But when do these endgame positions ACTUALLY come up?

This week, one of my students asked me an interesting question during an endgame lesson. This is all very well asking me to solve this position, he said, But when is that going to come up in an actual game? Well, after caning him for his insolence and setting him homework of a thousand lines, I calmly explained that the point of the basic positions is to give you a grasp of key concepts, which then inform your decision making in real positions. This is the basic study that prompted his question:

I agree - getting this exact position in one of your games is highly unlikely. Coaches do not set (and cannot predict) the same scenario you are going to get in your games; they can only ensure you know the technique. In this case, the technique of breakthrough. The goal (unlike in a lot of middlegame puzzles) is not an immediate checkmate or winning material; it is to create a passed pawn, which in this position is a winning advantage. It's a very basic position; I literally googled "chess pawn breakthrough" just now and a video came up with the exact same position. If you know the technique, you're more likely to solve:

Note this isn't even the same exact tactic. And yes, this is a position taken from an actual game I had (although the follow-up moves in the puzzle are different, because White didn't capture immediately). The passed pawn was in fact crucial in winning the game:

In the game, White resigned after c2, seeing what was coming. While this was just a general explanation for my student in the case of a breakthrough, there were actually practical applications:

This was the next position I showed him. I have not given this position as a puzzle this time, partly because he might object to my giving away the content of a whole lesson for free. (It wasn't the whole lesson). You can play about with the pieces at home if you wish, but you probably don't need to solve it to understand the theme. When I was originally shown this position, the takeaway was explained as "a King will always beat three unsupported pawns, provided they are not too far advanced". This is not strictly true; a King can always STOP three unsupported pawns; he may not "beat" them in the sense of capturing them. This might be an obvious distinction if we consider the following position:

This is a draw, because the Kings can do nothing other than shuffle between e1 (d8) and a diagonally adjacent square. Although they are able to capture one of the opposing pawns, they cannot afford to. So we know that a King is not "beating" those pawns unless they can be persuaded to move forward. Tweak the circumstances slightly, and you have a mildly interesting (though admittedly easy) puzzle:

Don't tell me endgames are boring when such subtle differences have such dramatic consequences for the evaluation! Versus three pawns is even more interesting, because although White should win that K v 3 pawns position above, it is not trivial. It is very easy for an uninitiated player to lose that position with the White pieces. But the basic idea is the same: to win that game as White, you need to force the Black King to move. Conversely, the Black King is hoping the White pawns have to move before he does.

The above was the position that my student had (as Black) in a game that prompted me to think: "OK... we're not putting off endgames any longer". The first thing he did in this position was advance his two central pawns. To an extent he could have got away with that, but it was not the winning idea. Had we already done this endgame lesson, he'd have known there was no point in advancing those pawns, because they can be stopped. So given that the first thing White is going to do (if they're following endgame principles) is activate their King, it makes more sense not to advance the pawns yet, so they are closer to their own King (and bishop) and thus will be better protected. The next position is also a trivial one, but can be frustrating when presented in puzzle format:

This is very rarely given as a puzzle position because if your first guess was incorrect, the chances are you still had A right answer. There are five first moves there that give the quickest checkmate. But in other rook endgames, the best technique is to move the rook as far away from the enemy King when it has a choice of squares, so that's what it did. Now that you know that's how the puzzle is set up, solving this will be easier, even though you start further away from mate:

However, if you know the technique, you'll have seen it immediately. Or, maybe you'll have figured out what the move should be from the lone fact that the King should not be allowed to move back towards the wrong corner (corner of the opposite colour to the one the bishop uses). If you fall into the first category, you'll have no problem with the whole thing:

Now, why have I devolved from talking about techniques like breakthrough and some actually interesting pawn ending nuances to the basic solved mates? (Admittedly, not everyone would call the N+B mate "basic"). Well, if you look at the two rook endgames (particularly the starting position of the second one), are you ever going to have that exact position? Odds against - yet I don't think anyone would have trouble extrapolating the idea that if you've learned the K+R v K mate, you know any variation of that position. For example:

Without knowing the ending, it might be tempting to try and preserve the Queen/pawns, and try and find an advantage another way. It won't work; Black will be the one playing for a win then. If you're versed in rook endings, you'll have no qualms about sacrificing on h1 and converting the win with the rook. Since most of us won't anyway, I hope you enjoyed the exercise of the conversion once (most of) the pawns were cleared. But since "endgames are boring" (apparently, according to some, I don't know who), let's come full circle to show two examples of breakthrough in opening theory. Yes, you read that right!

And a non-puzzle one so that you can enjoy from move 1. Also, yes, I have had this position and won - a handful of times. According to game explorer anyway, I'm 4/4. Those who know me/ regular readers will have probably guessed what's coming!