There are lots of "correct" answers to this question, but one great roll would be rolling double 3s, purchasing Oriental, then rolling double 1s, and purchasing Vermont, then rolling an 9 and getting the Advance to Go card. read more
double sixes followed by a 3-1 which would yield you Illinois Avenue and Water Works giving you a monopoly on the utilities. While not following the rules of the question, I did play a game where I my opening roll was a five so I bought Reading Railroad. On my next turn I rolled double fives followed by double fives followed by a 6-4. read more
Andrey Markov. Markov is best known (well, as well known as stochastic mathematicians can be) for inventing the statistical analysis method the Markov chain. read more
When doubles are rolled, the player resolves the roll as normal (including purchase, renting or passing "GO"), but rolls the dice again for another turn. The player moves forward as directed by the dice, and if this is also doubles, rolls again. read more