Knight and Bishop Checkmate: How and Why

Is is necessary to know a checkmate that you will never need to execute? Aside from deliberate choices due to underpromotion, I have never had to checkmate with a knight and a bishop in a game. I was on the weaker side in a blitz game on Internet Chess Club 25 years ago and got a draw because my opponent did not know how to perform the mate. I saw one young student try and fail in a youth tournament, and then in the very next round have the ending again, this time with the lone king and another draw.

In one tournament that I won, my last round opponent had failed to execute the checkmate in the previous round, else he could have won the event with a draw against me.

Many players never face it.

In Silman’s Complete Endgame Course: Beginner to Master (2007), Jeremy Silman writes:

I heretically decided not to include Bishop and Knight vs. Lone King because it’s far from easy to master, and it occurs very rarely in over-the-board play. In fact, I only got it once in my entire career, while IM John Watson and IM John Donaldson never got it at all! Is such a rarity really worth the two or three hours it would take to learn it? I say no. (xv)

On the other hand, Thomas Engqvist in 300 Most Important Chess Positions (2018) considers it of such importance that three of the 300 are concerned with this checkmate. Acknowledging its rarity (“it will probably happen once or twice in your life”), Engqvist states:

I used to teach children this endgame at a very early stage and they should know how to do it before they reach an Elo rating of 1500 to get a good feeling for how knight and bishop can harmonise together like a bishop pair. (184)

Practicing positions with few pieces develops understanding and appreciation of each piece’s unique capabilities. As Vasily Smyslov stated in Vasily Smyslov: Endgame Virtuoso (1997), "the properties and peculiarities of the pieces are most clearly revealed in the endgame" (6). Most chess study positions involve knowledge and skills that will be applied to other positions.

Yesterday, using the useful “Table of Computer Database Results for Pawnless Endings” in Karsten Müller and Frank Lamprecht, Fundamental Chess Endings (2001), I set up the knight and bishop ending that is longest distance to checkmate and played it against Stockfish. After my first five moves, I reached this position and noted the wall created on the central squares by the bishop and knight.

Black to move

I also worked through the three positions in Engqvist’s book. The first two involve the technique I have learned, forgotten, and relearned (see "Bishop and Knight Checkmate"). The third position is presented to teach the technique in lessons for beginners on Lichess that I have criticized it as more difficult.

It comes from Andre Chéron, Lehr-und Handbuch der Endspiele (1964). With Engqvist’s encouragement, I decided it was worth learning. It was not as difficult as I had thought and I spent some time practicing against the computer.

Then, I searched ChessBase Mega 2024 for endgames that reached a knight and bishop against a lone king. There are many more than I expected. Finding one that ended in a draw, I started going through the game. At several points where I thought I saw an improvement, I played from that position against Stockfish. Then, I used Stockfish and tablebases to identify areas where my play could be improved.

This exercise showed me that knowing more than one technique for executing the checkmate had practical implications. In a game, one might find one of the techniques is much faster than the other.

Here are some positions from that game. I do not know how much time pressure existed when the player was unable to finish successfully. An internet search turned up tournament information that listed the Black player’s rating as 1850.

Black to move

Black can force checkmate in 8 moves. The game went on another 20.

Nine moves earlier, Black had a mate in 9.

Black to move

A few moves prior, Black had a mate in 15, did not play it perfectly, but made progress as White did not offer the best defense.

Black to move

The closest Black came to finishing was mate in seven.

Black to move

109...Be3 (or Bf4, Bg5, Bh6) should be played, forcing White to the a-file. 110.Ka3 Kc3 111.Ka2 Bc1 and the bishop occupies the critical diagonal. 112.Kb1 Nd3 113.Ka2 Kc2 114.Ka1 Bb2+ 115.Ka2 Nb4#.

Students wanting to learn this checkmate could start with positions where checkmate can be forced in three to six moves and build from there.

Plagiarism and Related Crimes

Chess writers are notoriously lax with documentation. Many books contain none at all. Some highly regarded instructional manuals use positions from historic games, but do not name the players who produced the position through play. Knowing that Jose Capablanca won a particular endgame is not necessary to learn how a specific position that he played should be played. Even so, offering that information improves the instructional value by hinting at a direction for further study. Here, I am thinking of Jeremy Silman, Silman's Complete Endgame Course (2007), 294-296.

Garry Kasparov, My Great Predecessors, 5 vols. (2003-2006) serves as a terrific anthology of analysis of great games throughout chess history. Early volumes were criticized for poor documentation. Kasparov responded by including a partial bibliography at the end of volume 5. This reference list fails to address the sloppy practice of offering no more than a surname for most quotes from prior works, but at least acknowledges part of the problem in the early volumes.

Edward Winter has exposed many cases of lax sourcing as well as several of explicit plagiarism. See Chess Notes (search for plagiarism). Among the consequences of indiscriminate copying that he notes is the perpetuation of error. When one writer gets a date, location, players, or game score wrong, others will follow. It is the same with chess quotes. I'm tempted to speculate that fake chess quotes could be more frequent among chess enthusiasts than among politicians.

Chess Skills has previously noted errors in the history from which we get the name Pillsbury's Mate. Nonetheless, I often recommend Georges Renaud and Victor Kahn, The Art of the Checkmate (1953) for its pedagogical value despite sloppy sourcing (the Pillsbury Mate error may originate with the authors). Irving Chernev, The 1000 Best Short Games of Chess (1955) was instrumental in my growth as a chess player, but I criticized its sloppy history in my Amazon review of the book. Some readers have criticized my review.

For most chess players, instructive value is all that matters. Who cares if sources are cited? Who cares whether games are properly referenced? 

Social Media

Everything is free on the internet. Content creators find their work presented by others with no reference to who created it. Someone creates a puzzle from a game they are reviewing, but others have created the same puzzle from the same game before. Does it matter where you found it? Go ahead and share as if you were the one reading the book. 

A Facebook group that offers dozens of puzzles most days featured a puzzle from a game I was reviewing that morning. I shared it to the page. My post was presented under the name of the group’s administrator.

Two hours later, my original post was approved, placing that puzzle twice in that group’s feed. When I suggested that the administrator should have noted his source, we engaged in a heated discussion. He even claimed to have added the source information to the puzzle, although it is obvious that he copied and pasted. Note the proper use of a dash where 99.9% of everyone places a hyphen.* He even copied a typo in the book’s date of publication, which should be 1955. Copying replicates errors.

A few days later, he removed me from the group.

Several weeks earlier, I shared a different puzzle from an earlier game in the same book. I used a screenshot from chessgames.com to present the position and the names of the players. I did not mention chessgames.com. A comment accused me of plagiarism. I edited the post after some discussion with the accuser. Although I did not view sharing a screenshot from another site as plagiarism, providing a reference to chessgames.com did seem appropriate.

