Understanding Rook vs. Minor Piece Endgames

By Karsten Müller and Yakov Konoval

A Journey into the Land of Rook vs. Minor Piece Endgames

Knowing the abilities and limitations of the minor pieces and their cooperation with a rook is very valuable for mastering the secrets of the royal game and this can be studied best in the endgame. The book before you now will take you into a mysterious and charming world. The actors in these fairy-tale stories are the rook, the bishop, and the knight.

This book is the third volume in the authors’ acclaimed Understanding Endgames series. It follows a dual philosophy, like their previous works, Understanding Rook Endgames and Understanding Minor Piece Endgames. It deals with seven-piece minor-piece endings in some detail. These endgames are often so deep that pre-tablebase analysis almost always contained errors.

Many new discoveries are revealed here. In addition, the authors emphasize the important five- and six-piece endings every club player should know. But to really understand minor piece endings, these theoretical positions are of course not enough. Sub-chapters on the principles of each material configuration have therefore been added.

“If you enjoy beauty in chess, if you want to improve your handling of the endgame, and if you want to become closer friends with the rook, bishop, and knight on the chessboard, then this journey into the land of rook and minor piece endgames will reward you.” – from the Foreword by Alex Fishbein

• Language: English
• Publisher: Russell Enterprises, Inc.
• Release date: Jan 10, 2020
• ISBN: 9781949859126

Karsten Müller

International Grandmaster Karsten Müller is recognized as one of the world’s top endgame experts. He is the author of many books on endgames and chess tactics. He is the author of over a dozen chess books published by Russell Enterprises.

Book preview

Composers

Bibliography

Books

Dvoretsky’s Endgame Manual, Mark Dvoretsky, Russell Enterprises 2003, 4th edition 2014

Encyclopedia of Chess Endings (ECE)

Fundamental Chess Endings, Müller and Lamprecht, GAMBIT 2001

How to Play Chess Endgames, Müller and Pajeken, GAMBIT 2008

Nunn’s Chess Endings, John Nunn, GAMBIT 2010

Understanding Chess Endgames, John Nunn, GAMBIT 2009

Understanding Minor Piece Endgames, Müller and Konoval, Russell Enterprises 2018

Understanding Rook Endgames, Müller and Konoval, GAMBIT 2016

DVDs

Chess Endgames 1-14, Müller, ChessBase Fritztrainer DVDs, Hamburg 2006-2013

Periodicals and Magazines

ChessBase Magazine (CBM) and CBM Blog at ChessBase.com

Chess Informant

Chess Today

Endgame Corner at ChessCafe.com

New in Chess Magazine

The Week in Chess

Databases and Programs

ChessBase Let’s Check online database

ChessBase MEGABASE 2018

Harold van der Heijden’s study database

Komodo 12

Konoval five-, six- and seven-piece tablebases

Lomonosov seven-piece tablebase

Nalimov five-, and six-piece tablebases

Stockfish 9

Syzygy five-, six- and seven-piece tablebases

Preface

Knowing the abilities and limitations of the minor pieces and their cooperation with a rook is very valuable for mastering the secrets of the royal game and this can be studied best in the endgame. There are already many books dealing with the issue, so why have we added another one to the collection? Computer technology is getting all the time and it is advancing endgame theory.

Yakov Konoval and Marc Bourzutschky have created seven-piece tablebases and so the definitive verdict on all such positions and optimal lines are certainly known. Now seven-piece Lomonosov Tablebases are available online. They allow the evaluation of any given position. But Marc and Yakov have developed additional software which allows one to obtain additional interesting data automatically such as long wins, zugzwangs, typical positions, etc.. Thanks to this software, there are many new discoveries in this book.

As the previous two volumes in this series, Understanding Rook Endgames and Understanding Minor Piece Endgames, this volume follows a dual philosophy. We deal with the seven-piece endings in great detail. They are often so deep that pre-tablebase analysis almost always contains mistakes. Many new discoveries are revealed here. We have also added the important five- and six-piece endings a club player should know. But to really understand the fight of minor piece against and with rooks, these theoretical positions are of course not enough. So we have added subchapters on the principles of each material configuration. Finally we want to thank Vladimir Makhnychev and Victor Zakharov for assisting with access to the Lomonosov Tablebases and Alex Fishbein for his excellent foreword.

