I have some questions about how to go about figuring out probabilities when rolling dice. Suppose I roll three six-sided dice, take the two highest and add them together, dropping the lowest one. How do I figure out the probability of arriving at any given possible value? Such as, what would be the probability of rolling seven under this setup? What if I used four dice instead, dropping the two lowest? What if I rolled four dice and dropped only the lowest, how about then? How about if I used larger dice, say twelve sided ones? How about if I mixed different types of dice, say two six-sided dice and two eight-sided dice, dropping the two lowest?
I’m hoping there’s some relatively simple methodology I can use to solve these sorts of problems. Thanks!
There are analytical techniques for this sort of problem, but it’s much easier to write a program to consider all possible outcomes of rolling the dice and compute the probabilities from there.
The simple—as opposed to easy—is to list all possible outcomes of rolling the three six-sided dice (or whatever you’re doing) and counting up how many of them give you each possible result.
As ultrafilter suggests, this is much more easily done with the help of a computer program. With three six-sided dice, the number of possible outcomes is 216, and this number goes up rapidly with more dice or more sides.
At a guess, the total would tend toward 3.5 per die, since dropping the lowest one, or two, is of dimishing significance as to total number of dice grows.