31 December 2008


My central chess goal over the next year (plus a couple of months) is to achieve an A Class USCF Rating, that is over 1800. As part of the work needed to get there, I am putting on record three New Year's Resolutions. I welcome my readers to inquire into my progress and shame me for any failings.

1. Reduce Online Blitz

2. Intensify Endgame Training

3. Demand Consistency in Tactics Training Plus

Online Blitz

Without revealing how much blitz I've been known to play certain days, I am renewing a pledge I made two years ago to limit this drug to five games per day. As most of my online blitz is 3 0, five games devour less than thirty minutes, and only rarely close to that much time.

Robert Pearson is one among many notable bloggers that have decried the evil that results from online blitz addictions. He advocates giving up blitz (again).

Blitz fuels a chemical addiction. These chemicals--endorphins--are produced in the brain, and give distance runners a euphoric high, or draw other people towards extreme sports. Indeed, internet blitz differs from certain other chemical addictions only insofar as it is less damaging to the throat, lungs, and liver. Whether it is better or worse than bungee jumping and marathon running depends on whether one succeeds in keeping other aspects of life in balance.

Substitution is often the best way to remove a destructive habit. With respect to internet blitz, two excellent alternatives have worked for me in the past: longer online games, and correspondence or turn-based chess. Instead of playing 3 0 games one after the other, the time I spend at the Playchess server can be employed playing 16 0 to 25 0 games. The playing session still requires less than half a day, but there's time for strategic planning and some efforts towards accurate calculation. Even more effective is to reduce the time online. At any given time, I usually have from a half-dozen to two dozen games going at Chess World, Chess.com, and Red Hot Pawn. Sometimes I move carelessly due to haste (a consequence of too much blitz). Greater attention to the "quest for chess truth" in these games requires such attention that it leaves little time for live online play.

Endgame Training

Followers of Chess Skills well know that I advocate simplification of complex positions into easily won pawn or even rook endgames. In "Elementary Positions" and a few subsequent posts, I've discussed positions in Laszlo Polgar's massive collection. In the 318 "elementary positions," the first two are basic heavy piece checkmates. Then, number 3 through 99 are pawn endgames. It is my intention to finish these pawn endgames in January, then play against the computer the 100 in Finali di Pedone II from DejaScacchi (there may be some duplicates), followed by working through the other 219 elementary positions in Polgar's book. This endgame work should be finished prior to summer. At that point, further study of Dvoretsky's Endgame Manual and Silman's Complete Endgame Course may be in order.


Last June I put forth a resolution regarding tactical training and the consequent development of technique. In this endeavor, I have been inconsistent, averaging about half of that time, but missing many weeks. In 2009, I resolve to find these ninety minutes every week. Most often, this training will focus upon the positions in Fred Reinfeld, 1001 Winning Chess Sacrifices and Combinations, but from time to time will include play from problems in Paata Gaprindashvili, Imagination in Chess, or other texts.

Rating History

I crossed over 1600 into the B Class in late 2005 and climbed steadily to 1722 by February 2007, but then dropped below 1700 later that month. I next crossed 1700 on the way up in March this year, have maintained my rating in the 1700s since then, and am ending the year at 1722. In 2007, 1722 was my peak; in 2008 it has served as a valley.

When I started playing USCF tournaments in the mid-1990s, I established a rating in C Class, nearly won my section of the Washington Class Championship (see diagram), and only dipped into D Class through one dark period following my stellar 0-5 record in the 1998 Collyer Memorial Tournament. Five months and three tournaments later, I was back in the 1400s, but it took me seven years to climb out of C.

In round four on board one in the 1996 Washington Class Championship, I had this position and the move.

Black to move -+

I considered, but did not play the key move here. Since then, I've played it and defeated Chessmaster, Fritz, and Hiarcs. A win in this game would have guaranteed a tie for first, which is what my opponent earned as a consequence of my failure. Had I won this game, my first published established rating would have been in the mid-1500s. As a result of the loss (and the subsequent game), it was 1495. Instead of winning my section, I tied for places 8-15, and am listed as 15th in the crosstable.

In 2008, I played for the Spokane City Championship. In that match I earned my first rated draw with a chess master. I'd like to add some more scalps in 2009.

