Mate in Two

The following Mate in Two problem is from Yusupov's Build Up Your Chess I, and I think it's the hardest mate in two problem I've come across so far.



I'm not going to give away the answer, but it's a good test of your ability to analyze a dense thicket of short variations.

Laszlo Polgar's Chess: 5334 Problems, Combinations, and Games has a ton of mate-in-two problems in it, and I occasionally turn to a random page and try to solve some. Some of them are really devilish, and are good practice for practicing Kotov-like analysis (trying to analyze each branch of a variation once and only once).

I'm going to try and get a couple more chapters of Yusupov's book knocked out this afternoon.

Instructive Rook Ending

First: a shout out to chunkyrook. His endgame posts helped get my gumption level up to posting some endgame analysis of my own. I also rather liked this example of seizing a file...a fairly simple idea, yet one that was new to me.

Sometimes I get a basic ending that I thought I knew reasonably well , and then after analyzing it I realize how much of endgame play is still mysterious. I had two such instances recently where the analysis was instructive. Here is the first, which should have a dead-drawn R+P vs. R endgame. I was black:



I had just captured on c5. The defending king is able to get in front of the pawn, which should be an easy draw. A rule of thumb in 1-pawn rook endgames is the "Rule of 5": if the number of the rank of the pawn, plus then number of files the defender's king is cut off, is greater than 5 then the side with the pawn wins. There's exceptions but it beats assessing a position by coin toss. With a pawn on the third rank (counting from Black's side) the defending king would have to be cut off by 3 files to be winning according to the Rule of 5. Here, you don't even need to invoke the rule: the king isn't cut off at all and is free to get in front of the pawn, so this should be a cakewalk for White. However, after 76. Kd3 Rc1 77. Ra4 Kb5 78. Rh4 c5 79. Kd2 Rg1 80. Kc2 Rg3 81. Rf4 c4 82. Rh4 Kb4 83. Rh8 (threatens a series of checks from the rear, a theme of the Philidor position we are arriving at) Rg2+ 84. Kc1 Kc3 85.Rh3+ Kb4:



This should be a dead drawn Philidor position. For those unfamiliar with this ending, the Philidor position is one of the standard defensive techniques. All White has to do now is keep his rook on the third rank (e.g. 86.Rf3), which prevents White from getting their king ahead of the pawn. If Black delivers checks from the side, the White king just bounces between c1 and c2. If Black tries to make progress by advancing the pawn, White can play the rook to the 8th rank and deliver endless checks from the rear. If this drawing method isn't familiar to you, it's one of the first rook endgames you'll want to study.

However, my opponent played 86. Rh4?-+, probably thinking this prevented advancement of the pawn because of the pin. However, 86... Kb3 is now a win for White--but only barely! The king can use the pawn as shelter against a check on the 3rd rank. After 87. Rh8, a critical position has been reached:



87... Ra2?= If the pawn were on c3, and White was passively defending with a rook on the first rank, ...Ra2 would be involved in the winning line. This method of playing against passive defense is another basic rook endgame, but that's irrelevant to this position. Short on time, and with a 12-second increment on the clock, I was going with my gut at this point.

There is only one winning move here: 87... Rg1+! and it turns out that after 88. Kd2 c3+ white wins:



For example 89. Kd3 Rd1+ (89...Rg3+ also wins) 90. Ke3 c2 91. Rb8+ Ka4 92. Ra8+ Kb5 93. Rb8+ Ka6 94. Ra8+ Kb7.

I have not seen this winning method in any of my endgame manuals, yet it seems important. If anyone has seen this covered before, can you let me know where?