Some people care. Things on the internet are still protected by copyright.

*A hyphen is a unit of spelling. A dash is a unit of grammar. Adversaries in a contest should be separated by a dash. Such usage is extremely rare. Even so, my 99.9% is hyperbole.

Ten Books to Achieve 1800+

Having seen many lists of top ten chess books recommended for players at different levels, I thought it time to reflect on how books contributed to my rise from C Class to A Class. My first non-provisional rating was 1425 when I was in my mid-30s. I played chess competitively many years earlier, but no events were rated. In the late-1970s, I had a USCF correspondence rating. But when I returned to active play after graduate school, the USCF had lost the records of my postal chess.

I rejoined the Spokane Chess Club in late 1995 and played in my first rated OTB event in March 1996. In October, I played my sixth event and no longer had a provisional rating. By the end of the year, my rating had risen to 1495, but would not rise above that point until 2002. I remained in C Class until fall 2006. While on this plateau, I was gaining both knowledge and skills, but rating progress was slow. Too much online blitz may have held me back.

My journey from wholly ignorant beginner in the late-1960s, to competitive high school player in the late-1970s, to active C Class club member in the mid-1990s involved a lot of book study. Further progress from C Class in my 30s to high A Class in my early 50s included many books, active play, private lessons, chess videos, and I also started coaching elementary students in 2000.

It is no easy matter to choose ten books. By the time I reached A Class, I owned close to 300 chess books and there are very few I had not spent some time reading. At the same time, there are also very few that I read wholly. Some books, or my manner of reading them, may have held me back (just as hundreds of three minute blitz games every month may not have helped me).

The Ten

In November 1996, I played in the Washington Class in Federal Way. There was a book seller set up in one of the rooms near the playing hall. I spent a bit of time there talking with David Weinstock, owner of ChessMate. In our discussions, he recommended a book to me. I was skeptical. The title sounded more basic than my own self-assessment of my needs. Nonetheless, when I found the book at Auntie’s Bookstore when I was back in Spokane, I bought it and started to read it. It was transformative.

Consider my list of ten, pictured above and described below, as a provisional suggestion rooted in experience. What worked for me may or may not work for you. Read all recommendations with skepticism, but also with openness to trying something that might help. There are no magic books guaranteed to improve your chess, but only a few will fail to teach you something of value.

1) Georges Renaud, and Victor Kahn, The Art of the Checkmate (1953) was the book David suggested, and is my first recommendation. Having spent many hours in the 1970s learning the basic checkmates with heavy pieces and even two bishops, and having delivered many fine checkmates in many games, it was hard to believe there was much I could learn from such a book. Reading it, however, exposed me to new checkmate patterns, including some that I had seen, but not absorbed, from a book I studied in 1975: Irving Chernev, The 1000 Best Short Games of Chess (1955). Renaud and Kahn not only taught me new patterns, but they gave me a framework for thinking about checkmate and checkmate threats.

As David Weinstock had, I began to recommend The Art of the Checkmate to any and all who would listen, and also to many who ignore what I say. I still do. This book helped me, and it can help you. But there are other books that could substitute, and might be even better. Victor Henkin, 1000 Checkmate Combinations (2011) takes a slightly different approach. It also teaches an abundance of vital checkmate patterns and greatly exceeds Renaud and Kahn in the amount of study material. Antonio Gude, Fundamental Checkmates (2016) is another option. It is comprehensive and to an extent combines the approaches of Henkin with that of Renaud and Kahn. One can find dozens of other books on checkmate patterns, but these three stand above the others. Get one of them, or even all three.

Vital

2) For a year or longer, Lev Alburt, Chess Training Pocket Book: 300 Most Important Positions and Ideas, 2nd ed. (2000) was my bedside reading. I read it cover-to-cover twice. Alburt’s book was the only tactics book I finished prior to early 2023 when I finished all 1320 exercises in Sergey Ivashchenko, The Manual of Chess Combinations (1999). It is not an ordinary tactics book for practicing basic ideas, but rather, a small set of carefully chosen positions with tactical and positional concepts. It also has a small number of vital endgame positions.

Many grandiose claims have been made by different authors about the legendary 300 positions, but there should be no doubt that careful and deliberate study of a small number of carefully selected positions will take your game up a notch. Alburt’s book helped me. A few years after completing it, I began study of another book focused on 300 carefully selected positions: Rashid Ziyatdinev, GM-RAM: Essential Grandmaster Knowledge (2000). More recently, Thomas Engqvist has gained my attention, now with a trilogy of books containing 300 in the title.

An Idea Worth Considering

3) Quantity matters, too, when it comes to tactics training. A classic that has lifted the skills of generations of chess players has also been part of my training. Fred Reinfeld, 1001 Winning Chess Sacrifices and Combinations (1955) deserves a place in every chess player’s library. In 2008, I spent quite a bit of time playing these positions against the computer. Often I could find the tactic, achieve a clearly superior position, and yet still fail to defeat HIARCS (see "Where the Rubber Meets the Road"). Reinfeld organizes the chapters by themes—forks, pins, double attacks, and so on. I set my database containing these positions to open randomly so I did not know which theme to look for. But I also use the book, either solving from the diagrams or sometimes setting up the positions on a board.

Endgames have been vital to my success. In 2007-2008, I invested a lot of time teaching some elementary rook endings to my top student, the strongest third grader in my city. That summer, in the Spokane City Championship, I played two rook endings against FM David Sprenkle, drawing one game.

Currently, I’m on a collector’s quest to have 64 endgame texts in my personal library. The quest stems from my enjoyment studying positions with few pieces, my conviction that endgame knowledge is vital for all skill levels, and my involvement in an online community of book lovers, Chess Book Collectors on Facebook. During my rise from the 1500s in 2002 to high-1900s in 2012, much time was invested in endgame study.

4) The endgame book that did the most for me was Mark Dvoretsky, Dvoretsky’s Endgame Manual (2003). As one of ten books to recommend to class players, Dvoretsky is a controversial choice. Many players find it too difficult for anyone below master. Poppycock! Chess books are not novels. One does not read every word. Read the part that makes sense and push through a bit that stretches and challenges you. I have read the long chapter on pawn endings in Dvoretsky’s Endgame Manual several times and have flash cards containing the 48 blue diagrams that I use for review, study, and teaching (see "Pawn Endings Flash Cards"). I’ve struggled through perhaps half of the chapter on rook endings and made flash cards for the first 24 blue diagrams. Other chapters I have dipped into from time-to-time.

During the years spent studying Dvoretsky’s Endgame Manual, other books have also supplemented my work. These include, Bruce Pandolfini, Pandolfini’s Endgame Course (1988); Jeremy Silman, Silman’s Complete Endgame Course (2007); Karsten Müller and Frank Lamprecht, Fundamental Chess Endings (2001); and several others. My top recommendation for those looking to begin endgame study is Yury Averbakh, Chess Endings: Essential Knowledge (1993). There are many choices. Choose that one that you like, but do not neglect the endgame. Make endgame study a priority if you want to play better chess.

