### King and Pawn Endings, Part 4

A few days and many posts ago, I presented the following position

and challenged the reader to determine if 1.Re6 is a winning move.

It's certainly a plausible move and - if it works - a convenient and elegant solution to the problem of breaking down the Black fortress. Further, it's not clear to me that White can win the rook ending by other means (though it's not completely clear that it's drawn, either), so it's understandable that in this 1986 game with Dan Durham, he opted for 1.Re6.

I had deliberately provoked this a few moves before, and at this point I have no choice but to capture, as 1...Ra1 2.Rg6 followed by Rxg5 is hopeless for Black. So we have the following sequence:

1. Re6 Rxe6! 2.fxe6+ Kxe6 3.Ke4 (moves played will be given in bold letters), giving rise to our next critical position:

Black now has a choice between options, and two are bad.

(1) 3...g6 4.Kd4 Kd6 5.e4 Ke6 6.e5 Ke7 7.Kd5 Kd7 8.e6+ Ke8!

[KEY DIAGRAM]

This seems to draw, as 9.Kd6 Kd8 10.e7+ Ke8 11.Ke6 is stalemate, while 9.Ke5 Ke7 10.Kd5 Ke8 returns to the diagram.

(2) 3...Kf6 4.Kd5 Ke7 (else White plays 5.Kd6, guaranteeing an easy win after 6.e4, 7.e5 and depending on where Black's king is at this point, 8.Kd7 followed by e6-7-8 or 8.Ke6, either gaining the opposition one last time or collecting Black's g-pawns for free) 5.Ke5 g6 (else 6.Kf5) 6.e4 and wins.

(3) 3...Kd6 4.Kf5, when 4...Kd5 gives White a pleasant choice between going after Black's g-pawns starting with 5.Kxg5 and and 5.e4+.

What's the truth? Line (2) is an easy win for White, just as I've written, but the assessment of lines (1) and (3) are the reverse of what they seem: Line (1) loses and line (3) draws! I'll come back to the problem with line (1) later; for now, let's continue with line (3), which was the game:

3...Kd6!!

Here my opponent realized, to his shock, that 4.Kf5 doesn't win, as after 4...Kd5! Black draws after both White tries:

(a) 5.Kxg5 (it seems inconceivable that Black's king can get White's pawns in time, but that's just what happens) 5...Ke4 6.Kg6 Kxe3 7.g5 Kf4 8.Kxg7 Kxg5 is slightly equal, while

(b) 5.e4+ Kd4! (forced) 6.e5 Kd5 7.e6 Kd6 (thank goodness 8.Kf6 is illegal!) 8.Kxg5 Kxe6 9.Kg6 and again the Black king does the seemingly impossible: 9...Ke5 10.Kxg7 Kf4 and draws.

So White decided not to force things:

4.Kd4 Ke6 5.e4 Kd6 6.e5+

and now, another choice and again, I chose correctly:

5...Ke7!

5...Ke6? is the natural move, but after 6.Ke4 king moves allows 7.Kf5 and 8.Kxg5, while 6...g6 7.Kd4 Ke7 8.Kd5 Kd7 9.e6+ Ke8 leads once more to the KEY DIAGRAM.

6.Kd5 Kd7 7.e6+ Ke7 8.Ke5

and now Black faces his final test:

There are four possibilities: two draw, two lose; two look normal, two look crazy. Needless to say, it's the crazy-looking ones that draw, while sanity results in a loss...or should have.

A. 8...Ke8 looks obvious: everyone knows that in such positions, the right thing to do is go straight back, so that 9.Kd6 (9.Kf5 Ke7 will transpose to a line we'll look at via the 8...Kd8 9.Kf5 move order) Kd8 10.e7+ Ke8 11.Ke6 is a draw by stalemate. Except that it isn't here; Black's misfortune is that the g-pawn can move, and after 11...g6 12.Kf6 White will promote.

B. 8...Kf8 is just plain goofy-looking, both giving ground and apparently not even bothering with the opposition. However, as it has no independent significance but transposes to 8...Kd8 lines after either 9.Kd6 Ke8 or 9.Kf5 Ke7, we'll move on to line C.

C. 8...Kd8 and now another branch:

C1. 9.Kd6 Ke8 10.e7 g6 11.Ke6 stalemate! Now we see why Black has to take what looks like an anti-opposition approach; it's because of the g6 tempo (compare line A). By letting White "have" the opposition through e7, Black can regain it when it really matters.

C2. 9.Kf5 and once again, Black's king vacuums up the White pawns with amazing rapidity after 9...Ke7 10.Kxg5 Kxe6 11.Kg6 Ke5 12.g5 (12.Kxg7 Kf4=) Kf4 13.Kxg7 Kxg5.

