What endgames should you be drilling against the computer?

Can anyone suggest specific endgames to practise against an engine? Endgames that all aspiring players should know. First of all, I'm thinking of forced wins for the human player with correct play. (Note: I'm not interested in bishop and knight or bishop and bishop checkmate endgames versus a lone king as these rarely happen).

After the above, I'm thinking then of more open endgames where the engine has a chance to draw or win.

Can you provide diagrams to illustrate your suggestions?

Thanks.

KQ vs KR is a must. Humans dont defend as well, and get bored quite quickly.

Thanks. Are any pawns involved in that?

Q vs R is difficult but would not be at the top of my list, it doesn't happen often. Most important IMO are king and pawn endgames as if you can assess correctly if you are winning/losing it you then know whether you should exchange down to this endgame or not. Also rook and pawn endgames occur frequently so getting the technique down will be beneficial. It is said 'all rook and pawn endgames are drawn'. Whilst this is obviously an exaggeration, if you play these endings vs the computer at its top level you will see all kinds of sneaky tactics from the machine which make a draw from -1 or -2 pawns, or make the winning path extremely narrow. If you remember these methods you can use them yourself.

I always wondered about those (pawn endings/opposition) mentioned on post 5.

The recent ones found on Daily Puzzles for example:

9/30/17-Grigoriev 1936 and

9/28/17-Nadareishvili 1963

Composition of endgame studies are tideous, but interesting.

(unable to post images or FEN, sorry)

Personally,  I would enjoy practicing KBN vs K just to say I can do it well, but it's unlikely you'll ever encounter it. Much more practical is something like KRPPPP vs KRPPP, where the superior side has a lone passed pawn on the other flank. That happens a lot, and it's still not completely understood. I'd have to look up the specifics, but it would look something like this:

Then there's always the Philidor position (https://en.wikipedia.org/wiki/Philidor_position), which is well-known, fairly common, just tricky enough that it could take some practice, and there exist numerous variations where the standard strategy must be slightly altered.

Other basic mates that would be nice to know but that are rarely encountered are KR vs KB, and KR vs KN. Those are probably more common than KQ vs KR, though, which is very difficult and rare, as others mentioned.

Ditto to Strangemover's comment: The most common, important, and fundamental by far are K-P endings, especially the KP vs K endings. 

Thanks guys. I will be concentrating mainly on King and Pawn endings as I have limited time.

How about King, Rook,and Bishop versus King and Rook?

If you're serious, I'll answer that: That's so rare that I've never even heard of such an ending.

Lev Alburt covered it in his endgame book, "Just the Facts". One of my ongoing daily games has the potential to simplify down into that if I'm not careful. (I have an extra bishop, but he has 3 pawns for it.)

Pure rook vs bishop ending with no pawns is more common I guess. And losable at top level eg. Paikidze - Zatonskih US womens champs. 

It's happened it several of the most recent Titled Tuesdays, I know, off the top of my head, that GM Yasser Seirawan has played that endgame in competitive chess at least 6 times.

Thanks. I'll have to look into that ending. I have a thing for oddball endings, I guess.

I don't thinks that's a good one because the program might get bored. 

Here are some specific diagrams I saved from "Pandolfini's Endgame Course" of K-P endings:

8/3k4/1K6/8/8/8/P7/8 w - -

8/8/8/6K1/8/5k2/P7/8 w - -

5k2/8/5PK1/8/8/8/8/8 w - -

8/8/8/8/8/5pk1/8/5K2 w - -

3k4/8/4P3/3K4/8/8/8/8 w - -

8/8/8/8/8/5kp1/7K/8 w - -

7k/5K2/8/6P1/8/8/8/8 w - -

k7/8/8/8/4P3/8/1K6/8 w - -