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I am a relatively new player (less than 1 year, ungraded) but I feel I have made good progress so far. I am playing competitively with players in the 1300-1500 region and would like to continue my improvement.

Middle game is my strong point for sure, I am able to muddle through some common openings and get into a complex middle game quickly, as that is where I am strongest. But I can't get over the hurdle that more experienced players seem to be able to instinctively recognise if an endgame is won, drawn or lost.

I want to spend my efforts in understanding common endgame patterns and how to handle them. Here is an example of a position I found myself in recently as white. My opponent felt it was a draw but it took me a long time to agree.

[FEN "8/5kp1/5p1p/4p3/nB1pP3/1b1P1P1P/5KP1/2N5 b - - 0 1"]

My question

Other than simply playing more games and gaining more experience, are there any patterns I should be looking for in an endgame such as the example given, so I can more easily determine if a position is won/drawn/lost?

Note: I see a number of similar questions being asked, and the general responses tend to be "practice more, here's a book/website of endgame positions for you to analyse". I'm looking more specifically for people who can explain endgames in a bit more detail, I'm not afraid of a bit of maths.

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Introduction (if tldr; skip to analysis)

I'm afraid there isn't really a simple answer to this, though it's a very sound question to ask as endgames really are different than the other phases of the game. The main reason for this is that endgames tend to be extremely concrete, meaning principled approaches to them are not always guaranteed to work. For examples, a principle one is often told about is to keep your pawns on squares of opposite color to your bishop, as to not hinder the scope of your bishop's activity. That sounds reasonable of course, but whether it's really a good idea or not will depend on the context and on all the intricate details of the position at hand, namely, how advanced and scattered the pawns are, the relative position of the kings, interplay of minor pieces, rook activity, number of targets in the position, and so on. This is to say that, sure there are endless principles to learn about endgames, but they're always to be taken with caution.

One may ask why this is so specific to endgames, at least more so than other phases of the game, intuitively, that's because naturally in endgames there will be less pieces, therefore less ways to create play or compensate for small mistakes (in contrast to the middle-game, where e.g., there are usually enough pieces to parry weakened squares, or to create play elsewhere as to divert attention away from the weakened side). As a result, one small mistake in the endgame may either ruin your advantage or even cost you the game. So one has to resort more often to sheer calculation rather than intuition or feeling. This is also why even at the highest level, one regularly sees players ruining their endgames or admitting afterwards that they had no clue how to assess the position.

Analysing your example

For example the position you've given, it's a NB-vs-NB. Had there been simply the bishops, it would be very clear why it's drawish, because of opposite colored bishops (a principle that is generally true). But the addition of knights makes it very complex, because now the interplay of these minor pieces is very different: first observation to make is whether the bishops are equally enabled to zone out the opponent's knight. You notice black's bishop has completely cut your knight out of play, and any chance of re-routing the knight, say via e2-g3-f5 will be met with g6. On the other hand, black has placed all their pawns on dark squares, so the king is bound to defending them against your bishop, starting from the g7 back-pawn. The weakness on d3 really breaks the symmetry though, as black has no equivalent weakness. But that's not enough (at least at first glance) as black has no clear means of increasing pressure on it, or creating a zugzwang situation by exploiting it as all of black's bishop entry points to your king-side are covered by your king. More precisely, Bd1 will be met by Ke1 and Bc2 by Ke2. So that doesn't work. What instead looks more worrisome is the knight potentially penentrating your fortress and getting behind your pawns. For example, an immediate Bc2 followed by Nb2 to d1. Because a priori you don't really want to let the knight to get to e3, even if it's still holdable, it looks hell scary to allow. So we need to come up with something to prevent all this. If you don't find an active idea and sit still it's going to be very hard (even a bad plan will be better than no plan at all). Luckily, here it's still rather simple as there's no dilemma of choice, basically all you can do is to try and undermine black's pawn chain, in order to create a weakness and balance things up again. So let's look at a possible variation (comments added):

 [Title "Bc2 Nb2 variation"]
 [fen "8/5kp1/5p1p/4p3/nB1pP3/1b1P1P1P/5KP1/2N5 b - - 0 1"]