Karsten Müller and Yakov Konoval

March 2019

Foreword

When I was growing up, my bedtime story books included Averbakh’s endgame books. Today, German grandmaster Karsten Müller is no less an endgame authority and connoisseur than Averbakh back in the day. Karsten Müller’s latest work, Understanding Rook and Minor Piece Endings, co-written with Yakov Konoval, is especially interesting because of the variety of the positions it covers. The book before you now will take you into a mysterious and charming world. The actors in these fairy-tale stories are the rook, the bishop, and the knight.

As an endgame junkie myself, I agree with José Raúl Capablanca that the student should start with study of the endgame, before the opening and middlegame. But why is that? And, more importantly, how should you study the endgame and what do you need to gain from that study?

For me, a valuable endgame lesson is one where I come away with a deeper understanding of, or rather a deeper feeling for, what the pieces can do. I want the pieces to come to life before my eyes, so that I know when they are strong and when they are weak, when they should be sacrificed for a higher purpose or when they deliver the crushing blow. Positions with minimal material offer the best glimpse into the geometry of the chessboard. When only the rook and knight remain, for example, it is easier to see who they really are. That is why I study the endgame.

Karsten Müller offers many such lessons in this book. He starts, in fact, with the rook vs knight pawnless ending, and shows that it is not as simple as commonly thought. I was surprised how often even very strong grandmasters made mistakes in what looks like a book position, and I learned something about what to do with the knight when it is in danger of ending up on the vulnerable g2 (or g7, b2, b7) square.

My least favorite part of endgame study is memorization of exact positions. I almost never do it! I have seen many books that classify their material into an endless set of exact positions, most of which will probably never occur in your games. Müller is very careful to avoid this pitfall. He has structured the book around ideas rather than theoretical positions. To be sure, there are a couple of cases where the position and method need to be memorized, and on those rare occasions he makes a point to note that. But most examples are real-life games (not even endgame studies), where actual humans play, often making mistakes. A lot of positions are borderline cases, straddling between a win and a draw, and that is where the struggle between the pieces becomes the most fascinating and instructive.

There were quite a few revelations for me in this book. For example, the rook vs. bishop fortress with pawns on one side is not as easy to hold as I had been taught (position 02.58) or it can be altogether losing (position 02.60). There is long analysis which you are not going to remember, and on no account should you try to memorize it. Sometimes there are not any obvious generalizations to be made. But positions with no clear guidelines are perhaps even more valuable than positions in which everything can be broken down logically. When you study these border cases, you will improve your endgame intuition and come closer to the stage where the pieces and their possibilities become second nature to you. And besides, positions with a real struggle occur more often than positions where everything is already well known.

From a point of view of the relative value of the pieces, it was interesting to me that the rook and two connected pawns win against the two bishops when they sometimes have trouble winning against the bishop and knight (I thought the two bishops worked well together in the ending!) The strength of the rook is also illustrated in its ability to defend successfully against the knight and two or even three passed pawns.

Karsten Müller is undoubtedly well known to many readers of endgame books, as the grandmaster who has analyzed many historically important games and that analysis has appeared in many places. He has even analyzed one or two of my endgames, and I have asked him for his opinion on my play and analysis. His co-author, Yakov Konoval, is not as renowned. But his contribution to this book is crucial, and this brings us to another key distinguishing quality of the book you are about to read.

Of course, the 21st century has seen a revolution in analysis of chess in general, and of endgames in particular. For a long time, authors had to perform painstaking work on their own, or rely on established sources, and still could not avoid mistakes, even in positions with a small number of pieces. But about 15 years ago, the six-piece endgame tablebase became available to everyone on the internet. That means that any position with six or fewer pieces on the board (including kings) was solved exactly, for whether it is a win (and in how many moves) or a draw. More recently, the seven-piece tablebase has become available. Yakov Konoval is a programmer who has not only worked on tablebases but has also created methods to use the computer to find critical positions and improvements to previous theory. His status as co-author reflects the importance of the computer in the study of endgames today.

However, many endgames are not solved yet (for now). This book features some of the best examples of play in which there are many pieces and pawns on the board. Once you have learned how the rook and knight, or rook and bishop, relate to one another, you will learn how to tell whether the rook and bishop will work better than the rook and knight in a given position. Many endgame books define their scope to positions with only one piece on each side, or at most two pieces on one side and one piece on the other. Karsten Müller shows both positions with a relatively empty and relatively full board. The result, again, is a better practical value of the book as a whole.

