[After 21.Kf1] The play was extremely difficult. I probably did not find the best system of defense. I can not yet tell which was the best defense here, but it is my belief that with the best play White should win.
He forced the exchange of a pair of Rooks, leaving him with Queen and Rook against Queen and Knight. A few moves later the game reached the diagrammed position.
Havana 1921 (g.5)
Lasker, Em.
Capablanca, J.R.
After 31.h2-h4
Of Black's 31...gxh4, Capablanca noted,
This was Lasker's sealed move. It was not the best. His chance to draw was to play 31...Kg6. Any other continuation should lose.
He gave no variations to support his opinion. In fact, he gave no variations in any of his ten notes to the game. Kasparov's note to 31...gxh4, quoting Lasker, is more helpful.
It is usual to attach a "?" to this move. "31...Kg6 was better. Then if 32.hxg5 Ne4 33.Qd3 Qg4+ 34.Rg2 Qh4 35.Qb1 Kg7, the Pawn at g5 falls and Black has a good position" [Lasker].
At first sight here it is indeed impossible to convert the exchange advantage: the White King is exposed, and Black's Queen and Knight dominate. And yet White has a way to gain an advantage: 36.Qd1 Kg6 37.Qf3! (threatening Qf4) 37...Nxg5 38.Qg3, with good winning chances. So that 31...Kg6 was by no means better than the move in the game.
What does the engine say? First, it favors three moves over all others, with 31...h6 a definite favorite before both the game continuation 31...gxh4, and the suggested alternative 31...Kg6. After 31...h6, White has 32.h5, and Black has no way to break the pin of the Knight. In the time I had to look at the position, I couldn't determine how White should continue, but I'll trust the judgement of Capablanca, Lasker, and Kasparov, and assume that there is an obvious winning procedure.
As for the game continuation 31...gxh4, Capablanca and Kasparov agree that after the next moves 32.Qxh4 Ng4 33.Qg5+ Kf8, Capablanca's 34.Rf5 was not the best. The move 34.Rd2 was better. Kasparov again quotes Lasker -- '34.Rd2! was very strong. 34...f6 must be played and Black's King becomes exposed to attack.' -- without adding any additional comments of his own, except to give the next move, 35.Qf4. Black's problem is that White can eventually force a Queen swap, after which the Knight is no match for the Rook with Pawns on both the Kingside and Queenside.
That leaves 31...Kg6. The engine agrees with Kasparov's analysis, except after 37.Qf3!, it attempts to improve with 37...Qe1+, instead of 37...Nxg5. This lets Black prolong the game, but the constant threat of a Queen exchange again leaves Black without a solid defense.
Now if I could only understand the procedure after 31...h6, I would understand the diagrammed position. To play through the complete game, see...
Jose Raul Capablanca vs Emanuel Lasker; World Championship Match 1921 [g.5]
http://www.chessgames.com/perl/chessgame?gid=1241495
...on Chessgames.com. The comments there point out another curious aspect of the game: a triple repetition on Black's 34th, 36th, and 38th moves, unclaimed by either player.
***
Later: This appeared in Chess Improvement Carnival V: The Jedi Knight School Edition.
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