- does it change anything?
1. g5 hg5
2. fg5 Kd5
3. h5 gh5
4. Ne3 Ke5
5. Ng2 Ke6
6. Kc5 Kf7
We already know that white can’t be prevented from forcing the knight sacrifice for the a-pawn, so black’s fallback position is to try to win the g-pawn for a draw. However, this just can’t work:
7. Nf4 h4
8. Kd5
And white just changes the focus of his attack- the king now threatens to win the black pawns while the knight is forever tied down on the queenside. The barrier that the knight completes with the pawn is a familiar theme. The best black now has is
8. ………….h3 (to force open the g6 square)
9. Nh3 Kg6
10. Ke5 Na7 (black is in zugzwang again)
11. Kf4 Nb5
12. Nf2
And white will maneuver to double attack f5 to win- a7 is always in reserve if the black knight gets frisky. So, finally, we are left to talk about black’s alternatives at move 2. Should black play Kf4 to prevent white’s plan of pushing h5?
1. g5 hg5
2. fg5 Kf4
3. Kc5 Kg4
4. Ne3!
And now black can’t take at h4 without allowing the killing 5.Nxf5!!:
4. …………Kh4
5. Nf5!! Kg5 (gf5 6.g6+-)
6. Nd6! Na7
7. Kb6 and the black knight can’t stop the a-pawn at all. At move 4, then:
4. …………Kf4 (looking for repetition)
5. Nc4 Kg4 (we know moves like Ke4 are losing)
6. Kc6!
Most accurate move, I think. I think white will still win with a move like Nd6, but black can push the f-pawn and the chances of making a mistake increase. In any case, here is what I see: [6.Nd6!? f4! 7.Nc8 f3 8.Nd6! f2 9.Nc4! and now white can stop the f-pawn from advancing since an immediate f1Q is met by Ne3 forking the new queen and her hapless king]. With 6.Kc6, the calculation is simpler for me since I have already done it for all intents and purposes in the first comment I posted
6. ……………f4 (nothing better)
7. Kb7 and it is over.
This is more or less thorough, I think.
1.h5 gxh5 2.Ng3+ Kxf4 3.gxf5 Kxg3 or h4 (Anyway the pawn goes to the last rank if the N tries to stop it, the pawn on the A file goes to Queen and the black attack he is stopped by the power full Queen.)
3… Ke5 followed by 4…. h4
An interesting line I had considered yesterday for a time, but Bhat is correct- black defends best with 3. ….Ke5 with the plan to drive the knight away with h4. However:
1. h5 gh5
2. Ng3 Kf4
3. gf5 Ke5
4. Nh5 Kf5
Was interesting to me. However, this is drawn with best play with 100% certainty (I checked it with the online Nalimov Tablebase. So, can white improve on 4.Nh5? Consider:
4. Kc5 h4
5. Ne4!
The knight can’t be taken! It looks for all the world like a draw since black queens his pawn on the half move after white queens his in that line, but there is a brilliant win for white in there. Also, taking the pawn at f5 loses to the simple Nd6 fork since white queens on a8 one half move before black does on h1. However, black still likely draws by simply playing 5. ….h3 instead keeping the balance of power:
5. ………….h3!
6. Nf2 h2 (or Kf5 7.Nh3)
7. Ng4 Kf5
8. Nh2 h5
And this is drawn according to Nalimov Tablebase. All in all, a fascinating endgame.
So here is the line I proposed as a follow up to Leilo’s suggestion that contains within it another pretty ending problem based on the main problem:
1. h5 gh5
2. Ng3 Kf4
3. gf5 Ke5
4. Kc5 h4
5. Ne4 Ke4??
2n5/8/P6p/2K2P2/4k2p/8/8/8 b – – 0 1
I think it is 2n5/8/P6p/2K2P2/4k2p/8/8/8 w – – 0 1
6.f6 h3 7.f7 h2 8.a7 nice diversion sacrifice Nxa7 9.f8=Q h1=Q 10.Qa8+ Nice skew.
A funny idea by black K to move to d3 to isolate WN from queenside results in following catastrophe. 1.g5 h5 2.Kc5 Kd3 3.Ng3 Ke3 4.Nxf5+ Kxf4 5.Nd6 Na7 6.Kb6
Notes:
1. The a-pawn is well placed – it’s killing the knight, and it cannot be captured.
2. The white knight is very well placed on f1
3. The white king could be better placed ..
Plan:
Play g5 and then manoeuvre the king to f6 to win the g-pawn
or get the king to f4.
Effectively the game is king, knight and pawn vs king and 3 pawns
some lines
1 g5 hg:
2 fg: kf4
3 nh2 kg3
4 h5 etc
2 … kd5
3 kc3 ke5
4 kd3 kf4
5 nh2 etc.
1 … h5 (slow)
2 kc5 kf4:
3 kd5 kg4
3 ke5 kh4
There are variations but I think these are clear enough.