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.

Practical Rook Endgames 08: Super Skewer

An attacking rook in front of its own passed pawn gets weaker and weaker the closer the pawn gets to queening because pawn keeps shortening the rook's backward aura. Such a rook belongs behind the passed pawn when it gets stronger as the pawn advances, but often this is the only way to assure that the pawn can advance. Usually this is because the attacking rook has spent so much time capturing a pawn in front that the defending rook has time to get behind the passer. In such cases, the position of the defending king becomes critical, especially when the pawn reaches the seventh rank. With White to move in the following position, the green areas are the only spots where the Black King can be in order to draw.

White can queen the pawn by moving the rook, checking the king (except for king on h6), and then playing h8=Q. The difference between a draw and a win is whether Black can capture White's last two pieces. The cluster of green squares f7, f6, g7, g6, and h7 are spots where, after White moves, the Black King can move into g7 (or h7) and eliminate the queen as soon as it appears. The cluster of two squares on a7 and b7 are places where if the rook checks on a8 or b8 respectively, the Black King simply captures the rook and then the Black Rook captures the pawn. If the king is not in contact with the 8th rank or g7, the White Rook lives long enough to protect the newly queened pawn and recaptures after h8=Q Rxh8 Rxh8. On squares such as c7, d7, and e7, the Black King is still not safe because White moves Ra8, threatening h8=Q. If Rxh7, Ra7+ skewers the king against the rook and wins the game.
A friend of mine played a game and ended up in this position:

White to move, Black is better

Black just survived a mating attack, but emerged into a rook and pawns endgame with a decent endgame advantage. His rook is actively placed near White's pawn weaknesses on a2 and c3. Black's distant a-pawn has some room to run down to a3. If White tries to stall this by playing a3 or a4, the pawn weakness on c3 falls even quicker. If the black pawn gets to a3, then Rb2 becomes a threat. Black's King is also closer to the center. Plus, Black's g-h-pawns can form an outside passer against White's lone h-pawn. At the moment, Black threatens Rb1+ and exchanging rooks. Black would have the win in the pure pawn ending because this outside passer would distract the White King while the Black King picks up c3 and d4. So those are Black's advantages.

What does White have going for him? It turns out there is one move that goes a long way toward solving his problems. 1.Rg5! hits the d-pawn which is the base of Black's central pawn chain. Black can defend with Ke6, but then White resolves one backward weakness with 2.e4! Now, White gains a dangerous protected passer at d4 and the White Rook gains a path to get behind Black's dangerous a-pawn if not capture it outright. This active plan would have gone a long way toward securing a draw. Instead, White chose a passive posting for his rook. 1.Re2

It is true that the passivity of the rook is temporary because Black can't stop e4, but one additional defect of Re2 is that Black is dangerously close to forcing the exchange of rooks. 1...a4! 2.Kg2 Kf6?!

Centralization of the king is key in endgames, but here I thought Black was better served forging ahead with 2...a3. Although Stockfish endorses this move, the win is quite difficult as both sides proceed to gobble up pawns until all that is left is Black's g- and h-pawns. 3.e4 dxe4 4.Rxe4 Rb2+ 5.Kg3 Rc2 6.d5 Rxc3+ 7.Kf2 Rc2+ 8.Ke3 Rxa2 9.d6 Rxa2 10.d7 Rh3+ 11.Ke2 Rd3 12.Rxc4 Rxc7 13.Ra4 h5 14.Rxa3 and the connected passers should win. 3.Kf3 Kf6 I thought it was futile for Black to try to prevent e4.

4.e4+ dxe4 5.Rxe4 Rb2

Here again, White faces a choice to keep his rook active or passively try to consolidate. The pure pawn endgame is not so clear for Black any more since Black has no pawn on e4. The protected passer at d4 will likely be stronger than an outside passer at g3. White is close to a draw with a variation like 6.Re5+ Kf6 7.Ra5 Rxa2 8.h4 Ra3 9.Ke4 Rxc3 10.Rxa4. Instead, White chose 6.Re2

6...a3!

