White to move. How should white proceed?
Chess Daily News from Susan Polgar
More endgame improvement
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White to move. How should white proceed?
Another example where it is instructive to look at a couple wrong first moves:
1. Kd2 Kb4
I think black can win with Kc4, too, but this seems clearer to me:
2. Kc2 a5
3. Kc1
White loses with everything: [3.b3 Ka3 4.Kc3 b4 5.Kc2 Ka2-+]; or [3.Kb1 Kb3 4.Ka1 Kc2 5.Ka2 b4 6.Ka1 (or 6.b3 Kc3-+) 6. …a4 7.Ka2 a3 8.ba3 (or 8.b3 Kc3-+; or 8.Ka1 ab2-+) 8. …b3 9.Ka1 b2-+]; or [3.Kd2 Kb3 4.Kc1 Ka2 5.Kc2 b4 6.Kc1 b3-+]. Continuing:
3. …..Kb3
4. Kb1 b4
5. Ka1
Or [5.Kc1 Ka2 6.Kc2 a4 7.Kc1 b3-+]. Continuing:
5. …..a4
6. Kb1 a3! (only winning move)
7. ba3
Or [7.Ka1 ab2! 8.Kb1 Ka3! 9.Kc2 Ka2-+]. Continuing:
7. …..Ka3 (only winner of course)
8. Ka1
On 8.Kc2 or 8.Kc1, black plays Ka2 and pushes the pawn to b1. Continuing:
8. …..b3
Here, black can still win with Kb3, but must go back to a3 and play the line that follows anyway. The fact of white’s opposition is meaningless here. Continuing:
9. Kb1 b2
10.Kc2 Ka2 and black wins.
So, the penetration of black’s king to b4 on the first move was lethal to white. There are two moves that white can play to prevent this- Kb3 and Kc3, but only one of them is good. Let’s look at the wrong one first:
1. Kb3?? b4
Played to take c3 and a3 away from the white king. Black doesn’t care if white now tries Ka4: [2.Ka4 Kc4! (an only move!) 3.Ka5 (or 3.b3 Kc3 4.Ka5 Kb3-+) 3. …Kb3 (another only move) 4.Ka6 Kb2-+]. Now, on move 1, black can definitely win with a5, too, since this also forces white to give way: [1. ….a5 2.Kc3 a4 3.b3 (or 3.b4 Kd5 4.Kd3 Ke5! 5.Kc3 (or watch a-pawn queen) 5. …Ke4 6.Kc2 Kd4 7.Kb2 Kc4 8.Ka3 Kc3-+) 3. …b4 4.Kc2 a3 5.Kc1 Kd4 6.Kc2 (or 6.Kd2 a2-+) 6. …Ke3 7.Kc1 Kd3 8.Kb1 Kc3 9.Ka2 Kc2-+]. I think black can also win with 1. …Kd4, but I have not actually worked it out, but I think it mirrors the first of the variations immediately above. Continuing from move 1 above:
2. Ka2
Or [2.Kc2 Kc4 (an only move, I think) 3.b3 Kd4 (an only move for sure) 4.Kd2 a5 5.Kc2 Ke3 and the rest should follow directly from the lines I have analyzed above]. Continuing:
2. …..Kc4 (several wins now)
3. Ka1
On 3.b3, white will lose the pawn eventually after Kc3. On 3.Kb1, white loses to Kb3: [3.Kb1 Kb3 4.Ka1 Kc2 5.Ka2 a5 6.Ka1 a4 7.Ka2 a3 and we saw this line earlier was lost for white]. Continuing from move 3 above:
3. …..Kb3
4. Kb1 a5
5. Ka1 a4
6. Kb1 a3 (an only move for sure)
7. ba3
If 7.Ka1, black plays ab2 (only move): [7.Ka1 ab2 8.Kb1 Ka3 9.Kc2 Ka2-+]. Continuing:
7. …..Ka3 (only winning move)
8. Ka1 b3 (we did see it above)
9. Kb1 b2
10.Kc2 Ka2 and black wins.
I will break my comment at this point, and in the next comment, I will show how and why white draws with 1.Kc3.
The endgame is really an “open sea”.
The White draw but can also lose and even win (Obvious.).
After 1. Kc3! draw.
example
1. Kc3 Kd5
2. Kb4 Kd4
3. Ka5 Kc4
4. Kxa6 b4
5. Ka5 b3
6. Ka4 Kc5
7. Kxb3 Kb5 draw
Or
1. Kc3 a5
2. b4+ draw
or
1. Kc3 b4+
2. Kd3 Kb5
3. b3 a5
4. Kc2 a4
5. bxa4+ Kxa4
6. Kb2 draw
And the Black King does not go in critical squares in front of the pawn.