26 December 2008

Reinfeld Tactic

Black to move

Black wins material with a double attack, but not quite as much as claimed by Fred Reinfeld in 1001 Winning Chess Sacrifices and Combinations. I've listed this problem among my partial busts because Reinfeld's solution is flawed. Nevertheless, after the tactic, Black does get a winning advantage. At least my engine thinks so. Several moves into the position, however, I lost my way and my engine, playing White, built up a significant advantage.

For more on the training regimen that brought up this problem this morning, see "Where the Rubber Meets the Road," "Back to the Mines," and "Ninety Minutes."

19 December 2008

Outside Passed Pawn

Lessons and training positions emerged from another game with Ryan Ackerman. I traded our last bishops off the board to create a king and pawn endgame. I had a four to three majority on the kingside, but he had a passed a-pawn.

An outside passed pawn usually means a positional advantage sufficient to win. This pawn will draw off the enemy king, allowing our own king to be the first to attack the enemy pawns.
Mark Dvoretsky, Dvoretsky's Endgame Manual, 44.
From this assertion, Dvoretsky goes on to mention several exceptions, including Hansen-Nimzovitch:

Black to move

White threatens to play c2-c3, creating a passed a-pawn. Yet, Black won this game by activating his king.

In the game against Ryan, he pushed his a-pawn at the right moment, his king took care of my majority, and my king was too far away to do anything about his last pawn.

After the game, he created a position for us to explore further.

White to move

Playing around with an old version of Fritz on a slow computer, Black managed to draw this game once. But, most of our efforts resulted in White wins. Can Black draw with best play?

Explorations in History

Looking through my database for similar problems, I found these positions from the nineteenth century.

From Kolisch-Shumov, St. Petersburg 1862

Black to move

White has just played 45.Rxa2, to which Black replied 45...Rxa2. Does the resulting king and pawn endgame give White a decisive advantage?

From Tarrasch-Berger, Breslau 1889

White to move

Tarrasch played 36.Qxf8+!? Does this queen exchange maintain a decisive advantage?

From Weiss-Mason, Breslau 1889

Black to move

Mason played 27...Rxe6. Does this exchange of rooks give White a winning king and pawn endgame?

17 December 2008

Beware Stalemate

When I was preparing for the Spokane City Championship last summer, John Julian told me to figure out what my opponent needed to do to beat me, and take that away. It was good advice, but not so easy to apply when there is so much else to think about.

Corresponding to that idea is the recognition of the opponent's drawing resources when a win is imminent. Such is the case in this simple looking king and pawn exercise from Laszlo Polgar, Chess Endgames.

White to move +-

Among Black's resources is the sacrifice of the a-pawn with the hope of reaching this fantasy position.

Black to move =

15 December 2008

Solve This

Black to move

I had Black and this position against K. Korsmo in the Winter Club Championship two years ago. After the game, I was surprised when Fritz 9 required seven minutes to find my winning idea. It's not often that my understanding exceeds the abilities of my software.

Solve This

Throughout this blog, I use the label "Solve This" when a post has a problem, study, or position from a game, but I have not included the correct line of play within the post. These posts invite solving efforts from readers. Initially, I thought to post problems in this manner, and then a few days later I would follow with "Solve This Solutions." This effort proved more trouble than it was worth, so now I post the answers in the comments after there have been responses.

This post is the 37th labeled "Solve This." Many of these posts have no comments.

13 December 2008

Quest for the Best

Which epic chess battles stand above the others?

The World's Greatest Chess Games (1998) by Graham Burgess, John Nunn, and John Emms presents analysis of one hundred games from the sixteenth game of the 1834 match between Alexander McDonnell and Louis Charles de Labourdonnais to Viswanathan Anand's defeat of Joel Lautier at the Biel Chess Festival, 1997. The list of the best one hundred in Burgess, et al. needs to be updated to embrace games played since 1997, but it is a start.

Chess Informant's Best of the Best 1000 (2008) republishes games that appeared in Chess Informant from the inaugural issue in 1966 to CI 100, published in December 2007. Black's win in Nielsen-Ivanchuk was judged the best of that volume, edging out Sandipan-Tiviakov (Sandipan won) by one point.