White has something in that his rook cuts off the Black King from the passed d-pawn. However, Black just needs to stay in the square of the pawn and if White tries to advance it, an exchange of rooks should create a winning pawn endgame. White cannot exchange rooks on b2 as the passer is unstoppable. 7.Ke3

Since White is occupied with stopping the a-pawn from queening, Black can pursue a plan to create a second weakness. 7...g5! 8.Rf2+ Ke6 9.Rd2 If White does nothing, Black has a winning plan of advancing the g-pawn to g4, then the h-pawn to h3 and then creating an outside passer.

Here is a hard decision for Black. White is finally about to create activity for his rook with d5+ Kd6 Rd4. It would seem as if this should be prevented with Kd5, but then h3 h5 Rf2 seems to activate the rook anyway and now Black's g-h-pawns seem in danger. It turns out that the desertion of the second rank by the rook is good for Black's a-pawn such that even placing the g-pawn on the same rank where the rook will land is the strongest move for Black. 9...g4!

White has little choice but to follow through since h5 h4 h3 and g3 are coming. 10.d5+ Kd6 11.Rd4

Black has another interesting choice here: capture on a2 or h2. But then White has a choice also, capture on c4 or g4. The a-pawn is closest to queening, so trying to force the a-pawn to queen (and trying to prevent it) should make the choices easy. The game continued 11...Rxa2

White needs to make sure he can stop the a-pawn. If he captures Rxc4, there isn't enough time for the rook to come back to Rd2 or Rd1 to defend laterally. So Rxc4 commits to Ra4. Armed with the information given at the beginning of this post, you should be able to calculate a plan for Black after 12.Rxc4 and whether it succeeds. What's harder to calculate is that 12.Rxg4 is still lost, but Black has more work ahead. 12...Ra1 13.Rg2 a2 14.Re2! shielding the king from Re1+. Black's winning plan then is to advance his King to b3. White chose the worse variation 12.Rxc4

In this position, while watching the game, I hadn't appreciated that the plan starting with Ra1 was so fast. Here it is: 12...Ra1!

13.Ra4 a2

...and without a place to hide from check or a chance to get to g2 or b2, White is completely lost. Kf2 stops the check, but Rh1! Kg2 a1=Q queens the pawn or Rxa2 Rh2+ skewers the king on the rook. White's c-d-connected pawns are of no consequence if Black wins the rook. Instead, my friend made things hard on himself with 12...Kxd5?! Note here that White now has time to get his rook to e2 if necessary to stop Re1+. Exchanging pawns is good for the defender. 13.Rxg4 Rxh2 14.Ra4

Even with the reduction in pawns, the endgame is still quite interesting. Black retains the advantage of an advanced a-pawn. But he also has an unopposed distant h-pawn. The presence of this h-pawn as well as the placement of the Black King on d5 turns the Black Rook into a Super Skewer, able to operate on almost four whole ranks. Normally, Black would be content to advance a2, but his next move is both tricky and strong. 14...Rh3+!

Where can White's King go? Kf4 fails to Rh4+ skewering the Ra4. So retreat to the second rank seems necessary and Kd2 also holds the c3 pawn. 15.Kd2 Black exploits the position of the White King with 15...a2! White can't check the Black King indefinitely as it will just walk forward to b4 and stop the checks. White has little choice but to pursue the pawn with 16.Kc2

Here, my friend missed a golden opportunity to win easily. 16...Rh1!

The threat of course is a1=Q. White can prevent the new queen from living beyond a moment and White can also prevent Black from winning a clear rook. But because the exchanges happen on a1 or a2, Black's h-pawn runs free outside of the square of White's King. e.g. 17.Kb2 a1=Q+ 18.Rxa1 Rxa1 19.Kxa1 h5 and Black wins.

My friend was in time trouble and should be excused from missing some of the best variations. But the longer the game went on, the worse the time trouble. He played 16...h5?! 17.Kb2 Rh2+!

