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, and also on the person doing the deeming. 

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?

To take an extreme example, imagine a wheelbarrow-full-of-dice (ten thousand, say), each with a tiny individualized serial number. We tip the barrow out and exclaim "Whoah, what are the chances of getting *this*?" That is, of seeing say a "3" on die 1, a 6 on die 2, ... etc. If we work it out, $P(d_1=3)\cdot P(d_2=6)\cdot
\ldots P(d_{10000}=2)$ is $6^{-10000}$. The chance of that result is incredibly small. If we repeat the experiment, we get another equally unusual event. In fact, *every single time we do it, we get an event with probability so astronomically unbelievably small that we could almost [power a starship](https://en.wikipedia.org/wiki/Infinite_Improbability_Drive) with it*. The problem is that the calculation is meaningless, because we specified the event post-hoc.

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" actually hold.