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1. Nxc5 bxc5 (1. … Kd4 2. d7 Nxd7 3. Nxd7 etc. and white wins) 2. b4 cxb4 (a. 2. … axb4 3. a5 and white both pawns are unstoppable; b. 2. … Kd4 3. bxa5 followed by 3. a6 and white wins) 3. c5 Kd4 4. c6 Kd5 5. d7 1-0
The first move isn’t actually hard to find. White can draw with a number of moves here, but one has to assume a win is at hand, and there really is only plausible way to win- white must threaten to take control of the d7 square, and this leaves only….
1. Nc5! bc5
If black doesn’t accept the knight, white gets d7 in to win a piece and ultimately to win the backward b-pawn. Continuing:
2. b4! ab4 (alternatives below)
3. a5
And black’s knight can’t stop both passed pawns, and it will take black 5 moves to queen the e-pawn while white will queen in 3 more moves or less. Now, when white queens a full move ahead, it isn’t yet quite proven a loss for black, so let’s play it out to the critical point:
3. …..Kf2
4. a6 e4
5. a7 e3
6. a8Q e2
And now white must solve another problem. Normally, white would check from the back and force the black king away from the pawn, or force black to block the pawn, but the knight is in the way. So, white is going to have to let black queen the pawn:
7. Qf8 e1Q (b3 no better)
8. Qf6
And now white would prefer to force the queens off the board and win with the passed d-pawn. Right now, I don’t quite see how that is accomplished. It would very easy to do if black didn’t have pawns covering d4 and c3. I am going to have to come back to this later today after I have had some sleep.
In any case, let’s deal with black’s alternatives at move 2:
1. Nc5 bc5
2. b4 Nd7
3. ba5
Of course, if b5, the knight can hold up both pawns from d7, and if bc5, black just takes the pawn at c5 to win. Now black can’t stop the d and a pawns with the knight, and must push the e-pawn:
3. …..Kf2
4. a6 e4
5. a7 e3
6. a8Q e2
7. Qe4 e1Q
8. Qe1! Ke1
9. a5 and white will queen the other a-pawn or the d-pawn to win since the knight is still helpless to stop both.
Or, at move 2:
2. …..cb4
3. c5 Kf2 (Kd4 4.c6 wins)
4. c6 e4
5. d7 Nd7
6. cd7 e3
7. d8Q e2
8. Qh4 Kf1 (else 9.Qe1)
9. Kd2! and white will win the e-pawn and mate soon after.
And, finally, at move 2:
2. …..e4 (gains a tempo)
3. cb5!
The only move now- to make up for the tempo, white must queen a d-pawn in order to win the knight. If white plays 3.ba5, white only queens the half move ahead of black. Continuing:
3. …..Kf2 (Kf3 better here?)
4. c6 e3
5. d7 Nd7
6. cd7 e2
7. d8Q e1Q
8. Qh4! Kf1
9. Qe1 wins.
So, at move 3 in this line, black might want to play Kf3 just prevent white from that check at move 8:
3. …..Kf3
4. c6 e3
5. d7 Nd7
6. cd7 e2
7. d8Q e1Q with the same issue I mentioned before- is this actually winning for white? I need to work on this more in the morning to have a definitive answer.
Nxc5 (threatening d7) followed bij b4 seals the deal. Black’s N can’t stop two pawns, Black will not be on time in variations, black’s advance is stopped by the white King.
1.Nxc5 bxc5
2.b4! …cxb4 3.c5
or ..axbe 3.a5 and wins by move of pion
The best way to use that slow horse could be to sack it:-)
1. Nxc5 bxc5
2. b4! axb4 (alternative below)
3. a5 Nd7
4. a6
White obviously wins this, since after a7 and Nb6, d7 follows.
After:
2. … cxb6
3. c5
no reasonable N move seems to exist. Those connected pawns seem to be unstoppable.
