Contrast perception seems to be logarithmic, that is to say it's easy to detect a doubling in contrast, rather than standard linear changes.
So going from
1000:1 to 2000:1 is noticeable, then:
2000:1 to 4000:1
4000:1 to 8000:1
8000:1 to 15000:1
Obviously I picked random starting / doubling points, so you would perceive a 5000:1 pj to be noticeably better than a 2000:1 projector, but the difference between a 4000:1 and 5000:1 pj would be more subtle (not undetectable though, with familiar scenes, equal lumens and a side by side viewing.)
So a jump in contrast from 1000:1 to 2000:1 is more noticeable than from 14000:1 to 15000:1.
When you ask how well can you eyeball CR, on familiar scenes I would be able to place it in its general tier (1000-2000, 2000-4000, 4000-8000,8000-16000) reasonably well in a familiar environment with familiar scenes and some high APL to fade to black and hold type sequences.
Intrascene CR is harder but I do find it noticeably when you go from a high ANSI DLP to a LCOS type display like the Pearl. The ANSI seems 2x to 3x in certain scenes. In other scenes the difference is hard to detect. There are certain mid to high APL scenes with lots of dark colors where the pop of a high ANSI pj is detectable. I would say to within +/-100:1 since ANSI doesn't go too high on PJs.
So going from
1000:1 to 2000:1 is noticeable, then:
2000:1 to 4000:1
4000:1 to 8000:1
8000:1 to 15000:1
Obviously I picked random starting / doubling points, so you would perceive a 5000:1 pj to be noticeably better than a 2000:1 projector, but the difference between a 4000:1 and 5000:1 pj would be more subtle (not undetectable though, with familiar scenes, equal lumens and a side by side viewing.)
So a jump in contrast from 1000:1 to 2000:1 is more noticeable than from 14000:1 to 15000:1.
When you ask how well can you eyeball CR, on familiar scenes I would be able to place it in its general tier (1000-2000, 2000-4000, 4000-8000,8000-16000) reasonably well in a familiar environment with familiar scenes and some high APL to fade to black and hold type sequences.
Intrascene CR is harder but I do find it noticeably when you go from a high ANSI DLP to a LCOS type display like the Pearl. The ANSI seems 2x to 3x in certain scenes. In other scenes the difference is hard to detect. There are certain mid to high APL scenes with lots of dark colors where the pop of a high ANSI pj is detectable. I would say to within +/-100:1 since ANSI doesn't go too high on PJs.