 1...Bc2 2.Ke2 {Ba3 is possible of course, but then you allow Nc3 and that's another variation altogether, as you need to account for the king marching to g3} Nb2 3.Kd2 Ba4 4.Ne2 {preparing f4 to undermine the pawn chain by creating a weak spot on e5 after takes takes, just a tad safer than the immediate f4, though it may be possible} Nd1 5.f4 Nf2 {Ne3 is less attractive as Ne2 covers g3. So Nf2 is the only sensible choice, threatening Bb5 } (5...Ne3 6.g3 {and Nc1+ does nothing}) 6.fxe5 fxe5 7.Bd6 {You see f4 has made all the difference, our bishop is suddenly creating play} Ke6 8.Bf8 Bb5 {if Kf7 you can repeat} 9.Bxg7 Nxd3 10.Bxh6 Nc5 {perfect coordination of black's minor pieces, e4 falling next} 11.Ng3 Bc6 12.Ke2 Bxe4 {taking with the bishop to avoid an opposite color situation} 13.Nxe4 Nxe4 14.g4 {no tempo to spare, have to start pushing our own passed pawns to restrict black's king to that side. This is still not a trivial endgame.} Nc3+ 15.Kd3 Kd5 16.g5 e4+ 17.Kc2 Ke6 18.g6 Kf6 19.g7 Kf7 20.Kb3 {key move to go after the vulnerable pawns now, d3 drops the knight and e3 met with Bxe3} Ne2 21.Kc4 d3 22.Kd5 Ng3 23.Ke5 Kg8 {no useful moves left} 24.Kd5 {Draw! anything other than repeating ends in an immediate simplification and trade of remaining pawns.}

Looking back at the position we started from, we've come a far way to be able to reassure ourselves that black's Bc2-Nb2 variation is stoppable by Ne2 and f4, and that was just one variation! You see, it looks drawish, it feels drawish, but to convince oneself that it is indeed a draw, it's far from trivial and only through concrete considerations of these variations one can really be sure, for instance no one just knows that our g pawn push would be fast enough at the end of that variation without having calculated. I hope this has been the sort of analysis of the endgame you were looking for. Very rarely in a middle-game one has to go through such long variations in order to make a decision, but in endgames often there's no other way.

Recommendations

Some recommendations such that you can form a program for yourself (the list won't be exhaustive):

  • As boring and repetitive as it sounds, read a basic book on endgames and you'll be subjected to all sorts of common situations, where you'll learn how to maneuver with rooks, bishops, knights and their combinations. You'll learn how and when to cut off the king, how to trap pieces, how to push passed pawns covered by knight, a bishop, a rook. How to force draws in endgames that are known to be trivially drawn etc. You won't have to memorise everything per se, but rather pick up the key ideas and ways of reasoning about these positions. For instance how to play the Philidor positions (where does your rook belong, when do you start giving checks and from which rank, then all of that from the side that has the pawn), similarly for the Lucena position and many others. These are sorts of endgames that if you simply don't sit down to study for yourself, you'll end up messing them up regularly. A very good book to get started is: "100 Endgames You Must Know: Vital Lessons for Every Chess Player" by Jesus de la Villa.
  • Take the time to carefully study your own endgames after your games. First gather some ideas, then check the corresponding variations (mentally for as much of them that you can), and at the end go through your calculations with an engine. The routine is very similar to learning mathematics for example, nobody learns anything by immediately picking up the solution manual (here the engine). By the end of such study, you should have learned what kinds of questions you need to ask yourself in various endgames.
  • Solve lots and lots of endgame tactics next to other tactics or puzzles that you do. This will sharpen your technique (and fill up your bag of ideas), both in saving hard positions and in conversions. Again, mental calculation to be prioritized. There are many sources for this, specially these days. A good start would be chesstempo or lichess.
  • Study the games of strong players: follow their post-game analysis, go through their games and try to understand their decisions, watch the endless online content that is produced on a daily basis by strong players, as they play they will be explaining their reasoning, (couple of names: Yasser Seirawan, Peter Svidler, ChessExplained). This will add a new flux of digested knowledge in your way, and the goal will be to learn how they reason and asses positions under different circumstances (you will learn things that you may never necessarily find in books).
  • Preferably play longer time control games in order to have chance to think during your endgames. Start getting into the mindset of anticipating the kinds of endgames your middle-game decisions will lead you to (only then can you come to the conclusion of what pieces or pawns will give you the best chances). Don't expect everything that you learn and study to influence your play immediately, chess is a very hard game, and these things always take time and dedication to residue naturally into your play. There are no easy ways.