Splurge

5) Jacob Aagard, Excelling at Technical Chess (2004) also concerns the endgame. However, it is distinct from the endgame manuals listed above. The core of the book focuses on “seven technical tools”—schematic thinking, weaknesses, domination, do not hurry, passed pawns, how to arrange your pawns, and freaky aspects. Aagaard develops each of these ideas with compelling prose and detailed game analysis. As he states in the beginning, this book follows an approach that has made Mikhail Shereshevsky, Endgame Strategy so highly regarded. The technical tools are worthy of detailed attention, and I hope to find time to explore them in more detail. I blazed through this book is a couple of days, reading all the prose and glancing superficially at the game analysis. However, this superficial reading was enough to transform my game. My endgame play became more resilient. Formerly, I would often offer or accept a draw in seemingly equal positions. After reading the book, I play out most positions to the end, often lone kings. If there is any reason to play on—an imbalance, a weakness of any sort in my opponent’s position, even a better king position—a draw is anathema unless it secures a tournament victory.

Annotated games have always been a regular part of my chess study. In my youth, I spent many hours playing through games from three GM tournaments that resulted in books that I purchased: San Antonio, 1972; Leningrad, 1973 (the 42nd Soviet Championship); and Wijk aan Zee, 1975. In addition, I bought and still have two books by David Levy that were collections of games by specific players: Karpov’s Collected Games: All 530 Available Encounters, 1961-1974 (1975); and Gligoric’s Best Games, 1945-1970 (1972). All these books influenced my play as a teenager as I sought to imitate the play of the world’s elite.

6) In my 40s, I had many more chess books to choose from and studied annotated games from many of them. One source of such games that I returned to frequently is Garry Kasparov, My Great Predecessors, 5 vols. (2003-2006). Kasparov culls some of the best insights from many years of chess literature and presents many of the most important games of every world champion before him, as well as many contenders for that title who fell short. Chess history offers a reliable foundation for the development of chess skill. Although Kasparov does a poor job of documenting his sources (see my Patriots and Peoples blog for examples of sourcing problems in the writing of US history), the series remains an important practical overview of chess history.

7) Paul Morphy’s games are particularly useful to chess players who want to play well. Perhaps one day I will be able to report that I have played through every one of his available games. So far, I have been through at least one-third of them, some of them many times. His eighteen tournament games have been imposed by me on some two dozen students, who have been through all of them. I’ve shown the Opera game to students at least one hundred times and of course know it fully. For insights into Morphy’s play, few books are in league with Valeri Beim, Paul Morphy: A Modern Perspective (2005). This book has enriched my study.

8) Chess Informant was long the indispensable source for current master games from before I took up the game in the 1960s into the twenty-first century. Now, of course, these games are readily available from many sources. In 1996, as I was coming back to chess with some seriousness of purpose, I was curious about Informant, which I had seen only in the USCF sales catalog. At the Washington Class, however, David Weinstock had some on the table. He allowed me to look at them and we talked about how they were organized. A month or so later, I included Informant 64 in an order of books from USCF sales. It aided my correspondence play in a concrete way (see "Playing by the Book"). More importantly, learning the Informant system of codes changed my thought processes during play. There are so many things that one contemplates during a chess game while looking for the right moves or the correct plan. Sometimes these thoughts are noise that interferes with clear focus on what matters. To an extent, the limited analytical possibilities in the Informant codes distills chess down to things that really matter in the quest for advantage.

As I grew as a player, Chess Informant was a useful tool. Today’s Informants are changing with the information explosion and are oriented more towards the needs of class players than they were in the past. Give them a try.

A Growing Collection

Of course, I did not rise from C Class to strong A Class without studying the works of Jeremy Silman. His endgame book is already listed above, although it was less useful to me than Dvoretsky. In fact, the day I bought it, I read everything through the section on B Class, finding very little that I did not know. Silman’s endgame book has done more for my teaching than for my own progress as a player. That’s plenty! His writing is compelling and many of his metaphors and personal anecdotes are unforgettable.

I bought and read (partly, of course) How to Reassess Your Chess, 3rd. ed. (1993); The Reassess Your Chess Workbook: How to Master Chess Imbalances (2001); The Amateur’s Mind: Turning Chess Misconceptions into Chess Mastery, 2nd ed. (1999); and The Complete Book of Strategy: Grandmaster Techniques from A to Z (1998). When it finally came out, I added How to Reassess Your Chess: Chess Mastery through Chess Imbalances, 4th ed. (2010), but my rating had risen above 1800 before then.

9) Of these books, Reassess Your Chess and the companion workbook were most useful in helping centralize imbalances in my thinking. When I need to win a tournament game, seeking imbalances from the very first move often proves vital.

The Complete Book of Strategy did nothing for my game and very little for my teaching. Its usefulness has been so slight that I struggle to show proper supportive enthusiasm when a young student has shown me that they just acquired it. I must remind myself that there is a difference between this book’s presence in a chess library of more than 400 volumes that includes several dictionaries and encyclopedias, and a chess library for which this book is the first book acquired. It is a good book, even though it does not meet my needs.

What about the Opening?

In high school, I spent many hours studying lines in I. A. Horowitz, Chess Openings: Theory and Practice (1964). In the 1990s, Walter Korn, and Nick DeFirmian, eds. Modern Chess Openings, 13th ed. (1990) took its place. Even more time was spent on opening monographs, including several on two related variations of the Sicilian Defense that feature an early e5 push by Black. There is some evidence this study hurt my game, or at least retarded my improvement. I tried to memorize lines and often faltered when my opponents deviated from the lines that I knew.

Use at Your Own Risk

In 2003, I began to switch from the Sicilian to the French as my primary defense against 1.e4. The French Defense is not superior to the Sicilian. It might even be a worse choice, but for me it marked a shift in how I approached opening study. Rather than grinding through lines in a book, I sought understanding of the principles, of basic concepts, such as one finds articulated clearly in José Capablanca, Chess Fundamentals (1921), of the ideas behind the moves. Unquestionably, I learned many lines, but when my opponents deviated from these, I was prepared. My play improved.

Detailed opening study and learning concrete lines has aided my preparation for specific opponents in several cases. At a crucial moment while still a B Class player, I won the Spokane Contender’s tournament, earning a shot at the title of Spokane City Champion. Expectations of victory were nearly non-existent. No one expected a B Class player rated in the 1730s to prevail over FM David Sprenkle, rated in the 2250s, down considerably from his peak. As preparation, I spent close to 40 hours on two semi-obscure variations: the Raphael variation against the Dutch Defense for when I had the White pieces, and a seemingly risky Nh6 idea for Black in the French Advance. It took Sprenkle 72 moves to compel my resignation in the French, and I drew my second game with White. It was a very good day.

