The Chess Mind

A day or two ago, I watched the last few minutes of an online simul given by Hikaru Nakamura. Of the remaining games, one in particular seemed a sure draw, especially given the player's reasonable "standard" rating of 2047. Here's the starting position of their rook and pawn vs. rook ending:



And here are the remaining moves:

41. Ke3 Rh7 42. f4 Rd7 43. Re4 Kd8 44. Kf3 Re7 45. Ra4 Ke8 46. Kg4 Kf7 47. Kf5 Rb7 48. Ra5 Rc7 49. Kg5 Rb7 50. Rf5+ Kg7 51. Ra5 Kf7 52. Ra6 Rc7 53. f5 Kg7 54. Rg6+ Kh7 55. Rh6+ Kg7 56. f6+ Kg8 57. Kg6 Rb7 58. Rh1 Rb6 59. Ra1 Rb8 60. Ra7 {Black resigns} 1-0

(You can replay the entire game here.)

It's a good ending to analyze: Black did some things right, then made some dubious but not yet fatal decisions, and only then lost the game. And it's worth considering the possibility that White did something wrong, too. Can you figure out what's what without, of course, using external assistance? Answers will be provided in a day or two.

(A day later than intended, but hopefully it just means more of you had the chance to work on it!)

As you can see in the previous post, the task was to figure out what opportunities were missed by both sides in this seemingly trivial endgame that started from this position.



If you're ready, the solution is here - and even it is only partial on one interesting position, which will become fodder for a new blog post!

In my analysis of the Nakamura-NN simul game, I recommended 41...Rh8!



as an improvement on NN's 41...Rh7. Both moves have as their basic idea to play 42...Rdn, which leads to an easily drawn pawn ending (if White trades) or else lets the Black king get in front of White's f-pawn.

While neither 41...Rh7 nor 41...Rh8 is good enough for a draw, if White plays correctly, it's much harder for White to win after the latter move (though even after Black's inferior choice Nakamura immediately erred and allowed his opponent to reach a drawn ending). The difference is that the Black rook has sufficient checking distance from the White king, so the king cannot successfully approach the rook without allowing his f-pawn to be immobilized in variations like the one given to White's 42nd move: 41...Rhn 42.Kf4 Rfn+ 43.Kg3 Kc6 44.f4 Kc5 45.Rd1 Rgn+ 46.Kh4 Rfn 47.Kg5 Rgn+ 48.Kf6 and now if n=7, it's over, but if n=8, 48...Rf8+ forces the White king back and preserves the drawn position.

So if 42.f4 is bad against both 41...Rh7 and 41...Rh8, and if 42.Kf4 doesn't win either, how does White win? There are in fact two winning moves - neither of which is obvious (at least if you're not using external help!), and which I leave as an excellent exercise for the reader.

Solution in a few days.