The best game of each volume is chosen by a panel of judges, usually numbering nine, but volume 14 had seven, and three volumes have had ten. Through the past three years, eight judges have become the norm. Each judge rates the ten best games. Each judge's best gets ten points, number two gets nine, and so on. The tally determines the winner, which is republished in the next volume along with the scores. These one hundred Golden Games produce a list of the best games 1966-2007.

These two lists of one hundred differ, and not only because they cover different spans of time. In the Chess Informant series, Vladimir Kramnik's round six win with Black over Garry Kasparov at Dos Hermanas 1996 received the third highest vote total of all the Golden Games,* but it is Kramnik's eighth round win (again with Black) over Ivanchuk that appears in The World's Greatest Chess Games. That game finished second in the polling of judges, although it garnered first place votes from Bareev and Shirov. Kramnik earned 87 of 90 possible for the win over Kasparov, but 55/90 for the game against Ivanchuk. In the voting for CI 66, third place (Kasparov's loss to Topalov) and seventh (Ivanchuk's loss to Anand) were also from the Dos Hermanas event.

Concerning the win over Ivanchuk, Burgess and crew wrote:
This game embodies the best element's of today's younger generation: a carefully prepared opening novelty involving a positional sacrifice; dynamic and aggressive play; refusal to be content with a draw; finally, exact calculation in an ultra-sharp position. Ivanchuk's efforts at counterplay are no less ingenious than Kramnik's attacking manoeuvres, but it takes only a small slip for White's king to succumb.
Burgess, et al., World's Greatest Chess Games, 540
Against Kasparov, Kramnik's haste in time trouble did not produce the best move from this position, although his move was adequate for victory.

Black to move

What was Black's most convincing continuation?

Reader's Contest

I wrote about the Chess Informant text in "La crème de la crème," but did not emphasize the contest open to anyone that purchased the book. Readers are asked to pick the ten best Golden Games. Those participants whose selections are most consistent with the aggregate will win more Informant goods. As the end of December looms, the pressure mounts to complete my entry. It is not an easy matter to choose.

What criteria should I employ?

Brilliant innovation?
Triumph over stubborn opposition?
Instructive value?
Error free execution?
Historic significance?
Statistical analysis of voting patterns?
Political considerations?
Favorite players?

Among the candidates, there is certainly a lot to be said for Veselin Topalov's speculative sacrifice from Topalov-Anand, Sofia 2005.

White to move


In Anand's annotations to the game, it was the novelty 11.Neg5, preparing this move, that merited the good move symbol. It is a great game due to Anand's able defense through Topalov's persistent and ultimately successful attack from his opening novelty through the endgame.

White to move

After 52.Nf5, Anand resigned. Black can promote the pawn, but that leads to checkmate in four. The alternative--bringing the rook back for defense, then promoting the pawn--loses the newly made queen and the rook, and then White's a-pawn can promote unless White opts to mate with the two minor pieces.

This entire game is replayable at ChessBase News, and there are many places online to find analysis, including SimpleMind blog.

*Ivanchuk-Shirov, Wijk aan Zee 1996 (CI 65/417) also scored 87/90 in the vote tally. Alexei Shirov, who lost this game, was one of two judges that did not give it first place.

12 December 2008

Utter Chaos

As a rule I do not play dual rated events--events in which the USCF will apply changes to both the quick and the standard ratings of the participants. Blitz and rapid chess involve a lot of smoke and mirrors, while standard chess is a quest for truth. In dual rated events, the standard rating is put at risk by substandard play. On the other hand, ratings are insignificant unless one plays. Refusing certain events to preserve one's rating violates higher principles than not playing as a matter of principle.

Despite my inconsistent performance year after year, the gains over the past ten months have elevated me among the higher rated active players in my city. The top players have a responsibility to play in as many events as possible, donating their rating points to those able to take them. Raising their ratings only if they play without error.

David Griffin, who also has climbed roughly 100 points in the past year, was able to improve his rating a few more points at my expense, as he did in the touch move lesson in November.

There were two rounds last night in this game/45 event called Christmas Chaos. I played opening lines that are not my norm. As White, I played 1.e4, and an odd line of the c3 Sicilian--2.Nf3 before 3.c3. Against Griffin, I had Black and played the Dutch Defense.

After twenty minutes each, we reached this position for my move 24.

