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MatPlus.Net Forum Promenade Funny statistic on helpmate move length
 
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(1) Posted by Jakob Leck [Friday, Jul 26, 2024 23:02]

Funny statistic on helpmate move length


I noticed some weeks ago that the number of helpmates in n moves in the PDB seems to quite closely follow 64000 * 2^(2-n). Coincidence? Or some combinatorial background, likelihood of cooks, ...? I found it striking, and it doesn't look as clear for non-cooperative stipulations. (Or, well, to some extent for #n with n from 2 to 6 or 7...)

number of moves vs. number of problems in thousands in pdb, accessed at the end of April this year
helpmates
2 - 66
3 - 34
4 - 11
5 - 6
6 - 4
7 - 2
8 - 1
9 - 0.4
10 - 0.25
(Quality of the data is uncertain, e.g. h#3.5 should often be classified as h#4 here due to the "h#4, 0.1.1..." convention (should I say abomination?). Anyway, looks like we should be composing more h#4 and h#5...^^)

direct mates
2 - 81
3 - 68
4 - 25.6
5 - 10.4
6 - 5.2
7 - 3
8 - 1.9
9 - 1.2
10 - 0.9

selfmates
2 - 13.2
3 - 12.5
4 - 7.1
5 - 6.2
6 - 4.7
7 - 3.9
8 - 3.1
9 - 2.5
10 - 1.9
 
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(2) Posted by Kevin Begley [Saturday, Jul 27, 2024 05:06]

Would be interesting to see more correlation data like this (especially if fairies/orthodox are considered independently).
Also, would be nice to see data for Proofgames.
 
 
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(3) Posted by Jakob Leck [Saturday, Jul 27, 2024 12:42]

Ah, yes, I had done the same for proof games, not as relevant, I would say... For fairies I really wouldn't bother. Too diverse.

for proof games: number of moves - number of problems in pdb
5 - 52
6 - 93
7 - 140
8 - 174
9 - 235
10 - 189
11 - 176
12 - 155
13 - 174
14 - 148
15 - 173
16 - 228
17 - 209
18 - 191
19 - 175
20 - 161
21 - 134
22 - 99
23 - 105
24 - 79
25 - 71
26 - 49
27 - 55
28 - 52
29 - 32
30 - 28
31 - 17
32 - 17
33 - 7
34 - 11
35 - 7
 
   
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(4) Posted by Hauke Reddmann [Saturday, Jul 27, 2024 18:33]

Did you try the data from WinChloe instead? Then you'll get a Poisson distribution.
<runs for his life>
 
   
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(5) Posted by Kevin Begley [Sunday, Jul 28, 2024 11:37]

LOL. I admire Hauke for spitting funny name puns in such risky times.
 
 
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MatPlus.Net Forum Promenade Funny statistic on helpmate move length