3. … Kd4
4. c6
1. Nxc5 bxc5
1. Nxa5 bxa5 would result in the same position, however, Black is not forced to take the knight but can play e4 or Kf3. After
1. Nxc5 Kf3 Black is lost because of
2. d7! Nxd7
3. Nxd7 e4
4. Nxb6 Kf2
5. Nd5 e3
6. Nc3 +-
Or:
1. Nxc5 Kd4
2. d7! Nxd7
3. Nxd7 e4
4. Nxb6 e3
5. Nd5 e2
6. Kd2 +-
2. b4 and either the a-pawn or the c-pawn will queen soon, e.g.
2. … cxb4
3. c5 Kf3
4. c6 e4
5. c7 e3
6. c8=Q e2
7. Kd2 Kf2
8. Qf5+ and easy win for White
1. b4!!
A. If 1…..axb
2.Nxc5!!
A1. If 2..bxc5 3.a4 and black knight can stop only one white a-or-d-pawn from queening; he cannot stop both pawns.
A2. If 2..Kd4 3.d7 Nxd7 4. Nxd7 Kxc4 5. Nxb6+!!(better than Nxe5+) and white will queen a-pawn; black king cannot reach a file easily.If..Kc5 6. Nd7+ and black king has to fall back. Moreover white knight can easily capture black e pawn later while protecting own a-pawn with Kb3!
B. If 1…cxb3 2. Nxa4 similar to variation A above; here black king cannot reach white a3-pawn at all as his a4-pawn blocks access and white’s c-and-d-passed pawns cannot be stopped at all.
B1 if 2….bxa4 3.c5..Kd4 4.c6 and white queens in 2 moves; black needs 4 moves to queen.
B2.if 2….Kd4 3. Nc6+ kxc4 4. Nxe5+ Kc5 (how else to reach white a pawn as black e pawn is doomed anyway?; Kd4/d5 doesnot help either against next white move)5.d7 Nxd7 forced 6. Nxd7 and the black king cannot catch the knight. White simply plays Kb3 and Kxb4 and slowly captures the other b pawn with king and knight and avoids exchanging or losing the white a-pawn. Ultimately he queens or mmatess with King at b6 pawn at a6 knight at b5/d5/e6/e8 to play a7+ and Nc7#
Harry
Nc5!
b4 should be okay I guess .. then, I’ll sacrifice my knight to let my pawn passes ..
To mention is this line:
1. Nxc5 bxc5 (not taking fails to d7)
2. b4 Kd4 (taking on b4 fails to a5 or c5)
3. bxa5!
and black king can’t cach up with this pawn because his own pawn on c5 stands in the way.
1. Nxa5 (or Nxc5) b6xa5
2. b4 a5xb4
and now Nf6 can’t stop both passing pawns but Kc2 can stop b4.
At first I thought that 1. b4 might win. But after either 1. .. axb4 2. Nxc5 or 1. .. cxb4 2. Nxa5 Black draws with 2. .. Kd4
I obviously have a move order problem.
Very early this morning, I discussed two critical lines that appear to give white a win, but I couldn’t really prove that white can win the resulting queen and pawn ending. I think I can prove that now:
1. Nc5 bc5
2. b4 ab4
3. a5 Kf2
4. a6 e4
5. a7 e3
6. a8Q e2
7. Qf8 e1Q
8. Qf6
So, where can black put the king? Obviously Ke2 and Ke3 lose instantly to Qe6+ followed by Qxe1 and white then queens the d-pawn. This leaves Kg3, Kg2, and Kg1. Let’s take them in reverse order:
Variation With 8. …Kg1;
8. …..Kg1
9. Qg5! and no matter where the king goes now- f2, h2, f1, or h1- white will either check from d2 or pin the black queen to the king by playing to c1. In all cases, the queens are forced off the board and white wins with the passed d-pawn.
