Dennis M's Chess Site

This is a blog for chess fans by a chess fan. I enjoy winning as much as anyone else, and I've had a reasonable amount of success as a competitor, but what keeps me coming back to the game is its beauty. And that, primarily, is what this site will be about! All material copyrighted.

Thursday, February 03, 2005

King and Pawn Endings, Part Two

Ah, life for newbies in the blogosphere! I had almost completed a version of the post that now ensues, when an attempt to be clever led to my losing over an hour's worth of work. Grr...well, nothing to do but start over, so here we go:

A few days ago I presented a king and pawn ending I had composed many years ago, offering it as a challenge to any and all of the intrepid souls in the audience. Here now is the solution, with comments and a summary of the lessons to be learned.

White: Kg3, p's f2, f4, h4
Black: Kg6, p's f7, h5
White to move and draw.

[A key to symbols and conventions used below:

+- White has a winning position.
= The position is objectively drawn.
-+ Black has a winning position.
! A strong move.
? A poor move.
?? A truly terrible move.

Finally, bold type indicates a move in the solution's main line; that is, it represents the best move in the position.]

White has an extra pawn, but Black has (or is about to have) a space advantage due to his more forwardly mobile king. In fact, if White could capture his f-pawn, he wins:

1.Kxf4 Kf6 2.f3 (opposition!) and now Black is faced with a choice that will recur throughout our discussion:

(a) 2...Kg6 3.Ke5 Kg7 (3...f6+ 4.Ke6 followed by pushing the f-pawn as far as it can go leads to the win of Black's f-pawn and the game) 4.Kf5 f6 (4...Kg7 5.Kg5; 4...Kh6 5.Kf6 both win easily) 5.Ke6 Kg6 6.f4 f5 (or 6...Kg7 7.f5, winning) 7.Ke5 wins.

(b) 2...Ke6 3.Kg5 Ke5 4.Kxh5 Kf4 5.Kh6 Kxf3 6.Kg5 Ke4 7.h5 f5 8.h6 f4 9.h7 f3 10.h8Q f2 11.Qh1+ followed by 12.Qf1 wins.

Of course, White can't capture his pawn, so as we'll see, it's Black who gets to enjoy the position, often winning in lines similar to what we've just seen. For example:

(A) 1.f5+? Kxf5 2.Kf3 (2.f3 Ke5 3.Kg2 Kf4 4.Kf2 f5 -+) f6 (-+) transposes, but with colors reversed, to the position after (the very strong but illegal) 1.Kxf4 Kf6 2.f3.

(B) 1.f3? Kf5 2.Kg2 Kxf4 3.Kf2 f5 -+

(C) 1.Kf3? is very natural and the second-best move in the position. It doesn't lose any material right away and it tries to centralize the king. After 1...Kf5, we're again faced with the fundamental dilemma: Kg3 or Ke3?

(C1) 2.Kg3 Ke4 and the pawns start to drop:
(C1a) 3.f3+ Kf5 4.Kg2 Kxf4 5.Kf2 f5 -+ gives us a position we've seen twice already (in the parenthetical line in (A) and in line (B)).
(C1b) 3.f5 Kxf5 4.Kf3 f6 -+ is the position at the end of line (A).
(C1c) 3.Kg2 Kxf4 4.f3 Ke3 followed by pushing the f-pawn is a winning approach we saw in line (a) of the 1.Kxf4 discussion.

(C2) 2.Ke3 Kg4 3.Ke4 f6 brings us to a critical position.

If it were Black to move here, the position would be drawn: 4...Kxh4 5.Kf5 Kh3 6.Kxf6 Kg4 7.Ke5 h4 8.f5 and both sides queen; if anything, White has the better of the ending, though it's objectively drawn.

However, it's White to move, and that favors Black: 4.f5 Kxh4 5.Kd5 Kg5 6.Ke6 h4 7.f4+ Kxf4 8.Kxf6 h3 9.Kg6 ...

(Note that 9.Kg7 draws on h2 10.f6 h1Q 11.f7, because White will never have the chance to move the king closer without allowing Black to safely queen. Thus in a position with the White king on g8 and pawn on f7 and the Black king on f4 and queen on g6, White gets out of the check with 1.Kh8!, when 1...Qxf7 is stalemate. The problem with 9.Kg7, of course, is that Black plays 9...Kxf5.)

9...h2 10.f6 h1Q 11.f7 Qh8! winning the pawn and the game.

What have we learned so far? First, that if Black's king can reach e4, the game is completely over, while the lines with the defending side's king going to e3 (or e6, as in the illegal 1.Kxf4 case) are far more interesting. In short, space and activity can trump material even in a king and pawn ending!