With such a program and a consistent work routine, you will both improve your assessments of endgames, your calculations in them, and most importantly, become efficient in thinking about them. After some time, looking back at your example game here, you will very quickly convince yourself, with half the calculation we went through earlier, that such endgame ought to be drawn. Sure a lot of calculations will still be required, as is for everyone, but the difference will be that you'll have a better idea what aspects of the position you may need to pay a close attention to and what the key ideas are both for you and your opponent (for instance, you'll quickly know that if you're to stand any chance you need to start challenging black's pawn chain, and that you need some active plan to keep black's king out of play).

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    I found both answers given to be extremely helpful, was a difficult decision which to accept, but went with this one due to the extra effort put in to analyse the example given – Darren H Dec 27 '17 at 11:21
  • Sure, appreciate it :) Very glad to hear you've found the answers useful. – Phonon Dec 27 '17 at 15:41
  • Since posting this I have bought Silman's Endgame Course and I'm enjoying working my way through it. I don't usually enjoy books but this has just the right pace and level of explanation to suit my needs – Darren H Dec 27 '17 at 16:01
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    Great, that's a good one. I recall it has a very thorough section on rook endgames too, which tend to be the more frequent kind of endgames one faces, go through it carefully and couple each section with trainings. For example, on lichess you can setup any position and practice it against an engine (or a friend possibly), to get a chance of immediately applying the ideas in the book as you go along. Otherwise, just by reading chapter after chapter, it may get somewhat overwhelming. – Phonon Dec 27 '17 at 16:33
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There are all kind of endgames, so it is a bit difficult to generalize, but still there are a few things that are relevant in many cases.

Just like in the middle game you can evaluate the position based on for instance:

  • material (this is often the most important)
  • piece activity
  • weaknesses in pawn structure

Unlike in the middle game "king safety" is often irrelevant as with reduced material it is difficult to get mated and in fact the king often plays an active role in defending/attacking pieces.

If material is equal (as in this example), in many cases you can only win by promoting a pawn. The goal is then simply to create a passed pawn and push it to the other side of the board. To do this, you can either capture opposing pawns or make use of a pawn majority (basically, with the support of your own pawns to walk passed the opponent's pawns). So you should focus on how to create a passed pawn (and of course how to prevent your opponent from doing the same).

In order to improve your endgame technique you should also familiarize yourself with the most common endgames, such as:

  • mating with K+Q vs K, K+R vs K, K+BB vs K
  • winning or defending K+P vs K
  • various endgames with pawns on both sides
  • K+R and pawn(s) vs K+R (and pawn(s)). This is a very common endgame, but also very difficult to play properly. Perhaps too difficult at your current level.

Also you should know typical themes that appear in endgames like:

  • zugzwang
  • corresponding squares
  • triangulation
  • stalemate

With this in mind, regarding your example, you note that:

  1. material is equal
  2. opposite colored bishops (which tend to be more drawish)
  3. symmetric pawn structure
  4. blocked pawn chains
  5. pawns on squares of the same color as the opponent's bishop (i.e. they can be attacked by either player. If the pawns were on the same color as the players' bishops, the position would be even more drawish as pawns would be even harder to attack and there would be an additional defender for the pawns (the respective bishop).
  6. weak pawns on d3, g2 and g7

In order to win this position either side would need to create a passed pawn. Because of the symmetrical pawn structure it is difficult to achieve this by pawn breaks except for special situations like this. This leaves as the only option to somehow create a passed pawn by capturing enemy pawns.

How to do this? The most likely candidates for capture would be the weak pawns on d3, g2, g7, however these are easily defended by the king and if necessary the other pieces such as the knight on c1. Also note that it is not really possible to activate the kings (i.e. march the black king to somewhere around c3 or the white one to a more active square), because (i) white/black would have lots of time to attack and win the g7/g2 pawn and subsequently all the other pawns in the chain and (ii) the knight+bishop block the entrance on the a-b-c files (white covers the squares c4, b4, a3, b3 and black the squares c3, b3, b2, a2).

So it seems fairly impossible to just capture the weak pawns and also it seems impossible to create another weakness or passed pawn on the kingside through a pawn break. The last thing I'd check is if there is a possibility for a sacrifice (e.g. white could sacrifice a piece for two pawns on d4. However with the pawns being rather far from the promotion square it seems unlikely to succeed.

An agreed draw would be natural in this position, however at your level there is nothing wrong with playing on in order to practice and it is not impossible to make mistakes in this position. A plan for white could be to play g3 followed by f4 which could lead to another weak pawn on e5 (after capture fxe5 fxe5). Still with correct play it should be a draw.

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