Black to move

I played 24...Nh5 to continue my plan behind the strange positioning of my queen on the h-file.

25.Bxg7 Kxg7 26.Ng4 Bxg4

I spent five minutes on this move, calculating not it, but my next one.


Black to move

27...Ng3+! 28.hxg3

Black to move

Here I spent another seven minutes, running my clock down to just over six minutes remaining. I found the best move, but missed a checkmate in two on the next move.

Is the calculation easier without the pressure? Can you work out a clear win for Black?

I know the answer because I spent another thirty minutes with this position last night when I should have been sleeping.

10 December 2008

From the French

Yesterday, during the meeting of the Mead High School Chess Club, for which I am the advisor, I played some games with Ryan Ackerman, one of the strongest youth players in Spokane. I took White and played the advance against his French. As I too am a devotee of the French, I struggle psychologically when playing the White pieces--I'm playing for equality instead of for an advantage. By the third game I was doing better until I tried to press an illusory advantage, and that cost me a pawn. We reached a tense tactical position where I was able to pin almost all of his pieces. He didn't like that position so we backed up some moves and traded queens instead.

We then reached this position.

Black to move

I suggested that Black had a fairly straightforward win with simplification to a rook and pawn endgame. We turned the board around, and he tried to defend against my ideas. My argument was that Black gets a more active rook and king, and that when the a-pawn finally falls, White will have made more serious concessions in the center.

Am I correct?
Was this useful advice from a B player to a strong C player that will probably get to A class ahead of me?

Ryan and I discovered that Black needed to advance the a-pawn rapidly, then bring the king over. We were not certain what each side should try for on the kingside.

I tried it against Hiarcs 12 this morning before work.

1...Rxd2 2.R1xd2 Bxd2 3.Rxd2 a4 4.Rb2 (Ryan played Kf1) a3 5.Ra2 Kf7

White to move -+

After many more moves against the silicon beast, the box resigned in this position:

White to move

It seems from my play against Hiarcs this morning that my advice has merit. But, perhaps it's better to keep more pieces on the board. Perhaps these rook and pawn endgames are not so routine.

It may be worth remembering the adage:
All rook endgames are drawn.
Saviely Tartakower*
See "Okay, Not So Easy" for more discussion of similar endgames.

*It is not entirely clear that Tartakower ever made such a statement. An unsourced comment in Frank Brady, Bobby Fischer: Profile of a Prodigy (1973) states that Tigran Petrosian took comfort recalling this saying while defending a rook endgame against Bobby Fischer (166). Often the statement reads slightly differently: "all rook and pawn endgames are drawn." Others attribute the quote to Siegbert Tarrasch, who did write something similar: "In rook endings the weaker side generally has some chances of a draw right up to the very end" (Tarrasch, The Game of Chess [1935], 81, translated from Das Endspiel [1931]). See Edward Winter, Chess Notes 5822.

09 December 2008

Another day, another blitz trap

After Saturday's disaster, I won both games on Sunday. I ended the tournament with an even score: two losses and the "old man bye" on Saturday, two wins on Sunday. All of my opponents had lower published ratings than me , so mine took a plunge (down 20 to 1722).

In round two I reached this position with the move.

Black to move

I played 16...Rxh7?? and slowly was ground down. This position came as a result of both players missing tactics, just as we did in our game in September.

Nursing the Blitz Addiction

My Sunday morning warm-up contained a tactic that is easy when you know you're looking at a problem, but sometimes players fail to solve it with seconds on the clock. Here's another example of the same pattern.

White to move

Inexplicably, White played 20.Nxd4??

The rest was easy. It was a 3 minute game. The blunder from this position took 1.5 seconds off the clock. My last five moves also took 1.5 seconds.

See also Damiano's Mate.

07 December 2008


Bad day yesterday. I lost two games, a trauma last suffered in OTB play in February 2007. I have two more games today. A little online blitz to get ready produced this position.

Black to move

White has several checkmate threats.

05 December 2008

Endgame Calculation

White to move +-
Rinck 1922

Of course the king cannot catch the pawn. This one is too easy.

1.a4 Kb3 2.a5 Kc3 3.a6??

Black to move =


Something went wrong. Both players will promote and reach a drawn queen endgame.