The game continued 88. Rb8+ Kc3



89. Kb1! Well played. This ending appears similar to one covered in Dvoretsky's Endgame Manual as well as (if memory serves) Soltis' Grandmaster Secrets: Endings. Dvoretsky mentions Philidor's "second defensive method": if the rook can't occupy the cutoff rank, it should place itself behind the pawn. The king goes to the "short side" of the pawn (i.e. the side with less space between the pawn and the edge of the board...in this case the left side). Because the defending king is on the "short side", the attacking king is on the "long side" and if it tries to squeak out the long side it can be subjected to checks from the side.

89...Rh2 90. Rd8 This also draws, but 90. Rc8 is the thematic "attack the pawn from the rear" second defensive method. After 90.Rd8, White needs to be careful. 90... Rh1+ 91. Ka2 Kc2 (if the defending rook were on c8, this move would just lose the pawn to Rxc4)....



92. Rd7?-+

Now we see why the "short side" defence is an important resource. Because White's rook didn't stay behind the pawn, it is able to advance. Now the only way to draw is from side checks, e.g. 92. Rg8! (or 92.Rf8!) 92...c3 93. Rg2+ (93.Rg3 also draws) and if 93...Kc1 94. Kb3.

After 92.Rd7? there are still a few tricks involved in winning the endgame. 92... Rh5 wins, but the endgame tablebases reveal this shorter and sneakier winning line: 92... Rh8! 93. Ka3 c3 94. Rc7 Ra8+ 95. Kb4 Kb2!!



with the point 96. Rxc3 Rb8+ 97. Kc4 Rc8+ wins the rook. This appears to be an important resource. Several of the lines I analyzed in this endgame resulted in this position.

93. Ka3 Rc5?=


This allows checking from the side. It turns out the only winning move is 93... Rh3+! 94. Ka2 (94. Kb4 c3 95. Rc7 Kb2 is the sneaky win mentioned above) 94... Rh8 and wins.

94. Kb4?-+ (Many moves draw, but 94. Rh7 with the idea of checking from the side appears simplest, e.g. 94...c3 95. Rh2+)

94... Rc8! Now rook behind the pawn wins. Black can advance the pawn and use it as a shield from side checks. 95. Rd4 c3 96. Rh4 Kc1 (96... Kb2 is shorter) 97. Rh1+ Kb2 98. Rg1 c2 99. Rg2 Kb1 100. Kb3 c1=Q 0-1

Even the simplest rook endgames are difficult to play perfectly. Familiarity with the basic positions (e.g. Lucena/Philidor) and concepts (checking distance; Rule of 5; playing the king to the short side; defending via repeated checks from rear/side/front) help guide you in the right direction (86.Rf6; 89.Kb1!; 94.Rh7 etc.). However, sometimes there's no substitute for calculation (87.Rg1!).

Simple Forcing Variation

The following tactic is fairly easy to calculate, yet it gave me some trouble. I'm finding that, when calculating forced variations, I have more difficulty when I have a choice of moves than when my opponent has a choice of moves.

White to play:

4r1k1/ppn1bppp/q7/7Q/1nN1P3/1B1P4/PP5P/KN4R1 w - - 0 1

Black to play has a straightforward mate in 2 starting with 1...Qxa2+, so White's play either has to interfere with this mechanism, or be with check. Moves like 1.Nca3 or 1.Na5 don't lead to anything. That leaves two checks: 1.Rxg7+ or 1.Qxf7+. The former check doesn't seem to lead anywhere either (e.g. 1...Kxg7 2.Qg4+ Qg6).

1.Qxf7+ looks like an "obvious" queen sac, because after 1...Kxf6 the knight can move to e5 or d6 with a discovered, double, check. But which knight move?

Correct is 2.Ne5+, because on either 2...Kf6 or 2...Kf8, 3.Nd7#.

However, when I tried to calculate this as I would in an over-the-board game, I would stall at this point. I was seeing the king slipping out of the mating net with 2.Nd7, and didn't immediately see the mate after 2.Ne5 Kf6. That was enough for me to second-guess the entire line and try to find ways to get other first moves to work. In a real game I probably would have bailed out by playing a knight to a3.

