denis_berthier wrote:...gB ratings for the cbg-000 collection of 21,375 controlled-bias minimal puzzles.
The conclusions are similar to those in previous posts with the W and B ratings.
1) gW vs gB:
Note that one must always have gW ≥ gB
In reality, there are only 48 differences, i.e. a proportion of 0,22% differences.
And there are only 2 cases with difference > 1 (0,01%) and none with difference > 2.
2) B vs gB:
Note that one must always have B ≥ gB
In reality, there are only 32 differences, i.e. a proportion of 0,15 % differences.
And there are only 2 cases with difference > 1 (0,01%), including only 1 with difference > 2.
After computing the gB ratings for more puzzles (using an unpublished version of Defise/François Cordoliani's SHC software), here's an update of the above preliminary results, which only makes them more precise.
The collection of minimal controlled-bias puzzles used in the new comparisons now contains 212,416 puzzles (the first 10 "small" cbg collections), i.e. 10 times more than above.
[Edit 24 Jan. 2024: now 1,062,382 puzzles (the first 50 "small" cbg collections)]
[Edit 29 Jan. 2024: now 3,207,961 puzzles (the first 97 "small" cbg collections; more than half of all the cbg puzzles);
the reason why I'm occasionally continuing to add gB-ratings is mainly about finding the largest differences - the overall stats remain unchanged.]
[Edit 02 Feb. 2024: now the gB ratings are computed for all the cbg puzzles; as before, the overall stats remain unchanged;
a few cases of large differences ( i.e. > 3) between W, gW, B and gB have appeared (but they remain extremely rare).]
After checking that SudoRules and SHC give the same gB ratings for the cbg-000 collection of 21,375 puzzles, I used SHC* for the larger collection.
(*: a non-published version of SHC that has g-braids - it isn't published because the presence of g-candidates is not compatible with some of the optimisations done in the public version.)
Consider the graph for the following 4 ratings: W, gW, B, gB.
- Code: Select all
gW
/ \
W gB
\ /
B
As one moves from left to right, the ratings can only decrease (with possible extremely rare exceptions between W and gW due to non-confluence) and there's no a priori relationship between gW and B.
What the results say is, for each step to the right, the number of differences is of order 2 in 1,000 and the number of differences > 1 is of order 1 in 10,000.
Moreover, the number of combined differences (i.e. from W to gB, whichever if the tow path you take W-gW-gB or W-B-gB) is about the double of the direct differences - which means the differences "non-braided to braided continuity" and "non-g to g right-linking objects" are essentially independent.
Detailed results (including gB ratings and extended CB-stats.clp file) are available on GitHub: https://github.com/denis-berthier/Controlled-bias_Sudoku_generator_and_collection
Note 1: as usual for this kind of statistics, the above results can obviously not be extended to collections with specific conditions (e.g. hardest puzzles, puzzles with some pattern, ...)
Note 2: the fact that whips and g-whips have no loops make their proximity with braids or g-braids all the more interesting.
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