Variation With 8. …Kg2
8. …..Kg2
9. Qg5 Kh3
Here, of course, Kf1 and Kh1 lose to Qc1 pinning the black queen to her king. Also, Kf2 and Kh2 lose to Qd2+ forcing the exchange of queens. Finally, if black plays Kf3: [9. …Kf3 10.Qd5 Kg3 (or 10. …Kg4 11.Qd1+-; or 10. …Kf4 11.Qd2+-) 11.Qd3 Kh4 12.d7 b3 (or 12. …Qf2 13.Kb3+-) 13.Kb2 Qf2 (or 13. …Qe5 14.Ka3 Qa1 15.Kb3+-) 14.Kb3+-]. Continuing from 9. …Kh3:
10.Qd2 b3 (Qe4 11.Qe3+-)
11.Kc3 Qa1
If black tries Qe8, white just pushes d7 followed by Kxb3 with a fairly easy win. Also, Qe5+ is met by Kxb3 followed by d7. Continuing from 11. …Qa1:
12.Kb3 Qb1
13.Ka4 Qa1
14.Kb5 Qb1
15.Kc5 and a Nalimov tablebase confirms this is lost in 20 moves for black, but actually isn’t a difficult queen ending from this point since the pawns will be connected, supported by both the king and queen, and the black king is out of the play completely. Now let’s return to the last option at move 8 for black:
Variation With 8. …Kg3
8. …..Kg3
9. Qg5 Kf3
We have already seen 9. …Kh3 in the previous variation’s main line. I also covered 9. …Kf3 in the parenthetical note, but will outline it again since it was fairly lengthy for such a note. Of course, 9. …Kh2 and 9. …Kf2 lose to 10.Qd2+. Continuing:
10.Qd5 Kg3
Or [10. …Kg4 11.Qd1+-]; or [10. …Kf4 11.Qd2+-]. Continuing:
11.Qd3 Kh4
12.d7 b3 (Qf2 13.Kb3+-)
13.Kb2 Qf2(Qe5 14.Ka3 Qa1 15.Kb3)
14.Kb3+-
In my next comment, I will finish off the other critical line that was indeterminate in my first comment.
Straigtening out the move order problem:
After 1. Nxc5 bxc5 2. b4
2. .. axb4 obviously loses to 3. a5
2. .. cxb4 also loses to 3. c5 Kd4 (3. .. Ne4 4. d7 b3+ 5. Kb2 Nxc5 6. d8=Q) 4. c6 Kd5 5. d7
Black’s best try appears to be 2. .. e4 3. bxc5 Kf2 4. c6 e3 5. d7 e2 6. d8=Q e1=Q 7. Qxf6+ and White will be able to avoid a perpetual check and will win.
I can see from Yancey Ward’s comment that I spoke to soon about the results after
1. Nxc5 bxc5 2. b4 axb4 3. a5
I could add that after 3. e4 4. a6 Kf2 5. a7 e3 6. a8=Q Black can try b3+ immediately.
Then after 7. Kxb3 e2 the move 8. Qa2 only offers a draw. 8. .. Kf1 9. Qa1+ e1=Q 10. Qxe1+ Kxe1 11. Ka4 Ke2 12. Kb5 Kd3 13. Kxc5 Ne4+ 14. Kc6 Nxd6 15. Kxd6 Kxc4
But Yancey’s Qf8 move wins here too:
8. Qf8! e1=Q 9. Qxf6+ Kg1 10. Qg5+ Kh2 11. Qxc5
The last critical line arose in my very first comment when black pushes the e-pawn rather than capture at b4 at move 2:
1. Nc5 bc5
2. b4 e4 (gains a tempo)
3. bc5!
Note: in my first comment, I accidentally transposed the “b” and the “c” in this move and wrote the error “cb5”. This is the only move now- to make up for the tempo, white must queen a d-pawn in order to win the knight. If white plays 3.ba5, white only queens the half move ahead of black. Continuing:
3. …..Kf3
I showed in the very first comment that black loses quickly with 3. …Kf2 since white skewers the king and queen from h4 to force the queens off the board. Continuing:
4. c6 e3
5. d7 Nd7
6. cd7 e2
7. d8Q e1Q
So, the first thing to deal with is the forced exchange at d1, and it is a tricky king and pawn ending, but I am certain it is drawn:
8. Qd1? Qd1
9. Kd1 Ke4! (only move)
10.Kc2 Kd4!
11.Kb3 Ke5!!