White needed to play 3.Kg1

Drawing Resource

Black's defensive strategy in Henri Rinck's 1922 composition employs the idea from a study by Richard Reti from the previous year.

White to move =
Reti 1921

The White king can catch the Black pawn because of the strange geometry of the chess board. The shortest distance is not a straight line. The king's route h8-g7-f6-e5 combines the threat of supporting the c-pawn with the chase of Black's h-pawn. Either both players queen, or both pawns fall.

Rinck's 1922 study, which appears as #53 in Laszlo Polgar, Chess Endgames (1999), is not as simple as it looks. The first move is easy: the pawn must run. But from the diagram position, the solver must calculate the point at which the king must move to stop Black's drawing threats. Move three is critical. If Black tries 2...Kc3, White must play 3.Kg1. If Black tries 2...Kc4, White must play 3.a6.

After 1.a4 Kb3 2.a5 Kc4 3.a6 Kd3 4.a7 f2! Black also promotes and more calculation is needed.

If Black promotes to a queen, White wins the queen with a skewer. This line is the one given in Polgar's solution. Hiarcs 12 promoted with check: the pawn became a knight. Its tablebases revealed that queen promotion led to checkmate in eleven, while underpromotion to the knight was checkmate in eighteen.

After the underpromotion, White still has some work. A human under time pressure can easily falter and permit a devastating fork, Black's final drawing resource.

04 December 2008

Sixteen Million

How many possible legal endgame positions exist in which each player has a single pawn and king, and nothing more?

I flunked calculus. My pathetic performance was due not to inability, but lack of time. I took the course as a junior in college when I was deep in my upper division history, political science, and education classes. I was also active in student government. I tried to do all the week's homework on Saturdays. The quizzes were every Friday. I did okay on the exams, but flunked most quizzes, and finally dropped the class after the deadline.

That was twenty-five years ago.

I bring up this history to emphasize that I am not a mathematician, but that I went far enough in school that I should understand the rudiments of algebra.

Others have calculated the exact figure I'm looking for, but instead of finding their work, I tried to estimate it myself. My rough estimate is 16 million.

Method of Calculation

Each pawn has 48 legal squares. If an enemy pawn is on the board, this number is reduced by 1.

47 x 47 = 2209

Each king has 64 legal squares. If one king is in the corner (4 squares), the other king's number must be reduced by 4. On the edge, but not a corner (24 squares) reduces the other king's number by 6. A king that is not on the edge (36 squares) reduces the other king's legal squares by 9.

4 x 60 = 240
24 x 58 = 1392
36 x 55 = 1980
240 + 1392 + 1980 = 3612

The number of possible pawn positions must be multiplied by the number of possible king positions to arrive at an upper limit.

2209 x 3612 = 7,978,908

For each position, it can be White on move or Black on move

2 x 7,978,908 = 15,957,816

Our upper limit is just under sixteen million.

This number is too high. Each placement of the pawns reduces each king's placement by 3-4 squares. Neither king may occupy the same square as a pawn. A pawn not on the edge controls two squares, while a pawn on the edge controls one. The occupied squares plus the controlled squares is usually 4, but sometimes 3.

The actual number may be several thousand below that number.


This figure of sixteen million is a subset of all four-piece endgames, all of which were calculated to completion in the creation of endgame tablebases. Most chess engines contain these tablebases as part of the package. Thus the engine will play all these positions to perfection.

Humans are another matter.

We spend years studying elementary king and pawn endgames, yet still we blow them from time to time.

Mark Dvoretsky presents the following position as one of his many tragicomedies. See Dvoretsky's Endgame Manual (2003), 14.

White to move =

White resigned.

Postscript: 5 December 2008

Eric Holcomb wrote a two-part article for Northwest Chess: "So How Many Chess Board Positions Are There?" (August 2008), 13-14, and "An Inconvenient Chessic Coincidence?" (September 2008), 22-23. I asked him to look at this post and offer critique. He noted that the first pawn has 48 squares and the second 47, so the calculation above should be

47 x 48 = 2256

That pushes the upper limit above sixteen million to 16,297,344. He also wrote an Excel macro to perform these calculations, and found the result of 14,872,176, 91.26% of the upper limit.

