The difficulty of chess puzzles.

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Topic The Rybka Lounge / Chess / The difficulty of chess puzzles.

By deka

Date 2012-02-26 23:05

Here are five easiest three-movers from chesstempo.com that do not end in mate and have at least 25 solving attempts.

4rrk1/5qp1/p7/1p4b1/3PR1P1/1PP5/P3QPP1/4R1K1 w - - 1 1

1. Rxe8 Rxe8 2. Qxe8+ Qxe8 3. Rxe8+ *

2r3k1/p1r2pp1/1p1p2np/3Pp1q1/4P3/4RPP1/PPBQ3P/2R2K2 b - - 0 1

1... Rxc2 2. Rxc2 Rxc2 3. Qxc2 Qxe3 *

3n1r2/1pp1qr1k/p5p1/3Rp2p/4P3/1Q1R1PP1/PP2N1KP/8 w - - 1 1

1. Rxd8 Rxd8 2. Rxd8 Qxd8 3. Qxf7+ *

1k6/p4r1p/1p1R1pp1/1N2n3/8/8/PP3PPP/1K6 w - - 1 1

1. Rd8+ Kb7 2. Nd6+ Kc6 3. Nxf7 Nxf7 *

3r2k1/p2q1pbp/3r2p1/2RB4/8/P4Q1P/6P1/5R1K b - - 1 1

1... Rxd5 2. Rxd5 Qxd5 3. Qxd5 Rxd5 *

And five hardest puzzles, also 3 moves long:

2r2r1k/4N2p/3p4/p5Rb/2PbpPR1/7q/P1B1Q2P/7K w - - 1 1

1. Qd1 Bf6 2. Rxh5 Qxh5 3. Nxc8 *

r6r/pp3kp1/q6p/2QpB3/P4PPb/2Pb1K1P/1P1N4/R6R b - - 0 1

1... Be2+ 2. Kg2 Qd3 3. Rh2 Qxd2 *

8/5R2/R4pk1/4p3/8/5PK1/pr4PP/3r4 w - - 1 1

1. Raxf6+ Kh5 2. Ra6 Rxg2+ 3. Kxg2 *

6k1/1b5p/8/1p1P1Q2/2r5/4q1BP/6BK/8 w - - 0 1

1. Be5 Qh6 2. d6 Rd4 3. Bxd4 *

2r3k1/R4p1p/5B2/4Pp2/2p2P2/2br2PK/7P/2R5 w - - 1 1

1. Ra3 Bxe5 2. Rxc4 Re8 3. Rxd3 *

Where's the difference? Has it something to do with the amount of material, or the symmetry? Hardly, the average material is 50.05 for easiest and 44.85 for hardest puzzles. Neither is symmetry the cause, as the average amount of material in symmetry is bigger for more difficult problems; 3.6 - 4.2. The difference between two best moves is in all puzzles large and almost identical on average for both sets; 4.33 - 4.23.

Remarkably, both Stockfish and Rybka were able to spot the best moves and winning advantage in less than 1 second for all puzzles. For engines the difficulty is virtually nonexistent.

So, what factors make some puzzles more difficult than the other ones? What do you see?

By JhorAVi (***)

Date 2012-02-28 00:40

I see the easy set are just direct one deep material gains while the hard puzzles have more variations to consider.

Secondly, humans do better on positions that are usual to them. These are Positions they often come across from previous games and experience(pattern recognition). Patterns also count other positions but look similar. So the level of complexity of the puzzles might be the same for Engines but the positions that looks close to what humans have encountered or solved in the past should be easier.

By deka

Date 2012-02-28 16:56

>I see the easy set are just direct one deep material gains while the hard puzzles have more variations to consider.

So the main difference is the number of apparently sound moves that distract human mid during calculations?

Can you spot more factors?

By JhorAVi (***)

Date 2012-02-29 23:47 Edited 2012-02-29 23:49

That counts too but as what I've said, familiar positions human often encountered in the past should be easier to assess. Take a look at chess960(first row pieces are shuffled). Geometrically chess960 its no more complex than the normal start position as engines agree But it looks very very complex if you ask me. That's because I have less experience with it in the past.

By deka

Date 2012-03-01 16:55

Actually all puzzles on chesstempo were taken from real games, so at least in this case familiarity should be counted out.

But could you be more specific, which is what you meant?

1) positions that actually occurred before in published human or engine games.
2) positions that contain familiar typical elements, or are very similar, often differing by one or two pieces or their placement

By JhorAVi (***)

Date 2012-03-15 07:30

Familiar positions range from very familiar to not so familiar. That's why we do good on some but worse on others. Ofcourse the number of variations also contribute to the difficulty.
I will site myself as an example. I do tactics training at chess.com for years and peak at 2800+ by solving 3 problems a day(limit to free membership :-)) What's strange is I do good with problem ranges 2700-2800 and often commit mistakes with 2500 level problems on my other account. I believe the reason is I often encountered similar hard problems from my past tactics softwares like ct-art, chessimo and various puzzle books. I noticed (and you should agree) that brilliant problems are more popularly used in many sources than ordinary ones and that explains my familiarity with them.

By Uri Blass (*****)