How difficult is it to win a winning endgame against an engine?

Question

Consider an endgame like the one shown below (white to move):

[fen "5k2/5p2/r7/8/6R1/4b1PP/8/5R1K w - - 0 50"]

Stockfish gives white a solid +3 advantage here and that seems appropriate given that white is up the exchange with an extra pawn. I don't have strong endgame technique though, so when I try to play this position against the engine, I can't seem to win. I keep running into various tactics including forced draws, pins, forks, etc, or at least can't figure out how to make progress. If I kept playing against the engine in this position and also used the engine for help when getting stuck, I imagine I'd eventually be able to drive the victory home unassisted by recognizing the various defenses black can employ as well as the resources white has for making progress.

What's unclear to me about this and other endgame positions is the extent to which the difficulty of playing against the engine is due to (1) a lack of endgame technique vs (2) the engine's calculation advantage. In other words, would having solid endgame technique allow you to reliably win endgames such as the one above, or would it often be the case that the engine is able to find refutations to seemingly good moves on the basis of its ability to just churn through possible positions? A human player might avoid certain moves because the resulting positions look like they trap a piece or invite a tactic or allow a forced draw, but an engine of course knows definitively what the possibilities resulting from each move will be (up to some depth).

The possibility that some winning endgames are either difficult or impossible to win against an engine even with well-grounded play seems especially likely (at least from my perspective) for positions involving knights and bishops. At least with rook and pawn endgames, it's easier to calculate given their ability to cut off files and ranks and stick behind pawns. With knights and bishops, however, it seems to require much more accurate play to avoid running into strong coordination sequences from the engine.

One notable example of an endgame containing an outcome-changing move that seems near impossible for a human to find comes from a game between Carlsen and Caruana

[fen "5k2/8/5pK1/5PbP/2Bn4/8/8/8 b - - 0 1"]
[StartFlipped "0"]
[StartPly "139"]

1... Bh4 2. Bd5 Ne2 3. Bf3 Ng1!!

Black can surprisingly win with 68...Bh4 69. Bd5 Ne2 70. Bf3 Ng1!!, though the sequence seems out of the reach of a human player. Looking at this position on Lichess it seems move isn't even found with the cloud analysis used which is stated to be Stockfish 13+ at depth 72. What I'm curious about is how often and in what conditions this is possible - that a position with a seemingly straightforward outcome (according to GMs) has moves that only an engine could realistically find that lead to a separate outcome.

Answer 1

An interesting question! I set up the position, gave myself 10 minutes of time and tried playing against the most difficult engine on lichess. I failed to win even though I used one takeback as well. My playing strength is about 2200-2300, I'm a national master. I checked with the engine how I could've won and it wasn't that complicated. Although I didn't win the engine from that position, I still don't think it's too difficult.

I think the positions you gave are examples of endgames where engines are significantly more resilient defenders than human players. Being a pawn and an exchange up is quite a big advantage, so the margin for error isn't that small, there are still several paths to a win. That's why it's very much possible to beat the engine. In the Carlsen-Caruana game the path to the win is much narrower.

It's hard if not impossible to classify in simple terms which endgames have the property that engine plays them significantly better than humans. Chess is too complicated for such classifications. It can happen with many different material distributions. Some common characteristics are that the margin for error is small, the position requires a lot of calculation, there's not much strategy left, and the endgame doesn't occur too frequently (so that humans haven't studied it). For example no one studies how to win positions with an exchange and a pawn up. I guess there are two reasons for that: those are rare situations and too diverse. There's not really any engdame theory in positions that are really concrete, i.e. no generalizable plans and every variation requires different approach. Humans usually prefer positions with more strategy in them. Computers are good in endgames that are calculation heavy, require being tactically aware and enable tenacious defences.

Endgame knowledge is of course sometimes useful. In your example position, it could be useful to know when R+pawn versus rook is winning, when R + g- and h-pawns vs R is winning, in which situations R vs B is winning and is it possible to sometimes defend R+h-pawn vs B? Having that kind of endgame knowledge let's you liquidate to simpler endgames in favorable situations. But engines rarely give you those chances.

Answer 2

Note that I answered quite a few CSE endgame questions about how to bring a large advantage home safe. This position is different, though, as Black can offer much resistance. For once, I am not so sure if I could win this convincingly (in the other cases I would have agreed to blitz for the leading side - I have trust in my endgame technique). Here it is not so easy to split the win into smaller goals. I would try to push the pawns to g5/h6, double rooks to enter the 8th and then win with h7-h8Q. (Black should not move his f-pawn, as the king gets the wrath of two rooks, and a rook exchange should make the position hopeless.)

But to answer your question concretely, my problems in this position have nothing to do whatsoever with computer "trickery", but rather with the lack of a plan that convinces me. Likewise, I think a weaker player will have more problems to find the correct plan than the computer torpedoing the plan with tactics, and this is generic - wacko moves like Ng1 above should rather be the exception.

tl;dr: My opinion - tactics rarely are the decisive element in bringing home an endgame, and elusive tactics almost never.

Answer 3

What's unclear to me about this and other endgame positions is the extent to which the difficulty of playing against the engine is due to (1) a lack of endgame technique vs (2) the engine's calculation advantage.

