Question

Dice Probability Stuff, will post everything I have so far
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Main Question:
What is the probability of getting a sum <= K
and K <= Expected Value of throwing m dice with n sides.

M=number of dice
n= number of sides on each dice(constant for all dice)
K= max sum on dice we care about

Looking for a general expression for probability
P=P(m,n,k)

expected value is the upper bound on k which is (I think...)
median of (m and m*n)

floor(m*(n+1)/2)