Just a thought i had after you asked if it was possible to get a derived set of random numbers from roulettes random number stream....

So for example, considering we are talking about sets of 3...

If we look at the results of dozens for example 3,1,3,3...

Beginning with the sequence 1,2,3..

123

312 > 3 was in position 3

132 > 1 was in position 2

312 > 3 was in position 2

312 > 3 was in position 1

So from 3,1,3,3.. Our new derived set is 3,2,2,1..

From the 27 combinations you speak of,

18 contain 2 dozens with 1 repeating, for example 212, 113, etc

6 contain 3 "different" dozens for example 213, 123, etc

And 3 combinations contain the same dozen repeating, for example 222, 111, 333... So from that if we assume that the last 2 dozens to show up are more "likely" to appear, than that makes it clear that we should avoid playing for dozens in position 3, just like you are doing with your 1,2,4 strategy...

Just like you say though, these are the works of mathematicians, not me!