Black, of course, loses immediately with Kd3 and Ke3 since white just pushes the pawn. However, black will also lose with Kc5 and Ke4: [11. …Kc5?? 12.Kc3 Kc6 13.Kd4 Kd6 14.c5 Kc6 15.Kc4 Kb7 16.Kb5 and white will win the a-pawn while retaining the c-pawn. While I didn’t cover all the variations within this, white’s plan is basically the same in all but one of them (taking b6 instead)- force the black king back until b5 can be taken by white’s king- but see the next sentence]. Or: [11. …Ke4 12.Kc3! Ke5 13.Kd3! Ke6 14.Kd4 Kd6 15.c5! Kc7 16.Kd5 Kd7 17.c6 Kc7 18.Kc5! Kany 19.Kb6+-]. Continuing from 11. …Ke5 above:
12.Kc3 Ke4! (only move)
And white either repeats moves, or pushes the c-pawn:
13.c5 Kd5 and white loses the c-pawn.
So, white needs another plan to win at move 8 above. Let’s see how white should proceed:
8. Qd3 Kg4 (alternatives below)
Now, in the previous comment, such moves were deadly to black since white could force the queens off with checks from d2 and d1, but here with pawn on c4 instead of d6, black’s king is a player in stopping the pawns, so white must calculate carefully:
9. Qd1 Qd1
10.Kd1
Now, is this won for white? Yes, it is- black’s king is too far away now to force white to repeat moves or lose the c-pawn as above:
10. ….Kf4
11.Kd2 Ke4
12.Kc3
This is what black couldn’t prevent- reaching this exact position, but now black is the one that has to move instead of white. Continuing:
12. ….Ke5 (Kf4/f5 13.Kd4+-)
13.Kd3! and we have already shown this is lost for black above.
Now, let’s take a look at black’s alternative move at move 8:
8. …..Kg2
9. Qd2 Qd2
10.Kd2 and the white pawn runs away from black. The same will happen if black plays 8. …Kf2.
So, now we are ready for 8. …Kf4:
8. …..Kf4
9. Qd2 Qd2
10.Kd2
And, now, black’s king is a move closer in to e4 than in the previous variation, but then white’s king is also a move closer to c3. This ending is just as lost for black as the previous variation.
After Yancey’s 1. Nxc5 bxc5 2. b4 e4 3. bxc5 Kf3 4. c6 e3 5. d7 Nxd7 6. cxd7 e2 7. d8=Q e1=Q at least one winning continuation starts with 8. Qd3+
8. .. Kf4 9. Qd2+ Qxd2+ 10. Kxd2 Kf5 11. Kd3 Ke5 12. Ke3 Ke6 13. Ke4 Kd6 14. Kd4 Kc6 15. c5 Kd7 16. Kd5
1. b4 is more interesting than I thought at first glance last night, but there is a serious problem with it. As Lucymarie points out, 1.b4 probably won’t win for white. But the details are fascinating to those who like ending studies:
1. b4? ab4
2. Nc5 Kd4!
It is easy to miss this move since it looks like white can win the knight with d7 here, but the win is an illusion:
3. d7 Nd7!
4. Nd7 e4!
Taking at c4 looks dangerous for black: [4. …Kc4? 5.Ne5! Kd5 6.Nd7 Kc6 7.Nf6 and this should be won for white]. Continuing:
5. Nb6
Nothing better for white now, all the lines look drawn. Continuing:
5. …..e3
6. Nd5!
This is forced. If white plays to stop the e-pawn with 6.Ke2, black starts pushing the other black pawn and will win! Continuing:
6. …..e2!
Playing b3 here also looks dangerous to black: [6. …b3? 7.Kb3 e2 8.Nb4! and white will fork the king and new queen should black play e1Q, and e1N is probably lost, too, though it puts up more resistance than e1Q.] Also, Kc4 is surely lost after 7.Nxe3 with check. Continuing:
7. Kd2! b3! (Kc4 might hold??)
8. Nb4 b2 (Kc4 9.Nd3=)
9. Nc2 Kc4
10.Na3! Kb3
11.Nb1 Ka2 (Ka4 12.Kxe2=)
12.Nc3 Kb3
13.Nb1 with a draw.
1.b4 cxb4
2.c5 bxc5
3.Nxa5 Kd4
4.Nb7 Kd5
5.a5 Kc6
6.a6 Kb6
7.Nxc5!