You should not do a calculation of probability for an event deemed surprising *post hoc* as if it were an event specified before it was rolled (observed).

It's very difficult to to do a proper calculation of *post hoc* probability, because what *other* events would have been deemed at least as surprising depends on what the context is. 

Would three ones twice in a row at an earlier or later stage of the game have been as surprising? Would *you* rolling three ones have been as surprising as him rolling them? Would three sixes be as surprising as three ones? and so on... What is the totality of all the events would have been surprising enough to generate a post like this one?

(Even if it were legitimate to do the calculation *as if it were a pre-specified event*, it looks like you have that calculation incorrect. Specifically, the probability (*for an event specified before the roll*) of taking three dice and rolling (1,1,1) is (1/6)^3 = 1/216, because the three rolls are independent, not 1/56, and the probability of doing it twice *out of a total of two rolls* is the square of that - but neither the condition of being pre-specified nor the "out of two rolls" hold)