So 8...Kd8 and 8...Kf8 both merit exclamation marks, while 8...Ke8 and the move played in the game, 8...g6, both merit negative punctuation. But what's wrong with g6 - doesn't Black end up playing it anyway, as for example on move 10 of line C1?

Yes, he does, but it's only appropriate after White plays e7, as we'll see.

D. 8...g6?? 9.Kd5 Ke8

and here it is once more, our famous KEY DIAGRAM:

Some of you might be wondering how White can win this. After all, as mentioned earlier, 10.Kd6 Kd8 11.e7+ Ke8 12.Ke6 is a draw by stalemate, while 10.Ke5 Ke7 11.Kd5 Ke8 returns to the diagram.

The solution? Triangulation! If in this position it were Black to move, the task would be trivial: 10...Ke7 11.Ke5 and the White king devours the pawns, or 10...Kd8 11.Kd6 and White gains the opposition and queens the pawn (11...Ke8 12.e7 Kf7 13.Kd7 etc.). What White needs to do is find a way to "lose" (or gain) a move here, so as to force the same position with the hapless victim - me - to move and lose.

Thus 12.Ke4! (or 12.Ke4! followed by Ke4!) Kd8 (12...Ke7 13.Ke5 wins) 13.Kd4! Ke8 (again, 13...Ke7 14.Ke5) 14.Kd5! and Black would have to resign. Fortunately, Dan, 2418 player that he was notwithstanding, continued

12.Kd6 Kd8 13.e7+?? Ke8 14.Ke6 1/2-1/2

Note that it's move 13 that blows the win - White could have retreated to d5 and still executed the triangulation maneuver. A pretty remarkable ending, I think, and I'm proud of 19-years-ago self for having had the idea of inducing 1.Re6 and then playing the rest almost perfectly, but I'm also amazed, even dumbfounded by the exchange of blunders at the end of the game. Both of us as strong masters must have been aware of the idea of triangulation - it can be found in practically any elementary textbook on endgames. Yet in what was only a very slight alteration from the standard 101 example, we found ourselves more or less oblivious to the possibility of such a tactic. Apparently we "knew" triangulation then, but didn't really know it.

Chess is hard - and yet the richness of the game keeps me - all of us, I think, coming back for more!

and challenged the reader to determine if 1.Re6 is a winning move.

It's certainly a plausible move and - if it works - a convenient and elegant solution to the problem of breaking down the Black fortress. Further, it's not clear to me that White can win the rook ending by other means (though it's not completely clear that it's drawn, either), so it's understandable that in this 1986 game with Dan Durham, he opted for 1.Re6.

I had deliberately provoked this a few moves before, and at this point I have no choice but to capture, as 1...Ra1 2.Rg6 followed by Rxg5 is hopeless for Black. So we have the following sequence:

1. Re6 Rxe6! 2.fxe6+ Kxe6 3.Ke4 (moves played will be given in bold letters), giving rise to our next critical position:

Black now has a choice between options, and two are bad.

(1) 3...g6 4.Kd4 Kd6 5.e4 Ke6 6.e5 Ke7 7.Kd5 Kd7 8.e6+ Ke8!

[KEY DIAGRAM]

This seems to draw, as 9.Kd6 Kd8 10.e7+ Ke8 11.Ke6 is stalemate, while 9.Ke5 Ke7 10.Kd5 Ke8 returns to the diagram.

(2) 3...Kf6 4.Kd5 Ke7 (else White plays 5.Kd6, guaranteeing an easy win after 6.e4, 7.e5 and depending on where Black's king is at this point, 8.Kd7 followed by e6-7-8 or 8.Ke6, either gaining the opposition one last time or collecting Black's g-pawns for free) 5.Ke5 g6 (else 6.Kf5) 6.e4 and wins.

(3) 3...Kd6 4.Kf5, when 4...Kd5 gives White a pleasant choice between going after Black's g-pawns starting with 5.Kxg5 and and 5.e4+.

What's the truth? Line (2) is an easy win for White, just as I've written, but the assessment of lines (1) and (3) are the reverse of what they seem: Line (1) loses and line (3) draws! I'll come back to the problem with line (1) later; for now, let's continue with line (3), which was the game:

3...Kd6!!

Here my opponent realized, to his shock, that 4.Kf5 doesn't win, as after 4...Kd5! Black draws after both White tries:

(a) 5.Kxg5 (it seems inconceivable that Black's king can get White's pawns in time, but that's just what happens) 5...Ke4 6.Kg6 Kxe3 7.g5 Kf4 8.Kxg7 Kxg5 is slightly equal, while

(b) 5.e4+ Kd4! (forced) 6.e5 Kd5 7.e6 Kd6 (thank goodness 8.Kf6 is illegal!) 8.Kxg5 Kxe6 9.Kg6 and again the Black king does the seemingly impossible: 9...Ke5 10.Kxg7 Kf4 and draws.

