Practical Rook Endgames 11: Time, Efficiency, and Alternate Realities

About three months ago, a friend sent me a game where he had this position as White with White to play:

He chose to sacrifice his bishop on this move while Black's passer was on g3 and went on to win a nailbiting race in which his f-pawn queened just before Black's h-pawn queened, White forced the exchange of the queens on h1, and then White ran to capture a6 and successfully queen his a-pawn. Later, he had afterthoughts of whether he should have waited to sacrifice. His win would have been much easier had he just played f5. If Black played g2 next, he plays Bf2, and only after g1=Q, sacrifices with Bxg1+ Kxg1 f6, when his pawn is one tempo closer to queening than the played line. If Black played Kh3, then he plays Bxg3 Kxg3 and f6 when again, his pawn is one tempo closer to queening than the played line. I thought that I would advise him that logic dictates that one should always wait until the last second to sacrifice for a queening pawn, but the last second is difficult to determine if your opponent has a way to block the sacrifice. And then study of the following ending really humbled me with regard to timing and rules of thumb.

One lovely thing about chess is that you can relive the game from the recorded score. As long as the notation isn't botched, the record of the game contains the essence of what happened. There are no dice rolls or card deck draws to reconstruct. History is captured in a half-page of alphanumeric codes. The player's thoughts and calculations can be reconstructed afterward, but the logic engines can also look at relevant lines of missed or accurately evaluated variations. The variations are like parallel universes, alternate realities, counterfactual possibilities. Guy Pearce's "Time Machine" from 2002 was itself a remake of an earlier 1960 movie adaptation of H.G. Wells' novel. One of the ideas that came up is that despite Alexander Hartdegen's ability to alter some past events, he cannot change the the mortal fate of his girlfriend.

This post is the third installment from a semifinal game from my 2015 club championship run. The game is broken into phases running roughly in reverse chronological order.

• Practical Rook Endgames 09 is the final phase of the game.
• Practical Rook Endgames 10 is the penultimate phase of the game.

For this third installment, I'm going four moves into the past relative to the previous post. After White moved 50.Kd6, I had this position to contemplate:

I could see that I was going to have to sacrifice my rook, but that my pawns stood a chance if only I could give them enough of a head start. I needed to put my rook in a position to slow down the pawn, but still sacrifice for it when needed. My main move was Rc8. I don't specifically recall if Rh7 entered into my calculations during the game, but it's instructive to go through the exercise. So bear with me as we go into a long variation that wasn't played. Analysis variation 50...Rh7:

Black's idea is to play Rh8 and Rxc8 only when necessary. But those moments arrive earlier than expected due to some tricky variations. 51.c7 Rh8 and now 52.Rb1!!

The hard-to-see threat is that Rb8 guarantees a queen. "So what?" you say. Black can still get the pawn and try to queen his own with 52...Rc8 53.Kd7 Rxc7+ 54.Kxc7 Kf5

We've seen a position very similar to this. Recall in the previous post, that White had a choice to lock out Black's passers or try to race with his own a-pawn from this position, White to move:

In the race variation, Black barely held a draw with 54.Kb7 f3 55.Kxa7 Kf4 56.a4 f2 57.Ra1 Kg3 58.a5 Kg2 59.a6 f1=Q 60.Rxf1 Kxf1 61.Kb8 h3 62.a7 h2 63.a8=Q Kg1!=. The problem for Black is that he is now 2 tempi behind: the h-pawn is on h5 instead of h4 and when he plays f3-f2, White will not have to spend a tempo moving a rook on e1 because it moved to b1 already.

The new race would look like this:

55.Kb7 f3 56.Kxa7 Kf4 57.a4 f2 58.a5 Kg3 59.a6 Kg2 60.Kb8 f1=Q 61.Rxf1 Kxf1 62.a7 h4 63.a8=Q h3 and White just needs to use checks to get his queen to g4 and Black won't have a self-stalemate resource.

So after 50.Kd6, 50...Rc8! is the only move that draws.