Most of the time in tournament play, however, such extensive opening preparation is more of a crap shoot. Unless an opponent walks into your pet line, where is the benefit? Tactics win and lose games. Endgames keep chances alive as players grow weary or hungry.

10) Hence, my tenth recommended book is one that I’ve read very little, but that exemplifies how I have come to believe opening study should be pursued. Reuben Fine, The Ideas Behind the Chess Openings (1943) is out of date in terms of the line presented, as should be expected. But, players of the French Defense well-know that White’s pawn on d4 is always a target. The Sicilian Defense is always grounded in creating pawn imbalances and active piece play in the quest for equality and even winning chances.

Other Books

Many other books helped me in my successful quest to reach A Class, and remain there for fourteen years so far, as well as my quest to rise into Expert Class, falling just short and less a goal in my 60s than it was in my mid-50s. Learning drives me. My knowledge continues to grow even as my performance in competition is less consistent.

Progressing Through

After announcing in "Try, Try, Again" my resolve to play through the whole of the games section in Chess Informant 152, I have felt a sense of responsibility. Initially, I was racing through the games as Jeremy Silman appears to advocate, but I slowed down (see "Quality"). My routine has developed into one that satisfies me. I play through the games quickly, but with enough attention that I can write a few words in the margins of the print text for later review. I have also extracted key positions from a number of games that became lessons for my students.

This morning I compiled some data on my progress.

The numbers on the spreadsheet are approximate and low. They were compiled mainly through ChessBase's history feature. They do not include games that I played through on Lichess, Chess.com, or Chessgames.com. I used all of these sites, as well as FICS Database while writing my article yesterday on a Greco game that I know well (see "Following Greco").

Since 7 September, I have been through the first 80 games (there are 201) in Informant 152. With annotations that are full and partial games, that includes at least the opening phase of 113 games. In addition, I have been through 133 other games from books or database search. I have also looked at a considerable number of my own games, although the vast majority was only a specific endgame position in the game.

The principal reason I have not successfully completed the project of playing through all games in any given Informant in the past is that other projects crowd in. The past few days I have again begun a project of playing through all of the games in Irving Chernev, The 1000 Best Short Games of Chess (1955).

Last night I downloaded a PGN file of the games in Chernev's book for playing through on my iPad. I play through a game and then read what Chernev wrote. I went through 40 games in this manner last night and another 10 this morning. I expect to create this week's chess lessons for my students from Chernev's collection off miniatures.

After starting with Chernev, I spent half an hour or so going through games 76-80 in Informant 152.

I go through each game without seeing the game score or annotations. Often I am trying to predict the moves. For some games, I then go through the game again with notation visible and play through some or all of the analytical variations. After recording a thought or two in the margins of my print copy, I move on to the next game.

The game Inarkiev -- Sakaev, Russia 2022, 152/80 received my comment, "reminds me of a line by Steinitz". I'm thinking of his comment that the king can take care of himself. The game was drawn.

After 27.Kf3

Outside Passed Pawn

In Jeremy Silman, Silman's Complete Endgame Course (2007), he uses the term "the fox in the chicken coop" for the concept that I learned as "outside passed pawn". It is a skill that I routinely teach beginning students and require for completion of my Knight Award. The core idea that Silman explains--abandoning a passed pawn to create another--appears in the endgame book that I have had since my youth. Irving Chernev, Practical Chess Endings (1961) presents this position. Perhaps that is where I first learned the concept many years ago.

White to move

Chernev explains, "White abandons his passed pawn. Capturing it will keep Black busy on one side of the board, while White gets time to win on the other" (39). He gives the moves:

1.Kf5 Kh6 2.Ke5 Kxh5 3.Kd5 Kg6 4.Kc6 Kf6 5.Kxb6 Ke7 6.Kc7

When young players learn this simple idea, they have a requisite skill for navigating a great many pawn endings that will occur in their own games.

Chernev gives a second solution that employs a fundamentally different set of principles, but that leads to a faster checkmate. Hence, the position is less than ideal for my purposes. Even so, I had the exact position in a blitz game in July 2021 and played it according to book.

Silman's illustration is cleaner. While there are several winning moves that can be played, his solution appears to follow the top engine moves.

White to move

1.b5 Kb7 2.Ka5 Ka7 3.b6+ Kb7 4.Kb5 Kb8 5.Kc6 Kc8 6.Kd6 Kb7 7.Ke6 Kxb6 8.Kxf6 Kc7

White to move

9.Kxg5

Silman writes, "the rest is mindlessly easy" (67).

I would play 9.Ke7, which wins faster.

When teaching or testing students, I usually compose positions on the spot. But, perhaps it would be useful to have a printed sheet in my chess bag with some of the most instructive positions from books and game. Paul Keres, Practical Chess Endings (1974) offers one that is excellent. His term is "distant passed pawn" (55). As he notes, without the passed pawn that will be sacrificed (or exchanged for Black's passed pawn), White would be lost. 

White to move

1.f5 Ke5 2.f6 Kxf6 3.Kxd4 Ke6 4.Kc5 Kd7 5.Kxb5 Kc7 6.Ka6

Reviewing my own internet games stretching back to the late-twentieth century produced many positions where the basic idea of using a passed pawn to deflect the opponent's king from the main scene was required. In many cases, the correct move was not played.

I played it correctly in this position from the Internet Chess Club in 2001.

Black to move

38...b3! was the only winning move. My opponent resigned after 39.Kxb3 Kxd5 40.Kc3 Ke4 41.Kd2 Kf3

Thinking I was applying this idea, I managed to throw away the win in this game from 2001.

White to move

I played 45.h4 and succeeded in forcing Black's king to the h-file while gobbling Black's two remaining pawns with my king. However, Black's king was able to get back to the a-file in time. This position shows that calculation is necessary in pawn endings and sometimes there is more than one idea in play.

1.Kf4! is the only winning move.

If Black then goes after the a-pawn, White needs to win a queen vs. pawn ending where it is important that Black's pawn is two squares from promotion. If the Black king tries to get the the h-file, then the distant passed pawn is far enough away that White will be able to promote the a-pawn.

Quality

When I was just starting out (I was an instant chess addict!), I used game collections, tournament books, and eventually Chess Informants to zip through anywhere from 200 to 500 games a day, every day. That’s not too amazing when you consider that I only used 20 to 40 seconds a game.
Jeremy Silman, "Studying Master Games and Berkmaster's First Over-The-Board Tournament Battle," Chess.com (21 January 2014)

When I started my effort to quickly go through every game in the back half of Chess Informant 152, I went through the 39 games and game fragments classified as ECO A in two sessions of 20-30 minutes. That is much slower than Jeremy Silman claims to have been his practice as a young player, but much faster than my pace so far through ECO B. This morning I went through game numbers 40-45, which, including annotations, was nine whole games and one fragment. My wife says I was at my computer about an hour. Six minutes per game is still very fast and superficial, of course.