Black is still probably winning, but just barely. For one thing, White is close to a stalemate trap. 18.Ka1!? h4 19.Rg4 Through a combination of harassing checks and advancing the c-pawn, White just needs to get Black to play KxP and then the White Rook can check the king mercilessly, even giving itself away because the White King is stalemated.

Instead, White opted for some scary counterchances. 18.Kb3 h4 19.Rd4+

Black would like to keep the position under control by staying in front of White's passed c-pawn. Unfortunately, White has endless checks on the a- through d- files. For the win, Black has no choice but to move to 19...Ke5 Both sides race their pawns forward. 20.Rd1 h3 21.c4 Rg2 22.c5 h2 23.c6

Now my friend played an inexplicable move. 23...a1=Q 24.Rxa1 Afterward, he told me he thought he had a safe win with 24.Rxa1 Kd6? but then he realized that 25.Rh1 draws. I thought that the previous moves Rg2 and h2 set up 23...Rg1 24.c7 h1=Q 25.c8=Q

With the first move after queening, Black wins with 25...Qf3+ 26.Kb4 Rg4+ 27.Ka5 Qa3+ 28.Kb6 Rb4+ 29.Kc7 Rc4 The rook skewers once again, this time king onto queen. Once my friend realized 24...Kd6 draws, he went for 24...Rg1 25.c7 h1=Q 26.c8=Q

The Black Queen still moved first. With some judicious checks, he centralized his queen and won the rook. Then he weathered a bunch of checks, retreating with the king toward the relative safety of the space between friendly rook and queen. Finally, White ran out of checks and Black had a mating combination. 26...Qd5+ 27.Kb4 Qd4+ 28.Kb5 Rxa1 29.Qh8+ Kd5 30.Qd8+ Ke4 31.Qh4+ Kd3 32.Qg3+ Kc2 33.Qg2+ Kb3 34.Qf3+ Kc2 35.Qe2+ Kc3 36.Qg2 Rb1+ 37.Kc6 Rb6+ 38.Kc7 Qd6+ White resigned. After 2.5 hours for each side, Black had about 60 seconds remaining on his clock.

I Want The Certificate

A couple of my friends who are masters have flaunted their master certificates on Facebook or in a blog post. I want one. I covet one. It reminds me of three conversations in my favorite chess movie. ***WARNING SPOILERS AHEAD FOR SEARCHING FOR BOBBY FISCHER MOVIE***

- - -

BRUCE PANDOLFINI: I want to show you something else. This is very rare. It says, "Master Chess Certificate...awarded to..." and there's a blank here for a name... "for highest achievement on this day of blank, nineteen hundred and blank." Careful with it. It's a mysterious and powerful thing. It's only been given out...I don't know...a few times in history. And then only to those who achieve a lot of master class points. Then there's a big ceremony and so on.
JOSH WAITZKIN: How do you get master class points?
BRUCE PANDOLFINI: You earn them. You just earned ten for that knight to c8. Ten...master...class...points.

- - -

BRUCE PANDOLFINI: It's white's move. Can we expect it any time soon?
JOSH WAITZKIN: How many points is it worth?
BRUCE PANDOLFINI: To make the opening move?
JOSH WAITZKIN: Yes.
BRUCE PANDOLFINI: Forget the points.
JOSH WAITZKIN: How much is it worth if I do it?
BRUCE PANDOLFINI: Do it for its own sake. Do it for the love of the game.
JOSH WAITZKIN: I want to know how close I am to getting the certificate.
BRUCE PANDOLFINI: Forget the certificate.
JOSH WAITZKIN: But I want to know.
BRUCE PANDOLFINI: I don't know.
JOSH WAITZKIN: What do you mean you don't know?
BRUCE PANDOLFINI: I don't care. It's...white's...move.
JOSH WAITZKIN: I want the certificate.
BRUCE PANDOLFINI: [sighs] You want the certificate. You have to have the certificate. [gets briefcase] You won't move until you get the certificate. [opens it] You win. [gives him copy of certificate] Here's your certificate.
JOSH WAITZKIN: [takes it]
BRUCE PANDOLFINI: Fill it out. It doesn't mean anything. It's just a piece of paper. It's a xerox of a piece of paper. Do you want another one? [gives Josh another copy] Do you want 10? [gives Josh few more copies] Do you want 20? [continues stacking them on chess board one-by-one] 30? I've got a whole briefcase full of them. They mean nothing.
BONNIE WAITZKIN: [entering the room]
BRUCE PANDOLFINI: They mean nothing.
BONNIE WAITZKIN: Get out of my house.