In practical terms--constructing tablebases or human learning of critical positions--the number of unique positions is a fraction of the nearly fifteen million Holcomb found.

David Levy and Monty Newborn explain significance of symmetry in How Computers Play Chess (1991), 141-142. They present the example of a KQK database. The black king can be placed on any of 64 squares, but only ten must be considered.

With respect to pawn endgames, symmetry would seem to reduce the number of possibilities at least three quarters.


White's resignation in the position above overlooked that even though the pawn is lost, after 1.Kd4 Kf5 2.Kd3 Ke5 3.Ke3 Kxd5 4.Kd3 White seizes the opposition and draws.

02 December 2008

Ladislav Prokeš

Continuing through the Elementary positions in Laszlo Polgar, Chess Endgames, I came to number 50, attributed to Prokes, 1937.

White to move +-

The direct effort of pushing the a-pawn leads to this theoretical draw:

White to move =

The other logical try begins 1.Kf5 h3 2.Kg4 Kg2 3.a6 h2 4.a7 h1Q

White to move +-

Black queens first, but White gets the first check. After some maneuvering, Black will be in zugzwang. The queen finally can move, but every move results either in the loss of the queen with mate to follow, or to immediate checkmate.

Black to move +-

The Composer

According to Harold van der Heijden, Ladislav Prokeš (1884-1966) is the fourth most prolific composer of chess endgames ("My Computerised Collection," EG 130 [October 1988], 413). He published over one thousand studies through the course of his life.
If there is a single composer whose work is likely to make studies really popular, that composer is Prokes. His positions have few pieces, and the pieces are naturally placed. The solution is short. Profound and lengthy analysis is not needed. The position leads the solver to think that a direct game-approach is sufficient, so that when this proves not to be so the solver will have learned something, and he will have been pleasantly surprised. This means that what he learns he is likely to retain, and from a typical Prokes study he can learn not only the tactical trick or tricks that are the composer's idea but also the simple ground rules of theory that dictate the course of moves.
A.J. Roycroft, "Ladislav Prokes: The Player's Composer," EG 7 (January 1967), 157-158.
The Prokes maneuver, described well at Wikipedia with a link to a more detailed article at Tim Krabbe's excellent site, is worth knowing about. Also worth knowing is this elementary position that appears as Polgar #14 in Chess Endgames without attribution to Prokes. It is attributed to him in Irving Chernev, Practical Chess Endgames (1961), 15.

White to play +-

Chernev is succinct: "White wins this ending by getting the opposition, and maintaining it" (15).

30 November 2008

Elementary Positions

The heaviest endgame book on my shelf is Laszlo Polgar's seemingly rare Chess Endgames (1999). In the United States, Amazon.com lists one copy available from a vendor for $574.53, but Amazon.de lists seven used copies starting at 15.00 EUR and three new from 23.90 EUR. The text is out of print, and appears more readily available in Europe than in the United States. Fortunately, I bought my copy eight or nine years ago for something close to the list price of $29 plus shipping.

It is a daunting book that I use mostly for reference. On the other hand, from time to time I resolve to work through in a short period of time the first 318 problems--called "elementary positions".

This resolution always leads to failure because these elementary positions include quite a few that present difficulties. Consider number 42 for instance:

White to move +-

White has a decisive advantage, but how?

The Composer

This position is attributed to Crum, 1913, probably John Crum--Polgar's source gives no more than last name and date. Irving Chernev's Practical Chess Endings (1961) also has this problem (61), as well as another by Crum from 1913. Polgar has at least one more Crum composition, number 443, dated 1921.

White to move +-

A Google search for chess and Crum turns up in Google Books a J. Crum who was a "First-Class amateur" that lost game number 2659 published in the British Chess Magazine (October 1905). There is also a reference in Edward Winter's Chess Notes 4744 to a Mr. Crum who offered a suggested improvement in a game lost to Joseph Henry Blackburne, who won blindfolded. Crum was also the contact for entries to a problem composition contest sponsored by Chess Player's Chronicle, and open to all the world according to the announcement in the Westminster Papers 1 November 1878 (150).