As I went through games 40-45 in Informant 152 this morning on my computer, I made notes in the margins of the print edition. Every game has at least one note. Two tactical positions are marked as possible material to use with my students.

From Lupulescu,C.--Nanu,C., Romania 2022, 152/44

White to move

From Zhang,Zhong--Li,Di, Hangzhou 2022, 152/43

White to move

I marked Erdos,V.--Babula,V., Corte 2022 152/41 as "pins and forks". The next game, Esipenko,A.--Moiseenko,A., Deutschland 2022, "use every piece".

Silman asserts that quantity of games develops knowledge of patterns--"positional patterns, tactical patterns, structural patterns, piece placement patterns, timing patterns."* He suggests that to become an IM or GM, a player needs to look at 100,000 games. 

My ambitions to become a titled player, if I ever had them, dissipated a few years prior to my 60th birthday. Nonetheless, I enjoy the process of learning and seek a range of approaches to this process. I know that I have played through many thousands of games over the years, many very quickly and others that I have studied for many hours. A few years ago, I played through every available game on chessgames.com played by Rezső Charousek, of which there are only 171. The process took a week. The biggest impact on my play came from detailed study of a game that he lost. It inspired me to try my hand with the opening in that game (see "Losing My Virginity with the Ponziani" [2014]). This study of Charousek's games was influenced by Silman's claims.

I have played through a substantial percentage of Paul Morphy's games and have used at least thirty regularly in my teaching. I have been through more games credited to Gioachino Greco than can be found in any database, including my own because my hard drive crashed a few months after entering the 168 variations in William Lewis, Gioachino Greco on the Game of Chess (1819). Several years later, I entered all of the games from Francis Beale, The Royall Art of Chesse-Play (London 1656), which contains 94 games, many of which are not in the databases most people use.

As I work through these games with the objective of getting through all soon enough that Informant 153 does not arrive first, I am pulled one way by Silman's assertions that quantity and speed are beneficial. At the same time, slowing a little seems to offer better prospects of quality.

*Jeremy Silman, "Snarky Silman Presents: Reader's Questions," Chess.com (14 January 2014).

Surprisingly Strong Move

In mid-April, I played a move that was better than I thought. I played it in desperation because I was frustrated after reaching what looked like a drawn ending from what seemed like a clear advantage. It was a ten minute game and it sent me to my endgame books as well as extensive engine analysis.

Pawns were exchanged on move 33 and we shuffled our kings and rooks for another 20 moves before I pushed a pawn.

White to move

53.d5!

I expected 53...exd5 54.Kxf5 and maybe I can do something with my f-pawn. But I also thought that would still likely lead to a draw.

53...Kxd5

I was sure this move was an error. It equalizes material, but now Black's king gets cut off.

54.Rd2+ Kc6

I easily won Black's pawns. The rooks came off the board on move 77 and my opponent resigned two moves later.

To my surprise, the engines evaluate 53...Kxd5 as no worse than 53...exd5. That sent me into the endgame books to study rook endings with two pawns to one, three pawns to two, and four pawns to three. Such positions are often drawn.

Catching my eye as suitable for practice was a tragicomedy from Hebden -- Wood, Hastings 1994/1995.

Black to move

Wood's move here resembles what I thought to be an error in my game.

1...Kxf4??

Mark Dvoretsky writes, "A terrible error. The black king will be cut off along the f-file now, and the g7-pawn will be inevitably lost" (Dvoretsky's Endgame Manual, 5th ed. [2020], 189).

Dvoretsky gives two ways to draw. I opted for the harder one against Stockfish on the iPad.

1...g6 2.Rf7+ Ke4 3.Kg4 Ra1 4.Re7+ Kd5

White to move

My king is cut off from the pawns, but White's king has no points for penetration. Nine moves later, Stockfish moved the rook from the e-file, allowing my king to return. Another dozen moves and I offered a chance for the engine to force the exchange of rooks. My confidence that I could draw the pawn ending was grounded upon extensive practice with a pawn ending from Dvoretsky (see "Opposition and Outflanking").

White to move

Stockfish did not opt for 22.Re2+ Rxe2 23.Kxe2 Ke6, which I knew to be drawn. Ten moves more of rook shuffling, and Stockfish pushed a pawn.

Black to move

A Philidor position seems likely, but instead the game concluded with a rook exchange that left lone kings. It was good practice. My play was not error free, but one can also back up against a machine.

Reuben Fine, Basic Chess Endings (1941) offers positions where the weaker side's king is cut off from the pawns. No. 390b is presented without a diagram. No game is referenced, although the pawn structure is close to No. 390 (Saemisch -- Spelmann, Teplitz-Schoenau 1922) with colors reversed. Fine claims that White wins No. 390b (Saemisch was able to hold a draw because his king was with the pawns), according to Fine. Stockfish does not agree.

Black to move

1...Rb7

Stockfish gives 1...Kd6 2.f5 Ra3+ 3.Kf4 Kd7 and better for White by less than a pawn, usually an indication that the game is headed towards a draw.

2.f5 Ra7 3.g5 Kd6 4.h4

Stockfish recommends 4.Re8

4...Ra4 5.Re1

Black to move

5...Ra1

A common idea in such positions, but wrong according to Stockfish.

5...Re3+ 6.Kg4 Kd7 and the engine sees Black holding the position. White's Re8 is not possible.

6.Re8

White will give up the f-pawn for both of Black's pawns after Rg8.

Knowledge

When does a player refuse a draw offer in a dead drawn position? If time is a factor, such a refusal could make sense. Often a draw offer is refused because a player does not know the position is a draw, or suspects that the opponent does not have the requisite knowledge to hold the position.

I had Black in this position this morning.

White to move

49.b7??

After this error, the game is a dead draw. White should have played 49.g4, or started moving the king towards the b-pawn. I offered a draw after a dozen moves, having reached this position.

White to move

Instead of accepting the draw, my opponent played another 20+ moves, eventually setting a trap with 84.Rh8?? (White's king was on e4). I could take the pawn, stepping into a skewer. Or, I could take the free rook. After I took the rook, White resigned.

I have played similar endgames before in all sorts of time controls (see one example at "Winning" [2016]). I am guided in the knowledge that my king must remain on the seventh rank and the g- or h-file. With the pawn on g6, the king cannot move. I recall reading about this technique in a book that included a discussion of the resulting skewer tactic if the defending king strays.