- - -

BRUCE PANDOLFINI: I have something for you. It says, "This is to certify that Josh Waitzkin, on this day, has in the eyes of his teacher...attained the rank of Grandmaster."

- - -

So I decided to make myself a certificate. I googled "chess certificate" and found a suitable image to modify. The customized picture serves as the opening picture of this article. If you'd like to make your own certificate, just download the picture, add it to the background in your favorite word processor and then get to work on making up verbiage that sounds certificate-y. For my choices, I found an English Towne font to write medieval calligraphy letters. In the center of the certificate, I reproduced the club championship bracket for the year that I won the chess club championship. Printing was a bit of a disappointment because the printers within my reach don't print to the edge of the paper. Printed on 8.5 x 11" cardstock, the certificate serves as a tangible reminder of my road to the club championship.

Now if I could just pump my rating up about 67 points, I could get the certificate from the USCF that says "Master".

Practical Rook Endgames 07: Frontal Defense in Norway

According to some records I found on the internet, when David Letterman played a slow game of chess with Garry Kasparov in 1989, after the 14th move on November 21, David declared, "There just isn't enough televised chess." While I would love to see our beloved game get the love it deserves from the general public, I understand that watching people sit at a board thinking for 95% of the time and moving small pieces for 5% of the time would not make for very exciting entertainment.

In this internet age, when YouTube has essentially made cable TV obsolete in my household, I recently discovered a wonderful guilty pleasure of watching the first leg of the Grand Chess Tour 2015 at the Norway Supertournament. The big story through the first four and five rounds was the tragedies following Norway's favorite son of chess and current World Champion Magnus Carlsen. In round 1, Magnus worked to get a completely winning position by move 60 only to let his flag fall when he didn't realize that more time was not added for reaching move 60. After round 1, their fortunes diverged so much that by the end of round 4, Topalov was alone at the top, sitting on 3.5/4 while Carlsen's name was at the bottom of the standings alone at 0.5/4. This weekend, I watched the coverage of round 4 and 5 which was quite fun. European commentators New In Chess' Editor-in-Chief Dirk Jan ten Geuzendam and German Grandmaster Jan Gustafsson have provided very insightful commentary on the games, rotating through the five boards on a regular basis, and interviewing players afterward.

Today, in the Norway Round 5 video coverage, a possible endgame popped up in the video feed at time index 03:57:30. The scenario never showed, but I was tickled that it was exactly what I had been studying lately. I was also tickled that both GM Gustafsson and GM Yasser Seirawan struggled to correctly evaluate the following endgame:

White to move and draw

1.Kd3! Re6 White breaks for a Philidor and Black cuts him off.

White to move and draw. Rule of Five says Draw. Shredder says Draw.

The Rule of Five has pawn on 3rd plus 2 cutoff files equals 5 which is not more than 5, meaning draw. Shredder says draw, but only if White plays an only move here. Gustafsson thought this was probably a draw. Seirawan thought it was probably losing. If you read my Practical Rook Endgames 04, you should correctly guess the one drawing move. 2.Ra1! Now Black can play many moves that lead to a draw, but the most testing is probably the one that makes the Rule of Five point in his favor. 2...g5. Now the Rule of Five says 4th rank plus 2 cutoff files equals 6 > 5 should be winning. However, this is a knight pawn and the Rule of Five probably doesn't apply because Black's King doesn't have a wide avenue to walk serpentine down the board toward a rook checking from f1, g1, and h1. The pawn behind can be skewered on one of the Rg1+ moves.

White to move and draw. Rule of Five says Win. Shredder says Draw.