This demonstrates both quiescence errors (not calculating out until all checks, captures and threats are spent) and not "thinking like a tree" a la Kotov (calculate each branch of each line only once). And yes, Kotov's technique has been criticized by others, but in general (especially for simple problems like this one) it's an ideal worth striving for.

Name That Gambit

Here is a quest for my dear readers: does the following gambit have a name? Is there any theory associated with this, or a clear refutation?

1.d4 Nf6 2.Nf3 e6 3.e4:



There were very few examples of this in my large database. I couldn't find a clear path forwards for Black. Surprisingly, Fritz evaluated 3...Nxe4, which I think is the most testing response, to be nearly equal. Even after following plausible moves for both sides down to move 12 or so, Fritz didn't seem to notice that Black was up a pawn! For example, I played this series of moves that felt natural to me and that looked fine to Fritz at first glance: 3... Nxe4 4. Bd3 d5 5. O-O Be7 6. Re1 Nd6 7. Bf4 O-O 8. Nbd2 b6 9. Qe2 c5 10. c3 Nc6 11. Ne5 Bb7:



Fritz evaluates this as dead even, despite the pawn minus. I've only done some preliminary, superficial analysis, and I don't suggest the above variation is some sort of main line. My point is that there seems to be more going on here than meets the eye. It would be interesting to grab another chess engine and see its evaluations, or to play engines against each other and see the results.

Other moves such as 3...c5 and 3...d5 may transpose into other openings such as the Sicilian or the French, but that can't be the most serious test (otherwise this opening would be seen more often).

My conclusion right now is that Black takes the pawn and converts the material advantage with good technique. However, I would say that any unusual pawn gambit that Fritz can't easily refute is probably worthy of home analysis and potential use as a secret weapon.

How Far to Take Post-Mortem Analysis?

{I'm on the road for Christmas, and decided to post this with some minimal editing. I actually did end up taking some endgame resources with me--Karsten Muller's DVDs as well as Smyslov and Levenfish plus Chess Endgame Training by Bernd Rosen, which I may review in the near future.}


This post was partially prompted by BDK's question on how much time you should spend analyzing a game. The short answer, in my opinion, is: analyze it until you've learned about as much from it as you're going to. If it's "I blundered my queen in the opening and resigned", your work is limited: check what the best or book move would have been, understand the tactic or oversight that was responsible, resolve not to repeat it, and move on.

Then there's cases such as the following.


I'm going to show an extreme case of where analysis of a game may take you. This could have been a "throwaway" ICC blitz game, but there was a lot of information to mine from it. You get spared the scholarly dissection of the opening that I'd normally perform, because I uncharacteristically deviate from my repertoire on move 2. Instead I'll focus on how the game highlights weaknesses in my play, and suggests areas worthy of study.

Relentless Bastard-Grandpatzer, ICC 2007

1. e4 e5 2. f4 Nc6

This is quite uncharacteristic. My repertoire move is 2... Bc5. It turns out to be a happy experiment.

3. Nf3 d6 4. Bc4 Nf6 5. d3

I actually like the feel of this position. I intend to go back to playing 2...Bc5, but I feel that 2...Nc6 could be a good repertoire move. I imagine White players wouldn't be as prepared for it, although I have no idea what advice repertoire books for the King's Gambit give against 2...Nc6. This is an example of a place where you, a chess engine and a chess database could arrive at your own opening repertoire.

5...Na5

The logic being, "If he's willing to surrender the bishop pair, go for it." This is a common theme in these 1.e4 e5 openings. Apparently here ...Na5 is a novelty, suggesting it's not actually appropriate here. 5... Bg4 appears to be the main move. The pin strengthens e5, and it's a developing move. Challenging with h2-h3 would weaken White's kingside, yet I see Topalov has played it: Topalov,V-Morgenstern,H, Frankfurt 1997.