At this point, I noticed that White has two logical moves: c7 or Kd7. I was really relieved when the game continued 51.c7 h4 52.Kd7 Rxc7+! 53.Kxc7 Kf5 which brings us to the drawn position at the beginning of the previous post. During the game I didn't think that I could delay the capture of the c-pawn with a move like 52.Kd7 Rh8 because of 53.Re8. I didn't notice at the time that 53...Rh7+ could keep the sacrifice bid alive and 54.Re7 Rh8 might lead to repetition. It turns out that Black has a very narrow path to draw with 55.Re8 Rh7+ 56.Kd6 Rxc7 57.Kxc7

57...f3 and White has to run his king down to f2 and trade his rook for both passers. Back to the game, I really dreaded 51.Kd7

because I thought that I had no choice but to play 51...Rxc6 52.Kxc6. Compared with the barely drawing variation above, White's king is one step closer to e2 and Black's pawn is back on h5. Two tempi mean that White has the win. If White decides to go for the a-pawn race, he sacrifices one tempo because there was no advantage to play Kc6-b7 versus Kc7-b7, but chasing Black's passer with Kd5 means that Black's h-pawn hardly gets going before the f-pawn is dead. e.g. 52...Kf5 53.Kd5 f3 54.Kd4 Kf4 55.Re8 f2 56.Rf8+ Kg3 57.Ke3 h4 58.Rg8+! followed by 59.Kxf2. In home analysis, I was astounded to see the complexity of a draw beginning with 51.Kd7 Rh8!

Didn't we just refute something like this? Three diagrams ago, Black tried to save time with the narrowly losing variation 52...Rh8 53.Re8 Rh7+ 54.Re7 Rh8 55.Re8 Rh7+ 56.Kd6 Rxc7 57.Kxc7 Kf5 58.Rf8!. But here, the pawn is still back on c6. So let's try to win the game for White beginning with 52.c7 Kf5 53.Re8 Rh7+ 53.Ke6 Rxc7 54.Kxc7. Since Black had time for 52...Kf5, he is one tempo up on the losing variation and this is just enough to draw.

One more surprising idea is that Black has a very narrow path to a draw after 51.Kd7 Rh8! 52.c7 Kf5! 53.Re8 Rh7+ 54.Re7 Rh8 55.c8=Q Rxc8 56.Kxc8. Black to move and draw:

It's hard to believe, but the only move that draws is 56...a6!! Why that pawn and why just one step? With the rook on e7 already, it's worth it for White to spend the time to capture on a7 and maneuver back to b1 or behind the leading passer. Here are some sample variations if Black doesn't find 56...a6!!

56...f3?? 57.Rxa7 Kg4 58.a4 f2 59.Rf7 Kg3 60.a5 Kg2 61.a6 f1=Q 62.Rxf1 Kxf1 63.a7 h4 64.a8=Q h3. Again, White checks with his queen until he can get to g4.

56...h4?? 57.Rxa7 h3 58.a4 f3 59.Rb7! (or 59.Rc7!) Kg4 60.a5 h2 61.Rb1! Kg3 62.a6! Kg2 63.a7! h1=Q 64.Rxh1 Kxh1 65.a8=Q Kg2. Now the technique is standard to never let the f-pawn get to f2 otherwise a drawn queen versus bishop pawn ending can arise. The white queen checks its way to g4, forcing the black king to step on f2 and then the white king moves closer to the f-pawn.

56...a5?? This is the hardest to understand, but the key is that the white rook recovers some time with threats on Black's king or pawns. 57.Ra7! Kg4 58.Rxa5 f3 59.Rb5 h4 60.a4 h3 61.a5 h2 62.Rb1 Kg3 63.a6 Kg2 64.a7 h1=Q 65.Rxh1 Kxh1 66.a8=Q is just like the previous variation.

The reason why 56...a6!! escapes with a draw is that Black's f-pawn can run pretty fast if Black's rook is out of position and a6 is just such a bad spot. 56...a6!! 57.Ra7?! f3!. White can even lose with 58.Rxa6?? f2!-+. Instead, there is still time for White to draw with 58.Rb7, Rb1 and Kb7. If White tries to improve with 56...a6!! 57.Kb7, Black still draws with the just-in-time pawn race, making sure not to be caught on g2 when the a-pawn queens.

