I have noticed that, among opponents of Elo strength about 1300 (USCF class C to D), many play the opening and midgame almost as well as a 1400- to 1500-strong player but seem suddenly to drop to, say, 1100 strength as the endgame approaches. The 1300-strong player who blunders away endgame after endgame is a familiar character in the world of chess.
Without an excessive investment of the player's time, what are some ways a typical 1300-strong player can improve his or her endgame?
Some advices:
Replay their games and try to understand their moves and the evaluation of commentators. There are several good books, I think Evgenny Shereshevsky's excellent classic "Strategy in the Endgame" is understandable at 1300-level. At least most of it, and you can keep the most difficult examples for later when you will have developed a better understanding of general principles. Some books about Bobby Fischer's endgames have been well commented too. I suppose there are good videos/DVDs on the market as well. Avoid anything overly complicated right now, like John Nunn's works; Mark Dvoretsky's and Karsten Muller's ones are very good but too hard at 1300 elo - keep them for later.
The rules there are somewhat more clear-cut (there is basically one single goal: queening one of your pawns first), and they are mandatory if you want to understand more complex endgames later on, because several concepts are similar and because they may transpose to pawn endgames in case of exchanges.
Endgame theory can be surprisingly complex, it is a dry matter to memorize, and pratical endgames is what you should be looking for. At 1300 elo, I assume you already master the basic mates KQK, KRK and KBBK. KBNK is fun to look at but not super useful in practice, learn it if you enjoy it but don't force yourself if you don't.
I would still encourage you to learn KPK well enough to be able to evaluate any position with KPK in less than thirty seconds, and be sure about the next best move. Have a look at KPKP theory (counting in pawn races, opposition, trebuchet) and at KRPKR (Philidor, Lucena), but already here you merely want to get familiar with the ideas, not to remember everything.
like chesstempo or lichess offer endgame exercices and adapt their difficulty to your performances in solving them. If you have fun doing some once in a while (I sure do), do it! Usually the free registration is enough to get access to five or ten exercices per day - just the right amount for effective training !
You may use them to have a look at the evaluation of a given position if you have already studied it by yourself or with a book/video and want to check your conclusions. But going through variations generated by tablebases is disheartening enough : sometimes they lack logic, or make you feel that simple things are overly complicated because they try to minimize distance to mate, and they come without explanations (or explanations limited to even more complicated variations)...
The best way is: first alone or with your opponent, then write down your main conclusions/interrogations, and then review the endgame with a stronger player / a coach / a reference book if the position is a theoretical one / a software if really you have nothing better available. Finally, compare with your first notes, that's when you will make huge progress about your thinking process !
Good luck !
Here are two relatively simple endgame-related principles from which a typical Elo 1300-strong player could profit.
PAWNS ON SQUARES BISHOPS CANNOT REACH
When some but not all bishops have been captured, the 1300-strong player can learn to push his or her pawns to squares of the color the bishops cannot reach.
Here is an example from an actual game. The Black player's Elo strength is about 1300.
[FEN "8/pb3kp1/2p1p2p/2P1Kp1P/1P2pP2/P3P1P1/2B5/8 b - - 2 33"]
[Title "Black to move, the board seen from Black's perspective."]
In this game, White had been playing tactically until Black unwisely let the dark-squared bishops be exchanged. Foreseeing a won endgame, White stopped playing tactically, quickly exchanged rooks and queens along the open d-file, and soon reached the diagrammed position.
Material is equal, but White's bishop
Black probably never realized that his game was already lost. Indeed, Black probably left the board without understanding what had just happened to him, because he did not grasp the principle of pawns on squares bishops cannot reach. White won a game Black should probably have drawn. Black never knew why.
Now you know why. Next time in such a situation, you can do better.
If your strength is about Elo 1300, then you might add an easy 20 to 25 points to your strength merely by recongnizing—before the endgame arrives—how the colors of the squares on which the pawns stand can advantage the one player or the other once the endgame arrives.
KINGS BEFORE PAWNS
Players at an Elo strength of 1200 often fail to hurry their kings toward the fifth or, better, sixth rank when the endgame arrives. Some 1300-strong players too fail in this way. In the example, Black might have salvaged a draw if his king were further forward.
This is actually a complicated point, because sometimes it is preferable to push a pawn toward the seventh rank as soon as possible, temporarily leaving the king far behind. Admittedly, better players (Elo 1800+) disagree among themselves as to the general desirability of such pawn sprints, but even when a sprint is tried and even at the Elo-1300 level, the sprinting pawn tends to distract the opponent long enough for the king to be brought up a little later, so the principle still applies.
Most good players agree in any case that leaving pawns at home while the king hurries forward is often a prudent endgame practice, especially if all relevant pawns are on the same wing but sometimes even when pawns on both wings are in play. Once the king has centralized itself, preferably at least on the fifth rank, pawns can march as opportunity allows.
Kings before pawns: a little reflection on this principle can add another 5 or 10 points to one's strength in the 1200-to-1300 range.
COMPUTERS
Computers can calculate or tabulate absurd numbers of exact endgame variations a human master would never attempt. Therefore, it can be hard to learn proper endgame play when one's opponent is a computer. Playing Black, a computer might salvage a draw or even a victory in the diagrammed position, not only taking the game but also cheating White of the position's teaching value. For this reason, a 1300-strong player might prefer human opposition against which to practice endgame principles like the principles this answer discusses.
I am a big fan of ChessKing's material for mobile devices. Perfect for tablet size devices that you can study. Their applications range from opening, mid to endgame and tactics and more.
The catch is you have to pay for the app to get the full complete courses but they do allow you to try it for free.
I'm an Android user so here's the Google Play site if your interested.
https://play.google.com/store/apps/dev?id=8196632901699712832
