I think that this is brilliant. Nice work, nice creativity and I wish I had thought of it!
However, I am wondering how you got the second probability that Spock mentioned. The first, 7/36, is the probability of throwing a total of 7 with 2 regular dice. Dice are featured in the video, and I have menioned this in a lecture before now. So it is well-known.
With regard to second probability, which is otherwise 48/216, the obvious extension is consider the probabilty involving 3 dice. After all, the narrator talks about another throw. For 3 dice, the probability is more nuanced and eventually one gets the table:
n P(n)/216
3 1
4 3
5 6
6 10
7 15
8 21
9 25
10 27
11 27
and then it starts to decrease once more, getting to 1/216 when n=18 in a nice symmetrical fashion. Think of a diagonal intersecting a cube. But Spock’s second probability may also be written as 48/216 or as 2/9, and we don’t get as high in the second column above. How do we get this number? Sorry, I am a mathematician and I can’t help it!