If White had chosen 51.Kd7, I don't think I could have found the saving variations of 51...Rh8 and the impossible 56...a6!! I was just lucky my opponent didn't force the issue for me to go down in flames with 51...Rxc6?? I would say that the search for improvements in time efficiency are extremely important to look for in endgame variations, probably more so than rules of thumb about when is the best time to sac for a passer.

Practical Rook Endgames 10: Abandon a Sinking Ship

It's going to seem as if I am a big fan of Guy Pearce, which is not really true, but instead of posting continuing phases of this game with contrived parallels to scenes in "Memento," I thought I would introduce more variety by relating them to Guy Pearce movies. The title of my post spoils part of the ending of the "Lockout" movie which apparently had a working title called "Escape from M.S. One." The makers of "Lockout" were successfully sued by the director of the "Escape From NY" and "Escape From LA" franchise. This practical rook ending comes from a semifinal game from my 2015 club championship run. The game is broken into phases running roughly in reverse chronological order.

• Practical Rook Endgames 09 is the final phase of the game.

On move 53, my opponent captured my rook which had just sacrificed itself for White's c-pawn, threatening to queen.

Black's only hope is that the f- and h-pawns might beat the rook. There is a rule of thumb that two connected passers on the 6th rank beat a rook, but concrete analysis is necessary to verify that the rule applies. Without connection, the passers will need a friendly king escort from g2. But what if the enemy king comes to defend? Black's king is closer to the queening squares, but escorting both pawns will take black almost 3 tempi (king-pawn-pawn) for every one tempo that the white king uses to step closer. The battle between the kings is interesting in that Black will try to muscle White away from the queening square at f1. When the king and rook cooperate, White can push the black king around. With the way the tempi stack up, the white king is aiming for e2 to capture the f-pawn, so the rook will probably have to help push the black king to the g-file. However, Black may have to move to g2 even without the rook's help, just to maintain threats of Pf2-f1 or Ph2-h1.

The position of the white rook deserves some consideration. With the pawns isolated, being on rank 1 is good because it forces Black to get his king to g2 to assist in queening. If the pawns were connected, this rook defense would be far less effective. At some point, in coordination with a closer white king, the white rook will be effective checking the black king from behind his advancing pawns (Rooks belong behind passed pawns). Even though the seventh rank seems almost as far as the eighth rank, checking distance still comes into play as we will see.

From the above diagram, I played 53...Kf5. Stockfish at 30 ply evaluates this ending as drawn as long as Black played either 53...Kf5 or 53...Kg5. Don't dilly-dally.

Now White has a choice: stop the f-h pawns from queening or counterthreat by capturing a7 and advancing his own passer. Analyses conclude a draw with either plan, but mere mortals might have trouble allowing Black to queen while nurturing a slow a-pawn. Stockfish gives 54.Kb7 f3 55.Kxa7 Kf4 56.a4 f2 57.Ra1 Kg3 58.a5 Kg2 59.a6 f1=Q 60.Rxf1 Kxf1 61.Kb8 h3 62.a7 h2 63.a8=Q Kg1! and Black draws since he can stalemate himself with Kh1 in response to White maneuvering his queen to g3. Instead, my opponent tried to lock down (or lockout) the pawn uprising with 54.Kd6.

Play continued 54...f3 55.Kd5 Kf4 56.Kd4

Black can choose to advance f2 here, but calculation shows that White will encircle the f-pawn. e.g. 56...f2 57.Rf1 Kf3 58.Kd3! and Black can't make progress unless he moves Kg2, allowing White to play Ke2, and Rxf2, probably with check. If Rxf2 happens then Black will need to have h1=Q ready just to have drawing chances, so the pawn will need to get to h2 anyway. The h-pawn still can't queen without Kg2, allowing Ke2, but it's the only chance to draw. Still, the steady advance of pawns was enough to make my opponent panic. Strategy-wise, f2 makes White's choice easier: it must play to f1 or some other square on the first rank such as c1. Allowing my opponent moves like Re4+ and Re8 makes his analysis more difficult. Never help your opponent out of a jam.56...h3.

