In addition to the seven different vesrions in the TCR (blank, TUT, Circus Circus, Egypt, Luxor, Pyramid and Nile) some have mixed UV markings. I have some that are different from side to side. I can't recall which ones right now, but they include being blank on one side and having a UV on the other. Also, I have ones that are two different UV's, one on each side (as opposed to different UVs on one side).
I have not seen an appreciable difference in the distribution of blank to UV marked.
You should also know that (unless I am mistaken) the earlier checks were linen finish and later on, only satin finish is used. Therefore, the Luxor $1's (except for the mixed UV situations) have 14 varieties! Seven of each security code, and each in linen and satin finish.
The linen ones are harder to come by. BTW - The Luxor is constantly mixing in newer checks. I typically go to the cage, buy a rack of 100, go to a lighted area and pluck out the whiter ones. Usually they are newer. Last year (at the Convention) I got a hand-held UV light (thanks Mr. Knapp) which I use to check the security codes for the mix-up conditions.
If you do not have a blacklight, you can go to the Excalibur's Fanatsy Faire arcade. They have a glow-in-th-dark display of stuff for sale for the kids that is illuminated with a blacklight. (Perhaps there is one in the Luxor at the gift shop.)
My overall point is, BE CAREFUL. This stuff is addictive, and your questions are Slippery Slope kind of stuff.