Remember my old comparisons of ratings reported in [PBCS 1 to 3]
(https://www.researchgate.net/publication/280301697_Pattern-Based_Constraint_Satisfaction_and_Logic_Puzzles,...,
https://www.researchgate.net/publication/356313228_Pattern-Based_Constraint_Satisfaction_and_Logic_Puzzles_Third_Edition)
and recalled here:
http://forum.enjoysudoku.com/pattern-based-constraint-satisfaction-2nd-3rd-eds-t32567-11.html?
in particular those for the W and gW ratings, based on the 21,375 first puzzles of the controlled-bias collection (cbg-000 ):
denis_berthier wrote:W vs gW
Note that one must always have W ≥ gW
In reality, there are only 48 differences, i.e. a proportion of 0,22% differences.
And there are only 5 cases with difference > 1 (0,023%) and only one with difference > 2.
The question here is: what about the puzzles in T&E(3)? As this is a completely different collection - strongly biased, with all the puzzles having a particular pattern (tridagon) -, there's no a priori reason that would allow to extend the previous results to it. And indeed, they can't be extended. The differences are much higher.
To be more precise, consider the W+Trid-OR5W and the gW+Trid-OR5gW ratings (with ?*max-guardians* set to 8 and with all the ORk-consistency and splitting rules active). From my experience with puzzles in T&E(3), this is a good basis for comparison.
The comparison is here restricted to the first 10,000 puzzles in mith's collection of 158,276 min-expands.
Of course, one always has: gW+Trid-OR5gW ≤ W+Trid-OR5W
In reality, the W+Trid-OR5W and gW+Trid-OR5gW ratings are different in 3.69% of the T&E(3) puzzles (instead of 0.22% for W vs gW in cbg-000).
Also, 1.12% of the puzzles that are not solved in W8+OR5W8 get solved in gW8+OR5gW8
Whether this larger difference is totally due to the puzzles being much harder than those in cbg-000 or whether this is somehow specifically related to the presence of the anti-tridagon pattern remains undecided at this point.
For two examples of puzzles with different ratings, see:
- http://forum.enjoysudoku.com/1418-in-158-276-t-e-3-min-expands-t41482.html
- http://forum.enjoysudoku.com/5383-in-158-276-t-e-3-min-expands-t41504.html
The difference can appear with the presence of ordinary g-whips, ORk-gwhips or both.
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