PaulO is correct.

Since the length of the win streak (say 7 in a row) will be very small compared to the no. of trials you might as well drop the combinatorics.

Base chance is 1/10^7.
Expected value = no of trials * base chance
You do 10.000 trials. You expect 1/1000.

Now, this assumes the events are independent. This might not be the case. The code could have some sort of state space, i.e. in certain situations the checks are not independent or the chance of a parry might be not be constrained to between 0 and 1 in the code, etc, sort of like FlipsideOrego eluded to.

This would need to be modelled like some sort of Markov Chain.

Just because it is so easy to be wrong about probabilities I ran a few Monte Carlo simulations looking for win streaks in long sequences of trials.
They were consistent with the simple view.