Why do chess engines sometimes miss good moves (or take forever to spot)?

Question

It is not the first time that I found a greatly superior move than the chess engine did, it even takes them a while to understand these moves after you make them.

For example, the move 15 ... Bf2 in the game below:

[fen ""]
[StartFlipped "1"]

1. e4 e5 2. Nf3 Nc6 3. Bb5 Nf6 4. O-O Ng4 5. h3 h5 6. hxg4 hxg4 7. Bxc6
gxf3 8. Qxf3 Qh4 9. Qh3 Qxh3 10. gxh3 dxc6 11. Re1 Bxh3 12. f3 Bc5+ 13. Kh2
Bf1+ 14. Kg3 Rh3+ 15. Kg4 Bf2 16. Rxf1 Rg3+ 17. Kf5 Rxf3+ 18. Kg4 Rg3+ 19.
Kf5 f6 20. d3 Kf7 0-1

The move remains unnoticed by the engine for a while, it is not until I move that it starts to see the rest of the iceberg.

I know it all depends on how much time you give them to analyze though, but it is unacceptable that sometimes humans manage to find these moves in less time than computers.

• Why do chess engines fail to spot good moves in some positions? (I once read something about a 'horizon effect', maybe this is related?)
• Are there other notable examples? (e.g this famous puzzle, it takes a while for computers to solve)

These questions contain useful information to partially explain some factors that might be causing this anomaly: What algorithms and heuristics are popular in computer chess?, When playing a Computer opponent what situations should I create to give myself a better chance of winning?, Computer evaluations: How trustworthy are they?

Notes: The trap is known as the Fishing Pole, I am aware I missed a mate in 3 (and a mate in 7) :(, the time limit per move was days (correspondence chess) but it took me like 5-10 minutes to finish calculating everything.

Answer 1

Why do chess engines fail to spot good moves in some positions?

The reason are called forward pruning techniques (see http://chessprogramming.wikispaces.com/Pruning) with ProbCut in first line.

The move 15...Bf2 is pruned on shallow deeps because it includes the sacrifice 16.Rxf1 without regaining something concrete with evidence immediately after. The matenet is also hard to see, because it includes some further 'silent' move as for example 17...Ke7, and yes also engines, not only humans have difficulties to see distant silent moves as they are often pruned.

In this concrete case you even cannot say, that engines fail to spot good moves, because also the continuation 15...Rh3h1 is a very good move and leads to an absolutely won position.

Last but not least you have to remember, that an engine's strength is always measured in terms of elo-strengh and not in the ability to find the absolute shortest way to win. It does not matter, if a engine wins in 8 moves or in 25 moves. Seeking to much for the shortest win, would mean a waste time, because most time there does not exist such a secret good move at all. And waste of time would hurt the engines ELO-Rating.

Answer 2

I am trying this with Houdini 1.5 (the free version). At first 15...Bf2 doesn't show up in the top 5 moves, then when it reaches depth 15, it does, as #1. Takes about 19 seconds on my four year old computer, not that long.

So it doesn't fail to spot it, instead it only considers it the best move once depth 15 is reached. Apparently, as long as it only looks 14 ply deep, other moves are better (like the also winning 15...f5+).

Apparently 15...Bf2 is a mate in 8, which is 15 ply (8 moves by black, 7 by white). But at first it just considers it +10 or so, then +20, then mate in 10, then mate in 8.

The mate in 8 line is:

[FEN ""]

1. e4 e5 2. Nf3 Nc6 3. Bb5 Nf6 4. O-O Ng4 5. h3 h5 6. hxg4 hxg4 7. Bxc6 gxf3 8. Qxf3 Qh4 9. Qh3 Qxh3 10. gxh3 dxc6 11. Re1 Bxh3 12. f3 Bc5+ 13. Kh2 Bf1+ 14. Kg3 Rh3+
15.Kg4 Bf2 16.Rxf1 Rh4+ 17.Kg5 Ke7 18.Rh1 Rxh1 19.Nc3 Rah8 20.Nd5+ cxd5 21.d3 R8h5+ 22.Kg4 R1h4#.

Clearly when Houdini 1.5 thinks 15 ply deep, it doesn't consider all possible lines that are 15 ply deep, or it would see the mate in 8 the moment it finished its 15-ply-depth search.

I think that is because of pruning, it stops looking at some lines when it thinks they aren't promising enough. That way, it can spend more time on the promising lines, and the programmer thinks that the pros outweigh the cons. But I don't have an answer right now on what it decides to prune here (it probably makes millions of separate pruning decision at depth 15).

It may have to do with the silent moves ...Ke7, and ...Rah8, two non-check non-captures in a line where black is a piece down. It's likely that it decides somewhere that it's not useful to keep looking in this line. Only later, when it does continue the line and finds the mate at the end do other lines that prolong the game (with 18.Rh1 Rxh1 and so on) then show up.

Anyway, it's known that it doesn't work that well to let a computer think for a few seconds only if you want to get to the bottom of something, a few minutes is better.

Answer 3

after reading all answers and other sources, I now understand that they don't 'miss' or chose to miss these moves, the humans programmed them in such way that they follow a specific pattern on (where/how/when + to) search and more importantly when to pause search and look into more promising lines in order to save resources.

But given enough time, a computer will fin every possible combination on a certain depth.

TL;DR

• Q1: they never miss moves, they just haven't found them yet
• Q2: they take time because they are programmed to save resources and they will prioritize some lines over other ones (e.g the ones that don't have passive moves or don't recover material in the next few moves).

Answer 4

I think everyone is missing a much quicker mate. When checking the position with Houdini 3, black actually has mate in 3 on move 13. Instead of Bf1+, black should've played Bf2, and it contines with 14. d3 bf1+ 15. Bh6 Rxh6#. So, in a unusual answer to your question, maybe certain engines didn't see your move right away, but, in the case of Houdini 3, it found a much quicker mate.