Now, the drawing line is narrow, but doable. White uses the Frontal Defense and never lets the g-pawn get closer. 3.Rf1+! Kg4 4.Rg1+! Kh4 5.Rh1!+ Kg3 6.Rg1+! Kf4 7.Rf1+! and the Black King can't make progress. In the video, Gustafsson analyzed 3.Rf1+! Kg6 4.Rg1! Re8.

Here, Seirawan suggested 5.Kd2? but again, students of the Frontal Defense know that staying on the third and fourth ranks are the best bets for a draw. Gustafsson ignored Yasser's Kd2 and played 5.Kd4!.

Black to move, White to draw. Gustafsson and Shredder say Draw.

Gustafsson then proclaims the position a draw and goes on to admit that "I pretend like I don't, but I have read some endgame books in the old days." ten Geuzandam then asks Gustafsson what his favorite endgame book was. When he named Keres' Practical Chess Endings and Shereshevsky's Endgame Strategy, I was delighted to find both on my bookshelf.

Science versus Art

"What is chess do you think? Those who play for fun or not at all, dismiss it as a game. The ones who devote their lives to it, for the most part, insist it’s a science. It’s neither. Bobby Fischer got underneath it like no one before him and found at its center…art." - Searching for Bobby Fischer (movie)

I alluded to a debate that sprung up after I had won my most recent game. I was proud that I had produced a near-flawless game with an interesting pawn sac and exchange sac. The problem? I had memorized the first 17 moves in home preparation including the moves for the pawn sac and the exchange sac. At home I had delighted in how the evaluations given by Stockfish continued to tilt in White's favor and I had studiously tried to understand the many, many side variations that a potential opponent could try to complicate with. In my game, I still had to find 16 good moves after my 17 memorized moves. I had studied hard, played the right moves, used my brain to create technically sound moves over the board, and had gotten the win.

A friend who is also an expert seemed muted in his praise, basically stating that computer analysis distorts chess and that at least for him, playing chess with so much emphasis on preparation and results instead of creativity was likely not fun. Partly out of annoyance that my win was not being celebrated as the pure and good thing that I felt it deserved, I launched into a screed about how chess has a rich culture of named strategies (Minority Attack, Marshall Attack, Yugoslav Attack, Greek Bishop Sacrifice), and now openings deeply analyzed with computers, but this is the game we have chosen. To deprecate opening study is to stunt your own growth in a discipline that requires it of you. I attribute, perhaps wrongly, my recent ascent from a floored expert now to a middling expert as a result of my opening study system. At the very least, it serves as an enthusiasm engine so that I don't get into a weird love-hate cycle where I want to quit chess.

As part of his argument, my friend showed a game where he came up with several interesting moves over the board. Agreed, they were interesting concepts backed up by tactical bon mots, but I wanted to push back. To further my argument, I said, "But you can only create that move once. After the first time, it is knowledge, not creation." I went over the moves of Caruana-Carlsen from the Norway Chess supertournament. I'm certain that Caruana is a theoretician and his win in an endgame arising from the Ruy Lopez Berlin Defense was pleasing to replay. When a grandmaster catches another in a prepared opening variation, should we reject that as "not chess"?

Admittedly, I am also in it for the art. Why else would I adopt Gufeld's Search for the Mona Lisa as shorthand for one of my chess quests? But I include the science and knowledge and computer tools of chess as integral parts of my pursuit. I'm trying to be a Renaissance Man like Leonardo Da Vinci. It's not science versus art, but science AND art.

Practical Rook Endgames 06: Frontal and Long Side Defenses

I have thrown around the frontal and long side defense terms enough that it's appropriate to address them formally. Both of these defenses are for a lone rook to draw versus rook plus pawn when Philidor has gone awry.

