Just completed an analysis of all Doubles that have played in Texas Midday since 2-3-2003.
There have been 88 Doubles/Triples since 2-3-2003. Of those games there have been 36 instances where 1 or more digits repeated from a prior game as part of the Double. This is only a 41% repeat rate which is considerably less then the overall repeat rate of 60-62%.
I also looked at the repeat rate between Double games as I keep a database for nothing but Doubles & Triples. There have been 31 instances of repeats from a prior Doubles/Triples game which is slighlty less then the aforementioned 41% rate.
Of the 36 cases where there was a repeat digit it was pretty much 50/50 as to whether the digit that repeated was the single digit in the Double or the actual digit that did double. This was a 17 to 16 game ratio. There were 9 cases where the digit that doubled came over 5+ games out and five cases where all 3 digits came 5 or more games out. There were 23 out of the 88 games where 1 digit came 5 or more games out so the digit that did play from within the first 4 games was the one that Doubled.
In conclusion it appears that when a Double plays the majority of the digits will come from within the most recent 4 games as there were 50 instances out of the 88 games where ALL digits did come from the most recent 4 games.
A final note on the makeup of the Doubles games. If you divide the 10 digits into pairs (sort of like Vtrac for Doubles) with 0-1, 2-3, 4-5, 6-7, 8-9 you will have an overwhelming majority of the Doubles to be comprised of digits from 2 different sets of numbers.