The website Chess Scotland offers more information: John Crum was the first Scottish Champion, winning the title in 1884, and was a noted endgame composer. Tim Harding's Chess Cafe column The Kibitzer mentions the role of Crum in a postal match between the Glasgow and Copenhagen chess clubs that took place in 1879-1880 and was reported more fully in the Danish magazine Nordisk Skaktidende than in a Scottish publication where he had found part of the game.

28 November 2008

Okay, Not So Easy

In"Training Exercises" I claimed to have achieved "an easily won game" as a result of an exchange sacrifice that was far from the best move in the position. In the comments, both Chesstiger and Rolling Pawns questioned my assertion.
All rook endgames are drawn.
Siegbert Tarrasch*
Ten moves against the computer from the first problem in Imagination in Chess led me to this position.

Black to move

Hiarcs 10 - Stripes,J
Progressive Thinking, 26.11.2008

I played 11... Ra4 with the idea of attacking the knight and passed c-pawn.

Play continued 12.Rd7 Rxd4 the exchange sacrifice

13.Rxd4 Rxc2+ 14.Ke3 Ra2

White to move

6k1/5p1p/6p1/p5P1/3RP2P/4K3/r7/8 w

I propose that this position might be useful for training against the computer as a means of developing endgame skill. Black has an outside passed pawn and has better pawns on the other side of the board. On the other hand, White has some play. White will quickly bring the rook behind Black's passed pawn via d8 or d7, and the e-pawn might threaten some disruption. My first effort was smooth and successful, but I tried again several more times after reading the comments in reply to my assertion that it was easy. I tried the position against several different engines--Hiarcs 10 and 12, Fritz 9--with modest success. I did not succeed in winning every effort.

Black has a technical win, but my assertion that is is easy overreaches a bit.

Mixed Results

The "Easy" Win

15.Rd8+ Kg7 16.Rd7 a4 17.e5

17...Kf8 18.Ra7 a3 19.Kd4 Ra1 20.Kc4 a2 21.Kb3

21...Rh1 22.Rxa2 Rxh4 23.Ra5 Ke7 24.Kc3 Ke6 25.Kd3 Rg4 26.Ra6+ Kxe5 27.Ra7 Rxg5 28.Rxf7 h5 29.Ke2 Rf5 30.Re7+

30...Kf6 seems worth considering with the idea of keeping the White king from in front of the pawns

31.Kf2 Kg4+ 32.Kg1 h4 33.Re4+ Rf4 34.Re6 g5 35.Rg6 Rb4 36.Ra6 h3 37.Kh2 Rb2+ 38.Kh1 Kh4

If not for the h-pawn, White could play Ra3 and draw (Philidor position).

39.Ra4+ g4 40.Kg1 Rg2+ 41.Kh1 Rg3 42.Kh2 Rb3 43.Kg1 Kg3 44.Ra1 Kf3 45.Rf1+ Ke2 46.Rf2+ Ke3 47.Rf8 Rb1+ 48.Kh2 Rb2+ 49.Kg1 g3 50.Ra8

This move seems inexplicable. But sometimes when the computer sees that checkmate is forced, it will make a stupid move as if in despair.

50.Re8+ Kd4 51.Re1 Rf2 52.Kh1 Kd3 53.Rb1 Ke2 54.Kg1 Kf3 55.Rb3+ Kg4 56.Rb4+ Rf4 57.Rb2 h2+ 58.Kg2 Rf2+ 59.Rxf2 gxf2 60.Kxf2 h1Q 61.Ke2 Qd5 62.Ke3 Kg3 63.Ke2 Qd4 64.Ke1 Kf3 65.Kf1 Qa1#

50...Rb1# 0–1

An Easier Win

Hiarcs 12 - Stripes,J
Progressive Thinking, 27.11.2008

15.Rd8+ Kg7 16.e5 a4 17.Ra8 a3 18.Ra7 Kf8 19.Kd4 Ra1 20.Kd3 a2 21.Kc2

21...Rh1 22.Kb2 a1Q+ 23.Rxa1 Rxa1 24.Kxa1 Ke7 0–1

Often the key to winning a rook and pawn endgame is conversion to an elementary king and pawn endgame.

A Variation that Failed

Hiarcs 12 - Stripes,J
Progressive Thinking, 27.11.2008

15.Rd8+ Kg7 16.e5

16...a4 is better. Black's a-pawn is the key to winning.