If you enjoy beauty in chess, if you want to improve your handling of the endgame, and if you want to become closer friends with the rook, bishop, and knight on the chessboard, then this journey into the land of rook and minor piece endings will reward you.

Grandmaster Alex Fishbein

New Jersey

June 2019

The History of Creating Seven-Piece Endgame Tablebases

The idea to create chess endgame tablebases (EndGame Table Bases or in abbreviated form EGTB) arose in the late 1970s. Now this idea looks obvious and it is seems strange that EGTBs were not generated earlier. The idea behind such bases is that for a concrete combination of pieces, for example, the king and the queen against the king and the rook, it is possible to generate the complete table which contains evaluation for every concrete position – win in n moves, loss in m moves, draw, impossible positions.

Such table needs to be generated only once by the widely known method of retrograde analysis (the other name – width-first search). The key moment in construction of the table is the size, which strongly depends on the number of chess pieces on the board. With the tables containing three or four pieces, in general, there are no problems, and such EGTBs were created many years ago.

Tables for five pieces are hundreds of megabytes even compressed, but at the modern level of computer development, are constructed easily enough. They too have already been around a long time.

Tables for six pieces occupy, not compressed, on the order of several gigabytes. Here already there are some problems with their construction, mainly with time to generate them and hard drive storage space. Nevertheless, all six-piece tables in the Nalimov format (the most popular now) had been constructed by 2005. It is curious to note that the popular belief that tables with five pieces against a lone king do not exist, is not accurate; they have already been constructed. The six-piece Nalimov tables requires 1200 gigabytes of hard disk space.

The size of seven-piece tables is measured already in terabytes, and in 2005 many experts predicted the impossibility of construction of these tables given the modern level of hardware. The approximate parameters were not specified before 2010. Nevertheless, by the beginning of 2005, the American scientist and programmer Marc Bourzutschky had constructed the first seven-piece table base – a king and four knights against a king and a queen. This ending had been studied by the early 20th century study composer Alexei Troitsky. It is Interesting that his assessment that the four knights win has proven to be true.

Also in 2005, the Russian programmer Yakov Konoval had written a program to quickly generate the six-piece tablebases economically for PCs. The international collaboration of Marc and Yakov for the creation and the analysis of seven-piece databases has begun at the middle of 2005. Yakov developed the generator, and Marc – the program for verification of the constructed base (it guarantees almost absolute correctness of the tablebases) and a number of utilities for extraction of the information from the tablebases.

At present, work on the generator and the program for verifying bases has been completed. They are very efficient and it is possible to construct, with their help, all seven-piece bases. By the end of 2018, all seven-piece bases had been constructed by Marc on standard home computers with total size about 80 Terabytes. The calculation time for one seven-piece base fluctuates from several hours to one month, and the sizes of the bases generated are in the approximate range of one to 300 gigabytes.

Bases use the DTC measurement DTC – distance to conversion (i.e., captures and/or promotions of a pawn) unlike the Nalimov tablebases of Nalimov, which use the DTM measurement – distance to mate. Basically the measurement type is insignificant as the win with the tablebase will be reached using any measurement. The standard belief that the win with the DTM-base is faster, is at least debatable – a game usually does not proceed to mate. For example, in the ending the king and a queen against the king, the opponent, most likely, will resign. Karsten Müller believes that the DTM metric is often easier for human understanding as in the DTC metric, there might be hidden deep wins after the first conversion, e.g., in a resulting six-piece ending. But of course both metrics can have their advantages in certain specific positions: (D)

1.e7 is the normal human move and best according to the DTC metric.

1.Kc6 which is shortest in DTM-metric looks odd to the human eye.

00.01A DTC is better

00.01B DTM is better

The next position is mate in two and conversion in one:

1.Rg1! is DTM optimal and the human move.

1.Qg7+! is odd, but DTC optimal.

00.01C Underpromotions – 50-move rule, History table

Like in the Nalimov tablebases, in our bases, the en passant capture is considered, but the possibility of castling is not considered. Also we do not consider the rule of 50 moves; see below. At the end of 2006, we started construction of the seven-piece endings with pawns.

All three-seven piece endings from Understanding Rook Endgames were verified by Mark Bourzutschky and Yakov Konoval’s tablebases with all promotions. For Understanding Minor Piece Endgames we used seven-piece tablebases with only queen promotions, and then verified them with Lomonosov’s tablebases with all promotions. By the end of 2018, Marc Bourzutschky and Yakov Konoval had finished all their seven-piece tablebases with all promotions and we used these tablebases for this book.

