Alright, so I'm trying to figure out the expected value of dice throws in a game I'm making, because I would like for the options the player has to be statistically balanced.
A person, for their special attack, can roll four dice. However, if their opponent's special defense is in the same slot, they can remove the highest three of those dice, and I would like to know the expected value of this action: removing the three highest dice from four. (I need this for the rest of my balancing).
I saw this: The expected payoff of a dice game
And this: Expected Payoff for Dice Game Where Six = No Payoff
But don't think they necessarily apply here, or I can't figure out how to make them apply to this problem.
I knocked up a simply python simulation that does this for me, and got a mean of 1.755 over a hundred million trials, but I like statistics, and would like to know why this is the result.
import random
import statistics
def Rand(start, end, num):
res = []
for j in range(num):
res.append(random.randint(start, end))
return res
all_list = []
for i in range(100000000):
take = Rand(1,6,4)
take.sort()
all_list.append(take[0])
print(statistics.mean(all_list))