A theoretical endgame in group C

At the end of the fourth round of the Corus Chess Tournament, when almost everybody had gone home already, something unsual happened in the C-group: in the game between Stellan Brynell and Mihail Krasenkow, after 66 moves the ending of two knights agains pawn arose.

Brynell-Krasenkow
Wijk aan Zee (4) 2007

Immediately I was awake again. Holland’s two most famous chess writers, J.H. Donner and Tim Krabbé, have both written about this fascinating, terribly difficult endgame which, contrary to the endgame King+2 knights versus King Alone (KA), is sometimes lost for the pawn after a long an incomprehensible struggle. As Donner writes (in Het Eindspel, 1977, later reprinted in The King, 1987):

“It is a thorn in the king’s eye, a nail to his coffin. By the dubious possesion of this pawn, the king is more desolate than when he would be alone.“

Excited, I tried to remember if this position was also winning. It seemed so: the black pawn was still far away from promotion. But the path to the win was undoubtedly very tricky, and Brynell didn’t have much time left on the clock. Gone are the days when Krabbé could write (in Nieuwe Schaakcuriosa, 1977):

“The whole theory of the endgame two knights versus pawn is without any importance for the practical player. Should it ever occur in practice, he waits for the adjournment and looks in Chéron how to do it.“

Donner wrote his treatise when there were no computers yet, Krabbé when there was no ’sudden death’. But Brynell and Krasenkow had to play the rest of the game in some minutes - eternal shame, because Brynell’s position is, theoretically speaking, relatively easy to win.

By the way, the endgame has occurred more often in practice, Veselin Topalov had the endgame on the board no less than two times. He even beat Karpov with it! And another A-group player, Sergej Karjakin, has had to play the endgame as well, when he was real young. He was lucky it happened from the following position:

Lybin-Karjakin
Keres Memorial 2001

According to theory, with a black pawn on d4 the endgame is still just winning for the knights - but not when the pawn is blocked by the king instead of a knight! Lybin tried to win it for anohter 55 moves, but as soon as the his king moved, black quickly played d4-d3 with a theoretical draw.

So when exactly can the pawn draw and when is the endgame lost? For centuries, this has been subject of debate. Nowadays we all have tablebases to calculate where the line is, but in 1977 these didn’t exist yet. In that year, Donner stated that the endgame is always winning for the knights as soon as the pawn, blocked by a knight, has not moved beyond the following moves (look at the pawns only):

J.H. Donner (1977)
Pawns that, if safely blocked by a knight, always lose against king and two knights

By the way, this hypothesis was itself an improvement over an older hypothesis of the famous endgame composer Troitski, who suspected around 1910 that the b- and g-pawns had to stand on the sixth rank.

Back to Brynell and Krasekow. With a pawn on a6, this position was winning for Brynell. Was he aware of this? The position with a black pawn on a6 is sort of similar to the very first known position of this curious endgame. Around 1870, Chapais published the following winning position:

Chapais (1780)
White wins

How to win this position was the subject of ferocious discussion for many years. These days we feed the position to our tablebase and we immeditaly see in how many moves we can reach mate with perfect play. But how to do it without the database’s help?

Crucial in the endgame is the phase where the enemy king is driven into the corner, after which the second knights comes to deliver the final mate. This phase is preceded by a number of other phases, which in fact are already reached in Brynell’s position. The pawn is already blocked, the enemy king is already driven away from the pawn, and is even quite close to the corner already. In the initial position, White delivers mate ultimately on move 41, which is very modest considering the fact that this ending often takes more than 50 moves. (I saw Krasenkow, and also an arbiter who was watching, solidly record the number of moves, but isn’t there an exception for this endgame in the FIDE-rules?)

From the above diagram position, Brynell played : 67.Ne4 after which Black immediately played inaccurately: : 67…Kg7?! (much tougher is 67…Kh5) but
he next made a mistake with 68.Kf5?! where 68.Nd6! had meant a win-in-25.
You can find the variations in the attachment, but you can also feed the position in this beautiful online tablebase.
It’s not surprising that Brynell didn’t understand much of the winning plan. After hours of studying, I have not yet made much progress myself. There doesn’t seem to be a manual for tournament practice - Donner, too, is rather vague about the winning method and only gives very general principles like the above.
Anyway, after shuffling his pieces for a lot of moves, Brynell finally gave away the win on move 118 (!):

Brynell-Krasenkow
Wijk aan Zee (4) 2007

118.Nd8? a4! and the position can’t be won anymore. The second knight can only give up the blockade when the king only has two squares in the corner - which isn’t the case here. After 118.Nc4! a4 119.Na3 White could have delivered mate in 84 moves, but it’s obvious that this has absolutely nothing to do with reality

So this is what ‘progress’ looks like. No doubt chess players have become stronger by the years, but because of the increasingly faster speed of play, these endgames will probably never be played correctly anymore. Isn’t it a pity? It sure is. Is it reason to complain? Hardly. There are a lot of advantages to the fact that chess is becoming more practical and more digital, too. Apart from the drama and the excitement of making fast decisions, there’s the advantage of the digital boards that record all the moves - no matter how little time there is on the clock. Mistakes in this kind of deep endgames would not have been recorded in the past - but they are now. But above all, the abstract theory of this type of endgames will always remain, even when nobody plays chess anymore.

Replay the games here.