Bernice: Math: Chances for a triple sequence of x-y, x-y, x-y is (1:18)^2 = 1:384 = 0.3% [first roll is anything, second roll has a chance of 1 in 18 to match (as you wouldn't see a difference between 1-5 and 5-1), third roll another 1 in 18].
That means that you should see that about every 384 sequences of three rolls. If you play only 10 games in parallel and make four moves in each per day, you should see that every 9.5 days.
It doesn't matter if the identical rolls are in the same game or different ones, as the assumption is that they are random anyway.

On the other hand, there were many discussions about the bad randomness on BrainKing (and no, we do not want to hear it all over again, please). But your experience is hardly uncommon.

Even *four* times the same roll in sequence should happen twice a year. And *five* times the same roll in sequence about once every 9 years.