Second, the mutual zugzwang in line (C2) should lead us to consider how White can attempt to reach that position with Black to move. As pawn moves lose and 1.Kf3 steps on to the square prematurely, we can determine the right move by process of elimination (a useful method for defenders to keep in mind, by the way!):

D. 1.Kg2!

Now 1...Kf5 2.Kf3 f6 3.Ke3 Kg4 4.Ke4 would be Mission Accomplished for White, but Black can also play more subtly:


Now 2.Kf3? Kf5 is the same as 1.Kf3? Kf5, and the same, mutatis mutandis, goes for 2.f3? Kf5 and 2.f5? Kxf5. So once again, by process of elimination, we find

2.Kg3! Ke6! 3.Kg2! Kd5

Now it's time to think again. White might try to yo-yo some more with 4.Kg3?, but then Black seizes the critical square with 4...Ke4, winning (5.f5 Kxf5 6.Kf3 f6 leads to a position we've seen several times, and 5.f3+ Kf5 6.Kg2 Kxf4 7.Kf2 f5 is another recurring nightmare for White). Trying to run the pawn with 4.f5? doesn't work either, as 4...Ke5 5.Kg3 Kxf5 6.Kf3 f6 is just a long-winded transposition to 1.f5? Kxf5 2.Kf3 f6. By now we know our mission: protect e4!

4.Kf3! Kd4!

4...f5 won't win as long as White doesn't play Kg3 when Black can respond with ...Ke4. For example: 5.Ke3 Kc4 6.Kf3 Kd4 7.Kg2! Kd3 8.Kh3! Kd2 9.Kh2 Ke2 10.Kg2 Kd3 11.Kh3 Ke4 12.Kg3 etc., with a draw.

After 4...Kd4, 5.Kg3? allows the fatal 5...Ke4, so again the process of elimination gives us the right move:

5.f5! Ke5 6.f6!

6.Kg3? Kxf5 7.Kf3 f6 is Old Faithful, while 6.Ke3? Kxf5 7.f3 Ke5 8.f4+ Kf5 9.Kf3 f6 is hopeless as well.


Not 6...Kxf6?? when 7.Kf4 lets White win the way Black usually does - here, in fact, White even achieves the winning position without even needing to use his f-pawn to gain the opposition. After 6...Kf5!, we are faced one last time with the dilemma: do we go to g3 or to e3?


7.Kg3? loses, and even though the way it works is by now familiar to us, it's really quite remarkable, given that no White pawn is in immediate danger (because 7...Kf6?? 8.Kxf4 wins for White) and that Black has no tempo moves in case of a mutual zugzwang. Here's how it works: 7.Kg3? Ke4 8.Kg2 Kf4 9.f3 Ke5! 10.Kg3 Kf5! (forcing the White king back before capturing the f6 pawn) 11.Kg2 Kxf6 12.Kg3 Kf5 13.Kg2 Kf4 14.Kf2 f5 -+ etc.

Now it's Black's turn to be careful...


7...Kxf6?? 8.Kxf4 we've already seen, while if 7...Kg4?, which worked in the analogous positions, White wins with 8.Ke4 Kxh4 9.Kf5 Kh3 10.Kg5 h4 11.Kh5! when Black is in a fatal zugzwang.


Here at least White has more than one move - 8.f3 and 8.Kd3 are both good enough to achieve a draw. Perhaps surprisingly, though, 8.f4+? loses after 8...Kxf6 9.Ke4 (you would think that White's king having achieved the fourth rank with material equality would suffice, wouldn't you? Well, chess is a surprising game...) 9...Ke6 10.f5+ (10.Ke3 Kf5 11.Kf3 f6 and Black starts collecting) Kd6! 11.Kd4 f6 12.Ke4 Kc5 and the Black king heads for and wins the White f-pawn, and with it the game.

8...Kf5! 9.Ke3! Ke5! etc.

This ending offers us several valuable lessons:

1. A space advantages isn't just important in the opening and middlegame - even in a king and pawn ending, it can be more significant than a material advantage.
2. Likewise, activity is crucial, and can also outweigh a material advantage in significance. We're used to that idea in openings (with gambits, for example), and we might be familiar with the rule of thumb that in a rook ending, a rook on the 7th is often worth a pawn or even two, but it might be surprising in a king and pawn ending. It won't apply in a position where the side having extra material hasn't got any targets, but when there are weaknesses, make sure reflecting on king activity is a high priority.
3. Be aware of positions of mutual zugzwang, and try to figure out how to achieve that position with your opponent to move. If you're aware of those positions in advance, your chances of avoiding victimhood go way up!

And the last lesson is...chess is tough!

I hope everyone enjoyed this; I'll be offering a new pawn ending puzzle soon.


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