Of course, there's no reason to believe this phenomenon is limited to opening rolls. In general, it seems one should bear in mind the enhanced probability of duplicate or similar rolls in planning strategy.
Has anyone run a test on the distribution of single die rolls? One way that these observed deviations from the norm could arise would be if, say, the chance of rolling a 4 on a single die was significantly higher than it should be. Depending on the pseudo RNG that is used, this might be a simpler explanation than any theory involving pairs of dice.
My guess would be that the random number generating function is fine. After all, think how hard it would be try and write a random number function but actually write something that produces the results we are seeing. The bad code would be obvious. Instead, I suspect that the code is not being called properly. Consider this outline for the code:
Whose turn? - Player 1 What do we need to do (accept double, accept draw, roll dice, etc.) Roll dice Show dice Player 1 moves Player 2's turn What do we need to do (accept double, accept draw, roll dice, etc.) Show dice Player 2 moves
It would be pretty easy to bury a bug that could give us the results we are seeing with something like this.