17.Rd7 Re1+
Black still wins with 17...Kf8

18.Kf4 Kf8 19.Ra7 Ra1 20.e6 Rf1+ 21.Kg4 fxe6 22.Rxa5 Rf5 23.Ra7 Rf7 24.Ra8+ Kg7 25.Re8 ½–½

Learning from Errors

My first effort against Fritz 9 encountered a different defensive strategy, and I failed.

Fritz 9 - Stripes,J
Progressive Thinking, 27.11.2008

14.Rd8+ I cannot explain why this move number is now 14 instead of fifteen Kg7 15.Ra8 a4 16.Ra7 a3 17.e5 Kf8 18.Kf4!

Fritz opts not to chase the a-pawn, preventing its promotion by another method.

18...Ra1 19.Kg3 a2 20.Kg2 Ke8 21.Kh2 Kd8 22.Ra8+ Ke7 23.Ra6 Kd7 24.Kg2 Kc7!

It is not necessary to protect the kingside pawns so long as the a-pawn is menacing.

25.Ra8 Kb7 26.Ra5 Kb6 27.Ra4 Kc5 28.Ra8 Kd5 29.Ra5+ Kc4 30.Ra7 Kb3 31.Rb7+ Kc3 32.Ra7 Kd4 33.Ra5 Ke4 34.Kh2 Kf4 35.Kg2 Kg4 36.Ra4+ Kh5 37.Kh2

37...Re1 38.Rxa2 Kxh4 39.Rf2 Kxg5 40.Rxf7 h5 41.Kg2 Rxe5 42.Rg7 Ra5 43.Kh3 Ra3+ 44.Kg2 Kf5

I've already demonstrated that I could win this sort of position. But I later got mixed up.

45.Rd7 Ra4 46.Kf3 h4 47.Rd5+ Ke6 48.Rb5 Kf6 49.Rb6+ Kg5 50.Rb5+ Kh6 51.Rb8 g5 52.Rh8+ Kg7 53.Rb8 Rf4+ 54.Kg2 Kg6 55.Ra8 Kf5 56.Kh3 Rf3+ 57.Kh2 Kg4 58.Ra4+ Rf4 59.Ra3 Rb4 60.Rc3 Kf4 61.Rc2 g4 62.Rf2+ Kg5 63.Ra2 h3 64.Kg3 Rb3+ 65.Kh2 Kh4 66.Ra4

66...Rb2+ 67.Kg1 Rb7 68.Kh2 Rf7 69.Rd4 Rf2+ 70.Kg1 Rf3 71.Kh2 Ra3 72.Rc4 Ra2+ 73.Kh1 Kg5 74.Rc5+ Kf4 75.Rc4+ Kf3 76.Rc3+ Kf2 77.Kh2 Ke1+ 78.Kg1 Rd2 79.Rc4 g3 80.Rc3 h2+ 81.Kh1 Kf2 82.Rxg3 Rd1+ 83.Kxh2 Rh1+ 84.Kxh1 Kxg3 ½–½

Trying again from the diagram after 66.Ra4:

Fritz 9 - Stripes,J
Progressive Thinking, 27.11.2008

66... Rb2+ 67.Kg1 Re2!

68.Ra6 g3 69.Ra4+ Kh5 70.Ra5+ Kg4 71.Ra4+ Kf3 72.Ra3+ Re3 73.Ra1

73...h2+ 74.Kh1 Kg4 75.Ra4+ Kh3 0–1

It's a long endgame from my training position, and perhaps not so easy. But, neither is such technique horribly complicated. With a bit of practice, these rook and pawn endgames can be won consistently.

*It is not entirely clear that Tarrasch ever made such a statement. An unsourced comment in Frank Brady, Bobby Fischer: Profile of a Prodigy (1973) states that Tigran Petrosian took comfort recalling this adage, attributed to Saviely Tartakower, while defending a rook endgame against Bobby Fischer (166). Often the statement as attribed to Tartakower reads slightly differently: "all rook and pawn endgames are drawn." Others attribute the quote to Tarrasch, who did write something similar: "In rook endings the weaker side generally has some chances of a draw right up to the very end" (Tarrasch, The Game of Chess [1935], 81, translated from Das Endspiel [1931]). See Edward Winter, Chess Notes 5822.