For the frontal defense:

• Attacking pawn has not yet reached its fifth rank
• Defending king is cut off by the attacking rook on the long side of the board
• Defending king is not cut off so much that the pawn can easily get to its fifth rank (Rule of Five may help here)
• Defending king can quickly attack a rook on the second rank or one on the fifth rank (e.g. King is on 3rd or 4th rank)
• Defending rook is in front of the pawn with checking distance (3 ranks between rook and pawn)

Frontal Defense: White can draw with either side to move

With White to move, probably safest is just to shuffle Kd4 and Kd3. Decreasing checking distance just a tiny bit with 1.Rf2?? will lose to Kg5! and the Black King will advance on the White Rook until it reaches f3 and escorts its pawn to f4, making a classic Lucena position. Failing to defend the fifth rank allows the rook to briefly defend the pawn laterally. 1.Kd2?? Kg5! 2.Rg1+ Kh4! 3.Rf1 Re5! 4.Kd3 {one step out of position} Kg3! 5.Ke4 Ra5! {spread offense} 6.Rg1+ Kf2 7.Rg5 Ra4+ 8.Kd3 Ra3+ and Black gets Lucena. If White goes too far north with Kd5, Black cuts off another file with Rd8+. With Black to move, if the king ventures out, White checks it while it protects the f-pawn; if the king is not protecting the f-pawn, White attacks the pawn. e.g. 1...Kg5 2.Rg1+! Kh4 3.Rf1! Kg4 4.Rg1+! Kh3 5.Rf1! Kg4 6.Rg1+=. The pawn must never be allowed to get any closer, else Lucena happens. If the Black Rook shuffles 1.Re7, the White King shuffles Kd4 or Kd3. If the Black Rook tries to get into the Spread Offense e.g. 1...Re5 2.Kd4 Ra5 Ke3 should lapse into a Philidor. In a previous post, I blogged about how this frontal defense resembles the Space Invaders video game.

For the long side defense:

• Attacking pawn could be as far advanced as its seventh rank, so this defense works later than the frontal defense
• Defending king is cut off by the attacking rook on the short side of the board
• Defending rook has at least three clear files between it and the pawn (sufficient checking distance)

Long Side Defense: White can draw with Black to move

Black is in check, but he will find no shelter. If the Black King approaches the White Rook, the White Rook can get position behind the dangerous passer. e.g. 1...Kd1 2.Ra1+! Kc2 3.Ra2+! Kd3 3.Ra3+! Kc4 4.Re3 draws. The White King can take a stroll up to d7, but he will not find any respite from the checks. 1...Kd1 2.Ra1+! Kc2 3.Ra2+! Kd3 4.Ra3+! Kd4 5.Ra4+! Kd5 6.Ra5+! Kd6 7.Ra6+! Kd7 8.Ra7+! Kc8!? 9.Re7! draws. If White skewers the rook with 9.Ra8+ Kb7 10.Rxf8 e1=Q+ he loses. The Black King has to allow either White Rook to the e-file or get checked all the way back to d1.

Endgame Caveat #7: Two Rules Don't Substitute for Actual Calculation

I have had a lot of good luck lately. I played two three-game matches against average rating 2112 players and beat each player by a convincing score of 2.5-0.5 for a 6-game performance rating of 2379. My second-to-last tournament game was a peculiar one, especially the ending. Both of us thought that I had won and I accepted his resignation with relief. But when I went home and had Stockfish show me the unseen, it revealed that my opponent resigned in a drawn position.

My opponent had been close to winning at several points in the game. Disappointment when his expectation changed from win to a draw contributed to the downward trend and helped cause him to misevaluate. Also, my 58th move was probably surprising enough to be a psychological blow. Ultimately, laziness on both our parts caused us to misapply the endgame rules of thumb and blind us to the truth of the position. As I stated in the first Endgame Caveat, this series is not meant to teach dogmatic rules, but mostly show how caveats, or exceptions, make these rules hazardous.