Now some words about records and the rule of 50 moves. Before the construction of seven-piece bases, the longest known win in the endings was a win in 243 moves (before conversion) in the ending R+N vs. 2Ns, found by Lewis Stiller in 1991. Later it was established that the record to mate in this class of the endings would be 262 moves. It was further established that in the seven-piece endings there are longer wins. The previously mentioned win in 290 moves in the ending 2Rs+N vs. 2Rs became the first of them. And there are more.

In May 2006, the position with a win in 517 moves was found in the ending a QN vs. RBN. In general, in many pawnless endings, more than 50 moves before conversion are necessary for a win, which was already known for a number of six-piece and even five-piece endings, including an ending such as QR vs. Q. In this situation the rule of 50 moves, in Yakov Konoval’s opinion, demands clarification, as it apparently defies the logic of a chess struggle.

Note that in chess composition, i.e., studies and problems, this rule it is not taken into consideration at all. Of course it is easy to find positions where this rule is taken in account, but in some absolutely drawn positions, it is possible to play more than 500 moves.

Karsten Müller thinks that for a human over-the-board play, the 50-move rule should remain, as human play is not perfect anyway.

There were two interesting results which had been achieved by in 2009. The first was the construction of several eight-piece bases without pawns in which one side has two dark-square and two light-square bishops. The most interesting of them is the tablebase 4Bs vs. 2Rs. It appeared that generally four bishops win, and more than 50 moves are necessary to win.

The second result is the use of the idea about the limited promotions for finding of positions in which two underpromotions into different pieces are necessary for a win. This approach was suggested by well known mathematician and chess composer Noam Elkies and was implemented by Marc and Yakov. Thus the computer acts in a role of the composer of chess studies, while the human needs only to analyze the found positions and to decide, whether are they actual studies or not, possibly adding additional moves.

In fact, two studies by computer were already published and according to experts in chess composition (Oleg Pervakov and others) they are good enough.

In 2012 the team from the Moscow State University (Vladimir Makhnychev and Victor Zakharov) constructed seven-piece EGTBs using the supercomputer Lomonosov in the DTM format. Now their EGTBs are available online (for an honorarium) and it is possible to verify online any seven-piece position (except six pieces versus a lone king).

However, in our book, we use many utilities developed by Marc Bourzutschky and Yakov Konoval which allow the discovery of many interesting positions automatically from different chess bases.

Some main events in the history of creating chess endgame tablebases:

In 1965, Richard Bellman proposed the creation of a database to solve chess and checkers endgames using retrograde analysis. Instead of analyzing forward from the position currently on the board, the database would analyze backward from positions in which one player was checkmated or stalemated. Thus, a chess computer would no longer need to analyze endgame positions during the game, because they were solved beforehand. It would no longer make mistakes because the tablebase always played the best possible move.

In 1970, Thomas Strohlein published a doctoral thesis with analysis of the following classes of endgame: KQ vs. K, KR vs. K, KP vs. K, KQ vs. KR, KR vs. KB, and KR vs. KN.

In 1977 Thompson’s KQ vs. KR database was used in a match versus grandmaster Walter Browne. Ken Thompson and others helped extend tablebases to cover all four- and five-piece endgames, including in particular KBB vs. KN, KQP vs. KQ, and KRP vs. KR.

Lewis Stiller published a thesis with research on some six-piece tablebase endgames in 1995. More recent contributors have included the following: Eugene Nalimov, after whom the popular Nalimov tablebases are named; Eiko Bleicher, who adapted the tablebase concept to a program called Freezer; Guy Haworth, an academic at the University of Reading, who has been published extensively in the ICGA Journal and elsewhere; Marc Bourzutschky and Yakov Konoval, who have collaborated to analyze endgames with seven pieces on the board; Peter Karrer, who constructed a specialized seven-piece tablebase (KQPP vs. KQP) for the endgame of the Kasparov versus the World online match; Vladimir Makhnychev and Victor Zakharov from Moscow State University, who completed 4+3 DTM-tablebases (525 endings including KPPP vs. KPP) in July 2012.

The tablebases are named Lomonosov tablebases. The next set of 5+2 DTM-tablebases (350 endings including KPPPP vs. KP) was completed in August 2012. The high speed of generating the tablebases was a result of using a supercomputer named Lomonosov. The size of all tablebases