5... Be7 also appears to be common in this position, e.g. Larsen,B -Najdorf,M, Buenos Aires 1979.

6. Bb3 Nxb3 7.axb3 and here I ignore the threat to e5 by playing 7...Be7, which Fritz surprisingly agrees with. After 8. fxe5:


8... Ng4

Fritz prefers 8...dxe5. Both lead to positions where Black has the bishop pair, a two tempi lead in development (the customary rule of thumb is that three tempi is worth a pawn), and saddled White with darksquare weaknesses, whereas White has an extra pawn and a mobile pawn center.

Fritz surprisingly finds 8...dxe5 9. Nxe5 O-O to be about equal, suggesting a sound sacrifice.

9. exd6 Qxd6 and I don't think White had to be afraid of castling here, although the future development of the queenside pieces looks awkward. However, my opponent played 10. h3??



White already had serious darksquare weaknesses. Isn't this the sort of thing King's Gambit practitioners try to avoid? 10. Qg3+! 11. Kd2 Qxg2+ 12. Qe2 Qxh1 13. hxg4?! Bxg4 14. Nc3?



This is the first of many critical moments where Black, bit by bit, lets slip his overwhelming advantage by not finding the best move. I would be hard pressed to find a more extreme example of my thematic obtain-overwhelming-advantage-and-pee-it-all-away style of play Remember this position and compare Black's crushing advantage here to the game result.

14. Qxf3?!

The logic here was that, if I'm going to win the knight, I may as well offer to trade queens to simplify to a won endgame. 14... Bxf3! is actually clearly superior, e.g. 15. Qe3 Qg2+! 16. Ne2 (16. Ke1 Bh4+ 17. Qf2 Qxf2#) 16... Bg5 {and it's Good Night, Irene.

15. Qxf3 Bxf3 16. Nd5 Bg5+ (the bishop move looked good, but it seems that it would have been better to batten down the hatches and not allow ...Nxc7, e.g. 16...Bd8 or 16...Bd6) 17. Kc3



17...Bxc1 I felt I could let him have his knight fork, because it helps me simplify to a won endgame. 18. Nxc7+?! (18.
Rxc1) 18... Kd7 19. Nxa8



This is an instructive moment. My idea of allowing ...Nxc7 was correct, but it required a zweichenzug finesse to make it clearly good:

19...Bxb2+ ?

19... Rc8+ !? This or the immediate ...Be3 saves the bishop while the knight remains trapped. A typical "he takes, I take..." exchange series calculation oversight. Play might continue 20. Kb4 Rxc2.

20. Kxb2 Rxa8 Black is still a bishop and a pawn up 21. Rg1 Rg8

21... Bh5!? surprisingly works, because 22. Rxg7 Bg6 traps the rook.

22. c4



22...a5?!
I seriously considered Fritz's 22...g5! in the game but I wanted to try and put some brakes on White's pawn advance first.

23. Ka3 Kc6 24. Ka4 b6 25. Rg3 Be2 26. d4 f6 27. Re3 Bh5 28. e5

28...Re8



Fritz-approved, but maybe too tricksy for Blitz. I didn't like the looks of 28... fxe5 29. dxe5, but it's really OK: e.g. 29... g5 30. e6 g4.

29. e6 Re7

Throughout this sequence I'm ignoring active play (pushing my kingside pawns) in favor of prophylactic play. This is a recurring theme in my games....not pushing pawns early enough. At this point I'm planning to play my Bishop to the a4-e8 diagonal and sac it if necessary for a passed pawn or two. Again, I'm in the mindset that I have the luxury of jettisoning material to make the endgame simpler.

