For a project that aims to improve the estimate, I do not understand the statement
“Avoiding adjacent kings only improves the upper bound by 10%, which is not worth the complications and resulting slowdowns
I could understand it if it were claimed that there must be much larger low hanging fruit, so that we can postpone this one for now, but I don’t see any such claim.
Chances are, at some time, further progress has to come from such relatively small improvements.
You seem to misunderstand the relation between upper bound and estimate. Improving the upper bound by 10% would do nothing to improve the estimate. We'd just find that for instance 5.7% of the sample is legal instead of 5.2%. Generating a 10% bigger sample and filtering out adjacent Kings is way more efficient than complicating the generation process to avoid those instances. The only way to improve the current estimate is to make it more accurate by using a larger sample.
“Avoiding adjacent kings only improves the upper bound by 10%, which is not worth the complications and resulting slowdowns
I could understand it if it were claimed that there must be much larger low hanging fruit, so that we can postpone this one for now, but I don’t see any such claim.
Chances are, at some time, further progress has to come from such relatively small improvements.