In the post mortem, my opponent suggested 57.Re4+ as a way to improve. The problem is that the rook loses its checking distance and must go to the eighth rank anyway. e.g. 57.Re4+ Kg3 58.Ke3 f2 59.Rf4! h2!.

...and White still draws with 60.Rf7 or Rf8. Note the reliance on a skewer if Black queens the h-pawn, which is probably Black's most straightforward draw, e.g. 60.Rf8 h1=Q 61.Rg8+ Kh2 62.Rh8+ Kg1 63.Rxh1+ Kxh1 64.Kxf2=. Instead, my opponent went for the still-drawing variation of 57.Re8.

Here is where checking distance might have moved the game into a forced win for Black. 57.Re7?? seems like a multi-purpose move threatening Rxa7 at an opportune moment. However, watch the coming variations where the checking distance would have made a big difference. From the above position, 57...f2?? would have been a bad mistake punished by 58.Rf8+ Kg3 59.Ke3! and the h-pawn is not a big enough threat to hold the draw. e.g. 59...h2 60.Rg8+! Kh3 61.Kxf2 h1=N+ (spite check!) 62.Kf3 and Black is dead meat. I continued 57...h2!

White's safe path has narrowed. If 58.Rh8??, Black wins with 58...f2! The threat of queening one of the pawns succeeds after a move like Kg5, removing the immediate skewer. Other than the text, 58.Re1 would also have drawn. 58.Rf8+ is still drawing.

At this point, I almost played the automatic 58...Kg3, thinking "I have no choice but to support the pawns." But after 59.Ke3, I realized that with the king preventing the black king from getting to f2, f3, and f4, skewers from Rg8+ and Rh8+ were going to defang my queening threats. My plan is hopeless; the ship is sinking. But then I remembered that since the pawns are so advanced, they almost defeat the rook by themselves, so I searched for Plan B and hit upon 58...Kg5.

Abandon ship! Now the check in the back 59.Rg8+ allows me to get to the f-file and avoid the skewer of a short-lived queen on h1. White has no choice in this position. 59.Rg8+ is the only move that still draws and it is what was played.

Of course, my response was 59...Kf6!. Here is where the checking distance paid off for White. If White were checking from the seventh rank because he made the choice of Re7 on move 57, Black would now be attacking the rook on g7. A move such as 60.Rg7-h7 would be met by f2 and Black will queen successfully and win the game. After 59...Kf6, the game concluded with the first (last?) phase that I have already posted.

Looking back I realized that I used the f- and h-pawns to represent prison ship M.S. One, but in Practical Rook Endgames 05, I used the a- and c-pawns to represent the Death Star, another gargantuan space ship.

Practical Rook Endgames 09: A Helpswindle

In 2000, at the Venice International Film Festival, a not-so-famous Christopher Nolan debuted his film "Memento" about a man with short-term memory loss seeking revenge on those who had wronged him. The main character Leonard copes with his memory loss by using tattoos and annotated Polaroids as mementos to redirect him towards important information. Short-term memory loss would inspire comedic characters such as Dory of "Finding Nemo" and Lucy Whitmore of "50 First Dates".

But also groundbreaking in "Memento" was the use of reverse chronological order. The fact that the Leonard often began each cut with a jarring amnesiac disorientation helped to enable this nonlinear storytelling device. It is with this reverse order that I'm going to overanalyze one of last year's games. It was the second game of a 4-game match in the club championship semifinal. Game 1 had been a draw, to be blogged later. I played black in this game.

Here is the end, with White to move. What is the worst move? What is the best move?

Regarding the worst move, I was gifted an extra and undeserved half point when my opponent resigned??? in the position above. Savielly Tartakover said, "No one ever won a game by resigning." No one ever drew a game by resigning either. White must prevent 60...h1=Q so 60.Rh8! is necessary. But then, like the myriad zombies on today's video entertainment, Black continues 60...f2! How does White stop this f-pawn from queening?