However, looking through my endgame books, I could not find the remembered passage. Even so several books contain examples that are close enough that an attentive reader can easily derive the relevant knowledge.

The Books

Nikolay Minev, A Practical Guide to Rook Endgames (2004) shows a stalemate trap when the stronger side has a useful f-pawn, but prematurely sets up the skewer (21-22). From Khiut -- Alalin, USSR 1952.

White to move

1.Kf4 Kf7 2.Rh8??

White sets up the skewer.

2...Rxa7 3.Rh7+ Kf6 4.Rxa7 stalemate.

Yuri Averbakh, Chess Endings: Essential Knowledge (1996) shows an interesting drawing idea from Johann Berger (67).

White to move

1.Kf7

Black cannot get to the seventh rank fast enough, but can avoid checks using the Black king as a shield.

1...Kf5 2.Ke7 Ke5 3.Kd7 Kd5 4.Kc7 Kc5 5.Kb7 Rb1+ forcing Black's king back to the c-file.

Although it was fixed in my memory that I learned the technique employed this morning from Averbakh, it is not in Chess Endings: Essential Knowledge. I did find the idea expressed clearly in Edmar Mednis, Practical Rook Endings (1982), but I've known the technique far longer than I've owned this book. Mednis explains, "the stronger side wants to avoid the following two potential problems: immobilizing his Rook and depriving his King of shelter" (22). Both problems exist in the illustrative diagram. My opponent created the first with 49.b7. Pushing the g-pawn forward introduced the second, but there was no way to dislodge my rook from the c-file.

White to move

In his illustrative diagram, Mednis explains both Black's need to keep the king on g7 or h7, and the rook remains on the c-file, leaving only to check White's king when it gets near its pawn.

Two books that I have had for several years and have spent some time reading explain the ideas, too. One of the critically important blue diagrams in Dvoretsky's Endgame Manual (2003) shows the winning idea missed in Minev's example when the stronger side has an f-pawn (152).

White to move

White wins with 1.f6+ because taking the pawn leads to 2.Rf6+ followed by a8Q, while moving in front allows White to set up the skewer with 2.Rh8. Dvoretsky points out that a pawn on the g- or h-file, however, does not present problems for Black. Although Dvoretsky's description of the skewer does not match my recollection, it may be the book from which I learned this idea.

Jeremy Silman, Silman's Complete Endgame Course (2007) offers three pages of analysis with three diagrams with the white pawn on a7, and three more pages and diagrams with the pawn on a6. These are in the endgames for Class A. I recall that I read about that far within days of buying the book when it first came out. His "A key tactical idea" underneath the diagram below comes close to what I recall studying. Black attempted a "queenside trek" (230).

Black to move

So, I may have learned the idea from Dvoretsky, and certainly encountered it in Silman. It may also be in some other endgame books on my shelf. The simple idea appears in many books. My opponent either lacked this knowledge, or suspected that I did. In the end, he set up a skewer threat that was shocking enough I could have fallen for it on impulse. However, I took a few seconds to assess and grabbed the free rook.

What is Reading?

Some books are to be tasted, others to be swallowed, and some few to be chewed and digested; that is, some books are to be read only in parts; others to be read, but not curiously; and some few to be read wholly, and with diligence and attention.
Francis Bacon, "Of Studies" (1625)

What do you mean when you say you've read a book? Have you read every word?

During a class my first year of graduate school, my professor stated her view that for a master's degree, a history student should know 300 books. For the doctorate, she said, one thousand books was the expectation. Her statement was a little intimidating at first, for it meant reading one academic book every two to three days. Many of these books are densely written and run 400-500 pages.

For that class, we each bought the twelve required texts, and were each assigned one for our individual presentations, and two written assignments--an annotated bibliography and a 15-20 page paper. For my bibliography and paper, I "read" perhaps a dozen more books, and several journal articles. The assignment was to place the book in question in the context of other scholarship on the same topic.* Reading a book with this purpose meant spending as much as two hours identifying the central arguments and the nature of the supporting evidence of each book. An article should take fifteen minutes. With practice, and some familiarity with the subject matter, this level of reading can be achieved in about thirty minutes for most history books.

Reading a novel is another matter. It must be read in sequence and cover-to-cover. Some books may remain unfinished--there is a long list of popular classics that I started and did not finish because I did not like them. For other novels, reading only begins the second or third time through the book. This need for a second and third reading is a characteristic of the sort of dense fiction that I prefer. All reading is rereading, as some French theorist famously suggested.**

How do you read a chess book?

For some chess books, the practice of the historian--skimming, assessing, highlighting key points--might be all you need. A few weeks ago, I reviewed three chess books for beginners that were all terrible. Each was self-published and two seemed as if they were not written by chess players. The third read like a bad machine translation of a decent book in a language other than English. Perhaps two hours were required to read the combined 300 pages of these three books. I did not skip any pages, but did pass rapidly over the surface looking for points where the author said something of merit, or got something egregiously wrong.

There are many chess books on my shelves that I read for an hour or two on the day of purchase, often with the intent to go back and peruse with more attention to detail. Most chess books offer verbal discussion of key ideas, illustrative positions with diagrams, and detailed analysis of positions, sometimes with many branches of possible variations. Reading the text often does not take long, while pondering the variations can keep you tied up for years.

The day I bought Jeremy Silman's Complete Endgame Course (2007), I spent less than two hours racing through the first third of the book, pausing only to think through a few diagrams. Most of the content through what he calls "Endgames for Class C" consists of knowledge I assimilated before I bought the book. Even so, Silman's book transformed the curriculum I was using to teach elementary age chess players. He convinced me that checkmate with knight and bishop was an inefficient use of time, while the Lucena and Philidor rook endings deserved far more attention. Prior to buying his Endgame Course, some ideas presented in How to Reasssess Your Chess, 3rd ed. (1993) had worked their way into my teaching. I cannot say that I have read either of these books, except in part. But I have frequently reread a few parts of Reassess, both 3rd and 4th editions.

I read Excelling at Technical Chess (2004) by Jacob Aagaard more slowly and more deliberately, but still not wholly. It had a profound impact on my play that was vital as I rose from B Class to A within the USCF rating system. Where I was once eager to accept a draw in a seemingly equal position, I started refusing these offers after reading Aagaard. If there is an imbalance that allows me to create problems for my opponent to solve, I insist that we should play on at least a few more moves. I also began to see that some endings, while long and potentially difficult, were not at all equal. See "Excelling at Technical Chess" for an example of the fighting spirit Aagaard helped inspire.

Prereading

When reading some chess books, especially those that present whole games well-annotated, I often follow a longer process. First I locate the next game in the text in a database. I play through the game several times without reference to the book. The first few times, I use no aids, but seek the key moments in the game. Where did the player who lost begin to go wrong?