So White decided not to force things:

4.Kd4 Ke6 5.e4 Kd6 6.e5+

and now, another choice and again, I chose correctly:

5...Ke7!

5...Ke6? is the natural move, but after 6.Ke4 king moves allows 7.Kf5 and 8.Kxg5, while 6...g6 7.Kd4 Ke7 8.Kd5 Kd7 9.e6+ Ke8 leads once more to the KEY DIAGRAM.

6.Kd5 Kd7 7.e6+ Ke7 8.Ke5

and now Black faces his final test:

There are four possibilities: two draw, two lose; two look normal, two look crazy. Needless to say, it's the crazy-looking ones that draw, while sanity results in a loss...or should have.

A. 8...Ke8 looks obvious: everyone knows that in such positions, the right thing to do is go straight back, so that 9.Kd6 (9.Kf5 Ke7 will transpose to a line we'll look at via the 8...Kd8 9.Kf5 move order) Kd8 10.e7+ Ke8 11.Ke6 is a draw by stalemate. Except that it isn't here; Black's misfortune is that the g-pawn can move, and after 11...g6 12.Kf6 White will promote.

B. 8...Kf8 is just plain goofy-looking, both giving ground and apparently not even bothering with the opposition. However, as it has no independent significance but transposes to 8...Kd8 lines after either 9.Kd6 Ke8 or 9.Kf5 Ke7, we'll move on to line C.

C. 8...Kd8 and now another branch:

C1. 9.Kd6 Ke8 10.e7 g6 11.Ke6 stalemate! Now we see why Black has to take what looks like an anti-opposition approach; it's because of the g6 tempo (compare line A). By letting White "have" the opposition through e7, Black can regain it when it really matters.

C2. 9.Kf5 and once again, Black's king vacuums up the White pawns with amazing rapidity after 9...Ke7 10.Kxg5 Kxe6 11.Kg6 Ke5 12.g5 (12.Kxg7 Kf4=) Kf4 13.Kxg7 Kxg5.

So 8...Kd8 and 8...Kf8 both merit exclamation marks, while 8...Ke8 and the move played in the game, 8...g6, both merit negative punctuation. But what's wrong with g6 - doesn't Black end up playing it anyway, as for example on move 10 of line C1?

Yes, he does, but it's only appropriate after White plays e7, as we'll see.

D. 8...g6?? 9.Kd5 Ke8

and here it is once more, our famous KEY DIAGRAM:

Some of you might be wondering how White can win this. After all, as mentioned earlier, 10.Kd6 Kd8 11.e7+ Ke8 12.Ke6 is a draw by stalemate, while 10.Ke5 Ke7 11.Kd5 Ke8 returns to the diagram.

The solution? Triangulation! If in this position it were Black to move, the task would be trivial: 10...Ke7 11.Ke5 and the White king devours the pawns, or 10...Kd8 11.Kd6 and White gains the opposition and queens the pawn (11...Ke8 12.e7 Kf7 13.Kd7 etc.). What White needs to do is find a way to "lose" (or gain) a move here, so as to force the same position with the hapless victim - me - to move and lose.

Thus 12.Ke4! (or 12.Ke4! followed by Ke4!) Kd8 (12...Ke7 13.Ke5 wins) 13.Kd4! Ke8 (again, 13...Ke7 14.Ke5) 14.Kd5! and Black would have to resign. Fortunately, Dan, 2418 player that he was notwithstanding, continued

12.Kd6 Kd8 13.e7+?? Ke8 14.Ke6 1/2-1/2

Note that it's move 13 that blows the win - White could have retreated to d5 and still executed the triangulation maneuver. A pretty remarkable ending, I think, and I'm proud of 19-years-ago self for having had the idea of inducing 1.Re6 and then playing the rest almost perfectly, but I'm also amazed, even dumbfounded by the exchange of blunders at the end of the game. Both of us as strong masters must have been aware of the idea of triangulation - it can be found in practically any elementary textbook on endgames. Yet in what was only a very slight alteration from the standard 101 example, we found ourselves more or less oblivious to the possibility of such a tactic. Apparently we "knew" triangulation then, but didn't really know it.

Chess is hard - and yet the richness of the game keeps me - all of us, I think, coming back for more!

## 1 Comments:

At 1:52 PM, Anonymous said…

Always nice to see an endgame-site.

I will take your site as a link on the ARVES website.

http://members.home.nl/bloemansdall/ARVES/index.htm

Peter Boll, Netherlands

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