61.Ke3! It looks like chasing a pawn while out of its queening square is futile, but the rook gives the king just enough help. 61.Rxh2? fails to 61...f1=Q and 61.Rf8+ Kg7 62.Rxf2 fails to 62...h1=Q. Now it is Black who has to play accurately.

61...Kg7! 61...f1=Q fails to 62.Rf8+ and 63.Rxf1 and the h-pawn is no threat. Now it's White's turn.

62.Kxf2! Kxh8! 63.Kg2! Best play for both sides means there is no getting around the sacrifice of the rook and the two-pawns-who-would-be-queen. In the ensuing race toward the a-pawns, Black's king is 1-2 steps ahead and can capture on a7, but White's king has enough time to reach the critical square c7 immediately after Kxa7, and save the draw.

I think that my opponent probably thought that two pawns on the seventh beat the rook, but the particulars of having the Rf8+ skewer and the White King being barely close enough did not enter into his resource inventory.

Inclination

I caught the last two rounds of the US Championship as they happened with LiveStream coverage and concurrent sports commentary. It was fun to see the nation's best find computer-like moves and also miss opportunities that the commentary and computer analysis allow us to see. I almost felt an attraction to the game of chess again. I don't think this translates into tournament action any time soon, just that the positives are coming back. I keep thinking about blogging about a game I played last year, but there are so many positions where the tide turned that I might have to do it in installments. Unfortunately, it will likely mean that I will beat one game to death, but so be it.

The RBvR endgame came up crucially in a Caruana-Svidler Candidates game. The winning strategy is still so opaque even though I have spent some time trying to understand it. Frustrating.

I read an article on grit yesterday. I don't have grit, at least not in my current moods. Sticktuitiveness is lacking even with my current pastime of playing hand after hand of Spider Solitaire. I hate it when a position is too deep or difficult to analyze, so my tolerance for a tough position is poor. But there was a day when I played two skittles games and the strategies and even the moves stuck with me. And winning was a good feeling.

Declination

The three-peat is already out of the cards as I declined to defend my club championship title this year. After playing my last game at the end of September 2015, I really haven't come to the board with any feeling besides indifference with a touch of loathing. A couple of strong 2100+ players are currently contending and I would put my money on either of them, but they have at least 19 games on the road to the championship.

I tried to use the title of this post as a double meaning, but astronomical declination seems hard for me completely grasp: the angle from the celestial equator, analogous to the latitude on the globe. Practical astronomy always seemed too tedious. I once had a telescope to look at the neon lights downtown, but even trying to follow the moon through the sky involved constant readjustments.

Tinkering on my computer is my main hobby these days with a touch of writing and standard consumption of movies and books. I discovered recently that the film "Butterfly Effect" starring Ashton Kutcher has two endings: a theatrical release with mostly happily ever after, and a director's cut with the main character suffering a tragic end. I hadn't seen the happy ending, but maybe it will leave me with a better impression of the film. I mourned the death of Alan Rickman who played the love-to-hate-him slick Hans Gruber in "Die Hard", the loathsome but ultimately sympathetic Severus Snape of "Harry Potter", and the funny self-parodying Alexander Dane in "Galaxy Quest".

"The Force Awakens" fed into my confirmation bias that J.J. Abrams is a rather derivative re-booter of franchises, recycling entire scenes and plots. I don't think that I am so much a fan that I need to see the same movie made over and over again. A decent helping of originality would be appreciated. Perhaps this is just my hostility showing through toward Lucas for Episodes 1-3 and toward Abrams for the Lost disappointment and Star Trek's Vulcan and Khan heresies.

On the brighter side, I am looking forward to the "WarCraft" movie and the "Zoolander" sequel and perhaps trying to "publish" something in 2016. I use the term "publish" loosely here as if publicizing things on social media such as Twitter tweets or Facebook wall posts or even Blogger blog posts are "publishing".