Best regards
Stef
In my previous comment, I discuss a couple of the losing first moves for white. In the first line, white plays 1.Kd2 and the black king penetrates to b4 and eventually wins the game. In the second line, I showed where white plays Kb3 to stop black from reaching b4, but black then plays b4 and forces the white king to either play up the a-file, or back to a2 again allowing the black king to penetrate to the fourth rank. This is what white must stop to draw this position. The correct first move is 1.Kc3:
1. Kc3 b4 (alternatives below)
2. Kd3
A move like 2.Kc2 will lose to 2. …Kc4 (a line that is in my previous comment): [2.Kc2 Kc4! 3.b3 Kd4! 4.Kd2 a5 5.Kc2 Ke3-+]. In addition, white will lose with 2.Kb3: [2.Kb3 Kb5! (only winning move) 3.Ka2 Kc4-+ and we saw this earlier, as well]. I think white can still draw with 2.Kd2, but I am not 100% sure: [2.Kd2 Kc4 3.Kc2! a5 4.b3! Kd4 and I will discuss this position below]. Continuing from move 2 above:
2. …..a5 (alternatives later)
3. b3
White might draw with other moves, but I don’t want to spend more time than I already have. This is a key position, here. What b3 does is take away black’s waiting moves, and it takes away the c4 square from black’s king, so that the opposition is no longer effective for forcing the white king to give ground. Let’s continue:
3. …..Kd5 (alternatives below)
4. Ke3! a4 (Ke5 5.Kd3 etc.)
5. ba4 b3
Or [5. …Kc5 6.a5 Kb5 7.a6 Ka6 8.Kd3 Ka5 9.Kc2! Ka4 10.Kb2! b3 11.Kb1! Ka3 12.Ka1! Kb4 (or 12. …b2 13.Kb1=; or 12. …Kb4 13.Kb2 Kb4 14.Kb1! Kc3 15.Kc1 b2 16.Kb1=) 13.Kb1 Kc3 14.Kc1=]. Continuing from move 5 above:
6. Kd3 Kc5
7. Kc3 with a draw.
So, let’s work backwards and demonstrate that black had no better alternatives than this drawing line. At move 3 above, black could have tried to support the a-pawn’s advance by first playing Kb5:
3. …..Kb5 (a4 4.ba4 b3 5.Kc3=)
4. Kc2!
Almost certainly the only move for white (alternatives left to the curious). Continuing:
4. …..a4
5. ba4! Ka4
6. Kb2! and we don’t need to do this again, do we? This is a dead drawn position.
Back at move 2, black could have tried Kd5:
2. …..Kd5
3. b3 Kc5 (a5 transpose to above)
4. Ke3 Kb5 (Kd5 5.Kd3; Kb5 5.Kd3)
5. Kd3 a5
6. Kc2 a transposition to a drawn line above.
Finally, let’s look at black’s first move alternatives:
1. Kc3 a5
2. b4+!
I am pretty sure 2.b3 will draw here, too, but this move of 2.b4 is a cousin of the key drawing move from last night’s king and pawn ending in which white forces black to double his pawns, then wins the one in front by forcing black to move his king away:
2. …..ab4
3. Kb3 Kd5
4. Kb4 Kc6
5. Kb3= and if you want to see how this is drawn, just look up last night’s puzzle.
Or, at move 1:
1. …..Kd5
2. Kb4
White probably draws with the simple 2.Kd3, too, but I am too tired to look at it right now. Continuing:
2. …..Kd4 (what else?)
3. Ka5
Here, white must continue the plan now, to not do so loses. Continuing:
3. …..Kc4
4. Ka6 b4
5. Ka5 b3 (Kb3 6.Kb5=)
6. Ka4 and now it is black who must force the draw a pawn down (he can with Kc5 immediately).
And, I think this mostly covers it. I don’t see any obvious holes, but if you spot them, let me know, and I will try to answer them.
Hi Susan Polgar,
Well,nice puzzle.
To me,White can force the game to stalemate.
Game involves simple logic : White should make sure that its single pawn,goes for an exchange only and White King stays besides its pawn till the exchange happens then maneuvering between two columns/rows,more important allow not the opponent’s King to get placed in front of its pawn . – Ooooooops does the words confuse ? – then look at the example that I have given below.[ Variations exist ]
Given an example to support my view.
Example One
===========
1.Kc3 b4+
2.Kc2 Kc4
3.b3+ Kb5
4.Kb2 a5
5.Ka2 a4
6.b*a K*a4
7.Kb2 b3
8.Kb1 Ka3
9.Ka1 a2+
10.Kb1 Kb3 Stalemate
Example Two
===========
1.Kc3 a5
2.b3 a4
3.b*a b*a
4.Kb2 Kb4
5.Ka2 a3
6.Ka1 Kb3
7.Kb1 a2+
8.Ka1 Ka3 Stalemate
So the game ends in stalemate.
By
Venky [ India – Chennai ]
Venky:
In a configuration of blocked pawns like b3-b4, the black king is aiming the “limits” of the pawns, here the squares c3, d3 and e3. If he succeeds, b-pawn falls.
In your flawed first variation, it could happen in this way:
1.Kc3! b4+
2.Kc2? Kc4
3.b3+ and now Black wins with
3… Kd4!
4. Kd2 (the best, holding momentarily squares, because 4.Kb2 Kd3 and the win of the b-pawn doesn’t require much subtlety by Black)
4…a5! (an important “pass-move”. Now, King reaches his objective by force)
5.Kc2 Ke3 and black wins the b-pawn even without the a-pawn!
Check if you want to. Zugzwang is a deadly weapon in pawn endings… but not only in pawn endings.