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I may have misunderstood the question and be massively oversimplifying, but you wouldn’t actually need to roll any dice to calculate the expected probabilities of the two outcomes would you?
With two die there’s a total of possible 36 outcomes, only one of which produces 12, whereas there are two outcomes resulting in 11, so given infinite rolls you’d expect to see twice as many 11’s rolled as 12’s right?
Problem that I came across. Leibniz thought that rolling two die and getting 11 was as likely as getting 12. If he took two die and started rolling them,
I bodged an answer with Python but maybe a proper stats/Bayesian person can give a real answer?