Repeater

About a year ago, I blogged about an ending involving the snare-like properties of Plants vs. Zombies Winter Melon. Funny enough, a friend who didn't know I like PvZ noticed and we compared notes on the Survival:Endless levels. Here is my setup, which got me to level 1000 before I quit.

Well, I managed to survive some of my own attempts to mentally defeat myself and I won the club championship for a second year in a row. I struggled through the qualifier, grabbing the sixth seed. Funny enough, all four past club champions ended up on one side of the 8-man bracket. I defeated two players that I beat in last year's championship, this time more quickly as they each lasted 3 games each instead of last year's 8- and 6-game matches. But the finals this year took 8 games. Adding in the 9-game qualifier, the road to the championship lasted 23 games this year; last year it took 24 games.

I could complain about the length of the club championship, but perhaps the blame would be misplaced. I lack the stamina to concentrate on chess for a whole weekend swiss. Right now, I'm taking a break from chess, hoping that my natural rhythms will bring me back to it in time for the club championship qualifier after the New Year.

For now, here is the retrospective on 2015's year in chess, especially benchmarked against last year's assessment

On the positive side:
• Played 35 rated regular games, about 33% less than last year (54).
• Had fun for the first 6 months.
• Pushed my peak rating up to 2133, 1 point higher than last year (2132), but slid back down to 2105.
• Won the club championship for a second time
• Contended for the state championship for the second time (semifinalist)
• Finished the year with a plus score against experts for the second time 8W-8D-6L
• Five of my games against strong players went into trappy lines I had prepared resulting in 3 wins, 2 draws

On the negative side:
• Many of my games - wins, losses, and draws - seemed to be decided on luck as opposed to good technique
• I didn't win any money, didn't finish at the top of any non-match tournaments, and felt too tired to play in weekend swisses

Fewer positives, but also fewer negatives. I'm debating whether I have enough motivation to contend for the championship again. But Plants versus Zombies also has a Threepeater plant...

Hypercube

As a writer, I should research a lot of information about Rubik's cube before coming to this article, but I feel lazy today and am content to direct your attention to a long list of sayings about cubers.

My family received several Rubik's cubes from a visitor when I was in 5th grade. It came with a set of pictorial instructions that taught me how to solve the cube layer by layer. I learned the algorithms and began showing off in middle school where kids would pay me a quarter to fix their cubes for them. I once solved it in 46 seconds, but it was a lucky break where the pieces fell just right. I never got too far in speed cubing, but I can regularly finish in under 3 minutes. While watching the Double Fine Adventures documentary about how the Broken Age adventure game got made, I was fascinated by how often Tim Schafer was playing with his set of cubes ranging from 2x2x2 to 5x5x5. I purchased a set for myself and they finally arrived in July. For much of the summer and early fall, I had been lost in cubing, distracting me from chess. I had never signed on to Rubik's Revenge or the Professor's Cube sequels, but now I have. Two of my chess friends have been cube crazy.

My best times for the 2, 3, 4, and 5 cubes are 0:32, 1:20, 4:45, and 8:51, respectively, which aren't anything special. One friend told me he can do all 4 in under 8 minutes cumulatively.

For some reason, I wanted to compare some of the astronomical numbers that come out of chess and cubing. Here is what I collected:

Field	Permutations
2x2x2 - Pocket Cube, Mini Cube, Ice Cube	3,674,160
3x3x3 - Rubik's Cube, Magic Cube	43252003274489800000
4x4x4 - Rubik's Revenge, Master Cube	7.40x10^45
5x5x5 - Professor's Cube	2.83x10^74
Atoms in the Universe	between 10^78 and 10^82
Positions in Chess	between 10^43 and 10^47
Chess Game Tree Complexity	10^123

Hypercube refers to an n-dimensional cube of which the standard 6-sided cube is the 3-dimensional version and the tesseract, popularly introduced in Madeleine L'Engle's A Wrinkle In Time, is the 4-dimensional version. Don't watch the movie "Cube 2: Hypercube"; it sucked.