When I am comfortable with understanding some of the key tactical and positional points, I may use an opening database to research a bit. After I have worked to acquire a thorough understanding of the game, I read the annotations in the text.

Sometimes I will continue by looking at how other books present the same game. I have used this process for dozens of books on my shelves, but Logical Chess Move by Move (1998) by Irving Chernev is the only book for which I have taken this process all the way through every game. I went through the algebraic edition a few years ago, but also have vague memories of a more superficial reading of a library copy of the original descriptive edition in the late-1970s.

This process of "chewing and digesting" a chess book is one that I advocate. Perhaps, if I find the time, I will complete other books in this manner. I started this process a bit over a year ago with Paul Keres, World Championship 1948 (2016), which is a terrific book. Alas, work and other chess books got in the way.

*I discuss this specific book and that graduate class in more detail on Patriots and Peoples, "Pandemic History".
**Roland Barthes, S/Z: An Essay, trans. Richard Miller (1974).

Knight vs Bishop

Jeremy Silman devotes the first chapter of How to Reassess Your Chess, 4th ed. (2010) to the imbalance of knight vs. bishop. Somewhere in the third edition, he suggests that a player ought to play in a manner that makes his or her minor piece the superior one.

White to move

This position arose this morning in the seventh round of the World Open, being played on the Internet Chess Club. I had White. Black's knights are menacing with the threat of Nxc3, followed by Nxe2+. 

16.Bxd5 

My move seemed forced. Now Black faces a choice of how to capture the bishop. I would submit that my opponent's move was not the best choice.

16...exd5

I went on to win a knight vs bishop endgame where all my pawns were on dark squares and my king decisively penetrated to the center of the board.

It's Only Blitz

I beat a National Master yesterday afternoon. It has been a couple of months since my last win against a titled player, so I was happy to get this one. It was my last game in a blitz playing session characterized by poor play, but it was a better game. Of course, I made errors, but they were less egregious than in my previous several games.

I spent a little more than an hour playing blitz, and at least that much time analyzing this one game. This game was played in less than six minutes. Did it deserve more than an hour of post-game analysis? My opponent shall remain unnamed because he left a clue on his Chess.com page that suggests he would prefer it that way.


Stripes,J (1892) -- Internet Opponent (1926) [E11]
Chess.com, 07.08.2017

1.d4 Nf6 2.c4 e6 3.Nf3 Bb4+ 4.Nbd2

4.Bd2 is the most popular move. Some years ago, I bought and read partly through The Chess Advantage in Black and White (2004) by Larry Kaufman. Many of the lines that Kaufman recommends do not suit me well, but his basic idea has been an influence. He advocates "second best" moves early in the game when it reduces the amount of theory that one must learn.

I am not certain that 4.Nbd2 is second best, but it is second most popular. 4.Bd2 is played twice as often. 4.Nbd2 has a better scoring percentage for White and a slightly higher Elo performance as well. I had the impression that 4.Bd2 was the choice of top Grandmasters, but a check this morning refuted that. Garry Kasparov has played both moves. Magnus Carlsen has played both, but 4.Nbd2 more recently. Maxime Vachier-Lagrave seems to favor my choice.

I spent some time thinking about the relative merits of the choice that White makes here in the Bogo-Indian Defense. Why is 4.Bd2 more popular?

4...Qe7 5.g3 b6

The databases suggest that this move is rare, but the structure is certainly familiar.

6.Bg2 Bb7 7.0–0 0–0

Castling leads via transposition to a small batch of reference games.

8.Nb3

It is hard to believe that this move has not been played before. There must be something wrong with it. Perhaps, this move offers a clue to the popularity of 4.Bd2. The knight blocks the bishop when it stands there. It also lacks good squares that can be reached from d2. On b3, where I placed it, it interferes with queenside pawn expansion. Other moves seem worse.

Black to move

8...d5 9.a3 Bd6 10.c5!?

This brilliant pawn sacrifice was actually an oversight. I was unaware that I was down a pawn until at the end of the game, savoring my victory, I noticed that material was equal. This sacrifice creates a minor piece imbalance that sometimes favors White, but was it worth a pawn?

10...bxc5 11.dxc5 Bxc5 12.Nxc5 Qxc5 13.Be3 Qd6

13...Qe7

14.Rc1 Na6

14...Nbd7

15.Bf4 Qd7

15...Qe7

16.Ne5 Qe7 17.Nc6

Black to move

At this point of the game, I was pleased with my position. I seem to have my opponent's forces tied down.

17...Qd7 18.Qc2 Rfc8 19.b4 Nb8 20.b5 Bxc6

After this exchange, we have two bishops against two knights and only the c-pawns are blocked.

21.bxc6 Qe7

White to move

How might White squeeze Black from this position?

22.Qb3 with the idea of Qb7 seems to have some merit.

22.Bg5 threatens e4.

I did not spend much time on this position during the game, but invested about fifteen minutes with it on the deck in the evening. It might be one that could be added to the store of middlegame positions for performing Jeremy Silman's inventory of imbalances.

22.e4 dxe4 23.Bxe4 Nxe4 24.Qxe4 a5

Maybe 24...Qxa3

25.Rfd1 Qxa3

Maybe 25...Ra6

26.Bxc7! Na6

26...a4 27.Bxb8 Raxb8 28.c7 looks overwhelming for White.

26...Rxb7 27.Rd8+ Qf8 28.Rxf8+ Kxf8 and the material balance has shifted strongly in favor of White. Even so, a queen and pawn agianst a rook and bishop is not always a winning material advantage in time pressure.

27.Bd6 Nb4 28.c7 h6

White to move

29.Bxb4?

29.Be7! My target is d8. Why not make a move that contributes to this plan?

29... axb4

29...Qxb4 30.Qxa8!

30.Rc6

Black to move

30...b3

30...Qa5 is equal and takes advantage of my error a move earlier.

31.Rcd6 g6 32.Rd8+ Kg7 33.Qe5+ f6 34.R8d7+

34.R1d7+ Qe7 35.Rxe7#

34...Kg8 35.Qxe6+ 1–0

Maybe my pawn sacrifice was sound. Both players committed the sort of positional errors that one might expect in a blitz game.

Bishop and Knight Checkmate

Forcing checkmate with a bishop and knight requires piece coordination and foresight. It is the most difficult of the elementary checkmates. I remember being on the weaker side in a game on the Internet Chess Club in the late 1990s. I told my opponent, "I think this is a draw." He was convinced that it was a win, but he tried to checkmate me in the wrong corner. The game was drawn by the fifty-move rule. After the game, I looked it up. He was right and I was wrong.

Shortly after that game, I learned the checkmate through study of several key positions in Bruce Pandolfini, Pandolfini's Endgame Course (1988). Occasionally, in blitz games or against Chessmaster, I would underpromote a pawn so that I could execute this checkmate. Those instances were usually simple, as only a few moves were needed for checkmate.

