Dice Probability from Eldritch Horror! 1. How to calculate the probability of getting a minimum of one 5-die or one 6-die by rolling 3 dice at once? 2. And, is it mathematically correct that further adding 1 die into the dice pool has a diminishing return? PS: These questions perplex me; and they stem from playing "Eldritch Horror" board game!

The probability of a dice not showing 5 or 6 is $\frac{4}{6} = \frac{2}{3}$. Therefore the probability of not having any of the dice showing 5 of 6 is $\frac{2}{3}^3$. So the probabiliity of at least one die showing 5 or 6 is $1 - \frac{2}{3}^3$.

For $n$ dice this probability generalises to $1 - \frac{2}{3}^n$. The more dice you have, the larger this probability.