I suspect there would not be much difference in your performance against a GM. The reason being that the GM has far greater endgame knowledge than you rather than the GM having engine-like calculating ability.

Do you know when a K+P vs K endgame is winning? Can you tell at a glance? This is something that players well below master level should be able to do. Can you mate with K+N+B vs K? At one level it is a bit of a party trick. That said a few years ago an 1800 player in our club delivered mate with 30 seconds on the clock in an important 3+2 blitz game.

An important part of evaluating an endgame position is knowing how to win that endgame. It makes no difference if you are playing an engine or a GM, the result is the same.

If you are material up in the middlegame and you are calculating exchanges to reach an endgame still material up then you have wasted your time if you can't correctly evaluate that endgame. It is all too easy to deliberately play your way to an endgame which your opponent can draw without too much effort despite being material down.

Endgame knowledge is key.

would having solid endgame technique allow you to reliably win endgames such as the one above?

Yes. I would expect to beat an engine in that position and my FIDE rating is in the low 1700's. The plan is straightforward and there is little black can do to stop it.

Answer 4

The answer depends not only on your own playing strength and endgame experience/skill, but also the type of "winning" endgame. There are endgames that are numerically overwhelming according to the computer that would be very difficult for a human to win. Here is one such example.

[FEN "1n1k4/6Q1/5KP1/8/7b/1r6/8/8 w - - 0 1"]

This a "forced mate", but requires 549 precise moves, i.e. a mistake would result in a draw. Most of it would be utterly impossible for any human to understand strategically.

However, there also exist endgames with a small (yet ultimately decisive) advantage that a human might find trivial to play correctly. Stockfish evaluates the below position to be +0.3, which is about the same advantage as White gets at the beginning, yet it is fairly straightforward for an experienced player to win against any strength of opposition.

[FEN "5bk1/3p2p1/8/3p4/5p2/3KpP2/P1N3PP/8 w - - 0 1"]

1. a4 Bc5 2. a5 Kf7 3. a6 Ke7 4. Na3 Kd8 5. Nb5 Kc8 6. g3 g5 7. gxf4 gxf4 8. h4 Kb8 9. h5 Bf8 10. Nc3 Bh6 11. Nxd5 Ka7 12. Ne7 Kxa6 13. Nf5 Bg5 14. h6 Bf6 15. h7 Kb5 16. Nd6+ Kc6 17. Nf7 Kd5 18. h8=Q Bxh8 19. Nxh8 Ke6 20. Ng6 Kf5 21. Nh4+ Ke5 22. Ng2 d6 23. Ne1 Kd5 24. Nc2 e2 25. Kxe2 Kc4 26. Ne1 Kd5 27. Nd3 Ke6 28. Nxf4+ Kf5 29. Nd3 Ke6 30. Ke3 Kd5 31. f4 Kc6 32. Ke4 Kb7 33. Kd5 Kc7 34. Ke6 Kd8 35. Kxd6 Ke8 36. Ke6 Kf8 37. f5 Kg7 38. f6+ Kg6 39. Ne5+ Kg5 40. f7 Kf4 41. f8=Q+ Ke3 42. Qf3+ Kd4 43. Qd3+ Kc5 44. Qc4+ Kb6 45. Nd7+ Kb7 46. Kd6 Ka7 47. Qb5 Ka8 48. Qb8#

Answer 5

I'm not quite sure what is exactly the point of the question, but anyway. First, as it is correctly pointed out in the other answer, top players as GMs (and engine too) are extremely resourceful in defending bad endgames. We don't see it too often in their games because they don't play too much against amateurs, but it's very difficult to win a winning endgame against such a player. Moreover, in the endgames people usually don't have much time left, which makes it even trickier.

Second, there is a concept of "technical" positions - which anyone can win against an arbitrary strong player. As a simple example, you win a R+K vs K or K+2p vs K against anyone: one simply knows how to win, and the opponent cannot stop it. So if the question is whether the position on the first diagram is technical in this sense - I'd say maybe not yet, but it has good chances to transform into one. What I mean is that white has to make a few moves: improve the king, do not allow the pawn blockade on dark squares, threaten to exchange a pair of rooks and so on, and then it'll win itself.

I'd expect myself to be able to win it in any case if I had maybe 10-15 minutes left. I'd also be very surprised if a GM (of course I assume GMs have better endgames technique than me) would not win such a position in their serious game irrespective of their opponent.

Answer 6

First with the specific position you give: I think this should be quite easy to win based on the following:

1. Black can't trade rooks. if the rooks are traded then White could easily win either by trading his remaining rook for the Bishop and pawn, or just the rook for Bishop where it creates a winning pawn endgame.

2. White has a passed pawn.

3. White has a clear path with the king. White can place his rooks on the b and c files; like b3 and c4, then c4 and b5 etc. which would shield the kings walk up the board.
   After this White can double the rooks, say on the b-file, to generate threats of a rook trade check on the Black King.

If you play with the above plan you will see the analysis starts to go from +3 to +7.

Of course in general computers are harder to beat. It doesn't matter that it is an endgame, but it does seem more obvious how tough they are in such positions.