I dimension the die!

What's the functional difference between rolling a 12 sided die and two 6 sided die? Well, for one you can't roll a 1 with two dice. More importantly though, you'll see a stronger regression to the mean with more dice.

Let's say theoretically we have a 10-sided die numbered [0,9]. Your probability of rolling a 5 is 10%.

If you have three 4-sided dice numbered [0,3], the probability of rolling a 5 suddenly becomes 19%.

If you flip 9 coins, the probability of landing 5 heads is now 25%. Moreover, the probability of rolling either 5 or 6 (the expected value is 5.5) is 49%. Of the 10 possible numbers, half the time you'll only get 2 of them!

I assume this is why a lot of boardgames roll two dice, because it normalizes the probabilities; you're 6 times more likely to roll a middle value like 7 over something extraordinary like 2 or 12.

With Betrayal, the rolls consist of up to eight 6-sided dice with two faces each numbered 0, 1 and 2. Basically 3-sided dice. Therefore we should see some strong regressions to the mean; for instance, if we were to roll five such dice the probability of getting at least a 4 is 79%. To roll 3 or lower and be beaten by a roll with 3 dice has a probability of 11%. To do so twice in a roll is literally a 1 in 100 proposition.

So basically Michael really sucks at rolling.