30. d5+ Kc5 31. Rd3 Be8+ 32. Ka3 b5 33. cxb5



33...Kxb5 (Fritz found the far less emo 33... Kd6! The king blockades and Black will gain the b-pawn. The bishop sac is not essential) 34. d6 Rxe6 35. d7 Bxd7 {the planned sac of the bishop} 36. Rxd7 g5 37. Rxh7





This is the start of the rook endgame that I could spend a lot of time on. Black should be good here, but two features strike me as important: White's rook is behind the passers, while Black's defends from the side; Black's king is better poised to dash over to the kingside, but neither king wants to leave their queenside pawn and allow a passed a- or b- pawn.

37...f5 38. Rg7 g4

One factor I need to determine is whether the f- or the g-pawn leads. I know when the attacking king is there, it's typical to lead with the outside pawn and tuck the king in the short-side hole. For the defense, a typical fortress seems to be where the defending king is on f4 with a rook on the 4th rank. I have seen in endgame books that the case of a g- and an h-pawn is the most drawish, and there are fortresses like this to watch out for. I intend to bone up on this material.

39. Rg5 Rf6

Following the rule that rooks belong behind passed pawns. A cursory glance at these types of endgames indicates that there's a lot of exceptions, and in some cases having the attacking rook in front of the pawns can even work.

39... Re5 seems clearly best. The a-pawn will be protected, allowing the Black king to invade, and it also cuts the white king off from the kingside.

40. Kb2 Kb4 41.Kc2

We can see the problem emerging...White threatens to get his king in
front of the pawns. 41...Ka3 42. Kc3 a4?



I thought if I free my king (as well as his) from kingside defense that it made the win easier. It made the win harder or maybe even disappear. 42... Rc6+ (Fritz) appears to lead to the win.

43. bxa4 Kxa4 44. Kd4 Kb4 45. Ke5 Rf8 46. Kf4



Fritz is giving this a +2.38 still for Black, but this is looking like a draw {if you're not accustomed to the idisyncracies of computers, you need to realize that you can't rely on such an evaluation in an endgame. If the computer sees a material advantage, but can't see how to convert it via queening a pawn and/or mate, the line is still unclear.} Part of my homework for this game is studying these types of fortresses.

The game concluded: 46...Kc4 47. Rg7 Kd5 48. Re7 Kd6 49. Re3 Kd5 50. Re7 Rf6 51. Re1 Re6?! (or ?, depending on whether you thought Black still had winning chances) 52. Rd1+ Kc6 53. Kxf5 Re8 1/2-1/2

Compare this result to Black's position to that on move 14. Unfortunately, this game is all too representative of my style of play: obtain advantage, then fail to find the best moves and return material "to simplify to a won endgame".

Now, if you've read this far you may wonder why I said this was "extreme". Maybe an unusual amount of analysis for a blitz game, but not extreme.

What makes this extreme is that the analysis is not done, and there are several levels of "extreme" that I could justify passing through to get closer to the "truth" of this endgame.

I can't help but feel that a grandmaster would look at the position after White's 37th move and know exactly what's going on, and how each side must play. But the position is not one that you're likely to find described in an endgame book. The positions where the game has simplified down to two connected passers are more fundamental.

One less extreme option is to study these g+h-pawn endgames, see how the defender draws, and try to extrapolate to the case in my game.

A more extreme option is to open up Muller and Lamprecht, or Fine, or Dvoretsky, and work through the pertinent sections on R+2P vs. R endgames.

Another is to finally crack open Smyslov and Levenfish's "Rook Endings" and finally read the bastard cover to cover.

All of these options could be justified. Rook endgames are the most common, so even the last option mentioned isn't that extreme.

I think a characteristic of good players is that they don't put off learning something for a rainy day. They analyze their games and try to find the best moves for each side, and if something is unclear they try to figure it out. Here, I think that at least studying a few of the typical drawing fortresses is warranted, and I think I'll take this opportunity to brush up on my rook endgames in general.

I happen to have Muller's rook endgame DVD on order anyway, so I think I'm going to start with looking at the g+h-pawn endgames and then watch the DVD. But I think Smyslov and Levenfish is going to find its way into my luggage for my Christmas vacation.