I required students to demonstrate it for the Rook Award when I first created my youth chess awards. When I was teaching it regularly, I could perform it reasonably fast, but not easily. Ten years ago, however, I was persuaded by Jeremy Silman to drop it from my awards. It is excluded from Silman's Complete Endgame Course (2007) because it almost never occurs in actual play. In its place in my awards are the Philidor and Lucena rook endgame positions. There should be no question that rook endgames occur frequently and are of immense practical value. The Philidor and Lucena positions also are easier to teach.

Last year in a blitz game at the Spokane Chess Club, I underpromoted and then struggled to execute the checkmate. It had been several years since I practiced this checkmate regularly and my skills had atrophied. Success came well after the fifty-move mark. Last week, I tried the checkmate using Chess.com's "Drills" feature. Again, I struggled. To repair my deficiency, I went to YouTube and watched a video by NM Elliott Neff and another by IM Daniel Rensch. Both of these videos are excellent. After watching these videos, I succeeded with the drill quickly and easily. But, the next morning, I struggled again. Something about the knight's W pattern eluded me. Had I been more attentive during the last two minutes of Neff's video, I might have understood it better.

White to move

The W

Through the past few days, I have watched eight or ten videos, reread the relevant portions of Pandolfini's Endgame Course, and read the bishop and knight section of Karsten Muller and Frank Lamprecht, Fundamental Chess Endings (2001). I also have played out dozens of positions against Stockfish on my iPad. I have been in the diagram position above in game after game. I have played this position so often that my hand is learning the moves.


Transition to the Lock

For many years, I have had a vague memory of Pandolfini's Endgame 22, "Transition to the Lock".

White to move

1.Bg5 Ke8 2.Ng6

2.Ke6 is an easier system to remember.

2...Kf7 3.Ne5+ Ke8 4.Kc7

Black to move

When I was failing, I was always aiming at this position, but the bishop and knight swapped places in my memory. As a consequence, Black was able to shuffle the king between e7 and e8 and White failed to make progress. With these two minor pieces in their correct positions, the finish is easy.

4...Kf8 5.Kd7 Kg8 6.Ke8?!

6.Bh6 was the correct move.

6...Kg7 7.Ke7 Kg8

White to move

8.Bh6 Kh7 9.Bf8 Kh8 10.Kf7 Kh7

White to move

11.Nd7 Kh8 12.Bg7+ Kh7 13.Nf6#.


The Drill

Chess.com's drill employs the position that tablebases have identified as the one requiring the most moves to checkmate. This position is among those listed in the appendix in Fundamental Chess Endings. The engine Chess.com uses is less accurate than Stockfish on my iPad, or so it seems. With optimal play on both sides, this position leads to checkmate in 33 moves. Neither I nor the computer played the best moves.

There are three steps in the process:

1) centralize and drive the king to the edge,
2) drive the king from wrong corner to right corner,
3) checkmate.

White to move

Among the videos that I watched this week, some were better than others. One that is okay, but not to be recommended, is Kevin's from thechesswebsite.com. Through the first phase, he keeps repeating, "it doesn't matter," or similar phrases. I disagree. While slight inaccuracies in the first phase will not be the determining factor in success or failure, they can add up. When you have 50 moves to execute a checkmate that requires 33, an inaccuracy that requires four or five moves to correct can be repeated twice. The third time could be fatal. The inaccuracies through the first eleven moves here, however, add only one or two moves each to the final solution. Had the computer been more stubborn, however, checkmate might have occurred on move 40.

Stripes,J -- Computer
Chess.com, 26.05.2017

1.Ka7 Kd8 2.Bg6 Kc7 3.Nf3 Kc6 4.Bd3

Better is either 4.Be4+ or 4.Ka6.

4...Kc5 5.Kb7 Kd6 6.Kb6 Ke7

6...Kd5 resists longer.

7.Kc6 Kf6

7...Ke6 resists longer.

8.Kd5

8.Kd6 is better. Centralization is a good general concept, but should not supplant concrete analysis.

8...Kf7

8...Ke7 is more stubborn.

9.Ke5 Ke7

9...Kg7

10.Bf5

10.Bc4 is more accurate.

10...Kf8

10...Kf7

11.Kf6 Kg8

White to move

Black's king is on the edge and seeking refuge in the corner where checkmate is impossible without a dark-squared bishop. White's king is optimally placed, as is White's bishop. The knight must go to f7 to evict the king. In Neff's video, the knight gets to f7 via g5. Objectively, there is no difference between g5 and d5, but as a practical matter, it is worth remembering that the knight wants to be on the center square that is two spaces diagonally from the wrong corner. In some cases, the knight might take up this position before the bishop is posted on its ideal diagonal.

12.Ne5 Kh8 13.Nf7+ Kg8 14.Bg6

Here, in his video, Kevin states that the bishop "improves its position" ("Chess Endgames -- Bishop and Knight, Part 1"). Nonsense. The point of the bishop's move is to lose a tempo without altering the position.

14...Kf8 15.Bh7 Ke8

We have reached the position with the colored W near the top of this post. The letter W highlights the route the knight will take through the course of the second phase. Rensch offers a useful principle, "lead with the knight, follow with the king."

16.Ne5 Kd8 17.Ke6 Kc7

White to move

This was the point where I failed on the second day, earlier this week. As panic set in, I struggled to find a route to Pandolfini's position (after move 4 in "Transition to the Lock"). But, there is another lock available.

18.Nd7 Kb7

White to move

19.Bd3

This move completes the lock by covering the squares highlighted in yellow.

19...Kc6 20.Bc4 Kc7 21.Bd5

21.Bb5 pursues Pandolfini's "transition to the lock", which also works.

21...Kd8 22.Kd6

Black to move

We have a sitiuation identical in all its particulars to one that existed two squares to the right after evicting Black's king from the wrong corner. Here, the same maneuver as before drives the king back in the direction we wish.

22...Ke8 23.Be6

Losing a tempo.

23...Kd8 24.Bf7

Denying Black's return to the e-file.

24...Kc8 25.Nc5

The knight reaches the third point of the W. White repeats the process--knight moves, king follows, bishop either loses a tempo or cuts off the escape.

25...Kd8 26.Nb7+ Kc8 27.Kc6 Kb8 28.Kb6 Kc8 29.Be6+ Kb8

White to move

Now, the third and final phase. It is checkmate in four. White's only difficulty is easily solved. The knight must check the king on g8 without blocking the bishop's control of the long diagonal. Two squares are available: d7 and a6. However, d7 would allow the king to return to c8. If we had this position with Black to move, then the bishop could check first and the knight deliver checkmate from d7.

30.Nc5 Ka8 31.Bd7 Kb8 32.Na6+ Ka8 33.Bc6# 1–0