After 56...h4-h3

Having sacced my own rook for one of White's passers at c7, I have been trying to for the last 6 moves to create enough trouble with my f- and h-pawns to at least draw. To that end, my Black King has been trying to muscle the White King away from blockading a pawn by staying toward the center on the f-file. Now I have two pawns on the 6th rank. The endgame after the rook sacrifices for the h-pawn and the White King captures the f-pawn seems to be drawn unless White can capture the f-pawn and get a 4-step lead on the Black King. Two rules of thumb are coming into play. #1) It is often said that "Two connected pawns on the sixth rank beat a lone rook." I am hoping that with my king's help, two disconnected pawns on the sixth or seventh can beat the rook. #2) The Rule of the Square, which is probably the first endgame rule taught to beginners, seems to indicate that the f-pawn is currently outside the White King's range of stoppability. White played 57.Re8. After the game, my opponent thought that 57.Re4+ was a better try for a win, but concrete evaluation says no: 57...Kg3 58.Ke3! f2 59.Rf4! h2! 60.Rf8! h1=Q 61.Rg8+! Kh2 62.Rh8+ Kg1 63.Rxh1+ Kxh1 64.Kxf2=.

After 57.Re1-e8

During the game, I thought that 57.Re7 would have been better for White, but checking distance again becomes crucial, so the attempt to gain an advantage with Rxa7 loses because of insufficient checking distance in the main variations below. I am still trying not to let the White King into the blockade, so I felt that 57...h2! was the right move and it is. 57...f2 looks like it might be a viable alternative, but f2 actually loses to 58.Rf8+! Kg3 59.Ke3 h2 60.Rg8+ Kh3 61.Kxf2 and whether Black promotes to queen or knight, White's Rook will triumph. Allowing the White King to get closer to the f-pawn is anathema.

After 57...h2

Even though White has committed to checking from the back, guarding the queening squares is still a drawing option. e.g. 58.Re1 f2 59.Rf1 Kf3 60.Kd3! Kg2 61.Ke2 h1=Q 62.Rxh1 Kxh1 63.Kxf2=. His next move was 58.Rf8+.

Instead of making an automatic Kg3 move, I stopped to examine my options. My opponent was probably counting on 58...Kg3 59.Ke3 h1=Q 60.Rg8+ Kh2 61.Rh8+ Kg1 62.Rxh1+ Kxh1 63.Kxf3 which is a drawn endgame. Once I knew that, I felt that as long as it wasn't losing, 58...Kg5! was going to be my move.

After 58...Kg5!

I'm adding the exclam to Kg5 because of its psychological shock value. The move is neither singularly necessary to maintain the evaluation, nor is it winning in an objective sense, but for intangibles, it was enough of a bluff to help me tremendously. The Rook can kill the f-pawn now, but the h-pawn safely queens. It looks as if two advanced pawns DO beat a rook. 59.Rg8+

White's last move was actually necessary to save the draw. It looks as if it is helping Black get his King to attack the White Rook, but the reason Rg8+ was necessary was to put the Black King on a skewerable square and indirectly defend against a queening f-pawn. Notice that if White had moved his Rook to e7 on move 57, this crucial skewer possibility would be gone and White would be lost. Continuing the idea of not being skewered against the h-pawn, I played 59...Kf6. At some point here or in previous moves, I had grabbed my captured Black Queen from his side of the board, ready to queen my pawn. This also may have added to the psychological pressure.

Here my opponent offered his hand and resigned??? Out of sheer stubbornness and not giving up, he might have just played on and then the additional moves may have revealed his drawing path. The exclams show all moves are necessary for both sides to draw: 60.Rh8! f2! 61.Ke3! Kg7! 62.Kxf2! Kxh8! 63.Kg2! and the game is drawn. If Black queens either pawn, the Rook can kill the new queen where it stands and be in position to blockade the other pawn, meaning White wins. White had to let his Rook die on h8 to buy time for his King to catch both pawns. In contradiction to the two Rules, the White King should have caught the f-pawn even though it was outside the square and two pawns shouldn't have beaten the rook even though they might have both gotten to the seventh rank. Here are diagrams of the drawing variation:

After 60.Rh8!

60...f2! 61.Ke3!

61...Kg7!

62.Kxf2! Kxh8! 63.Kg2!

So the game ended in a study-like draw, but my opponent resigned in a drawable position. I'm pretty sure I haven't gotten an extra half point before from someone resigning a drawn position. I have resigned before in a drawn position, so maybe this is the karmic payback. Luck has a bizarre way of distributing points and leading us on strange left turns.