Just_The_theoretical_Code.py

#The first binomial 
def firstBinomialCoff(num_of_dice,k):
    return (math.factorial(num_of_dice)/(math.factorial((num_of_dice-k))*math.factorial(k)))

#The second binomial
def SecondBinomialCoff(num_of_dice,k,s,Total):
    return (math.factorial((Total-s*k-1))/(math.factorial((Total-s*k-num_of_dice))*math.factorial((num_of_dice-1))))

#The full expression of Prob
def ProbofEachNum(num_of_dice,s,Total):
    Probof6thsidedDiceto_n = (1/s)**num_of_dice
    Total_prob = 0
    for k in range(0,int((Total-num_of_dice)/s)+1):
        Total_prob = Total_prob + ((-1)**k)*firstBinomialCoff(num_of_dice,k)*SecondBinomialCoff(num_of_dice,k,s,Total)*Probof6thsidedDiceto_n
    return Total_prob

#The theoretical distribution, Prob for each possible value 
def Full_Theoretical_Distribution(num_of_dice,s):
    The_range = range(num_of_dice,num_of_dice*s)
    The_distribution = np.zeros(len(The_range)+1)
    count = 0 
    for each_possible_number in range(num_of_dice,(num_of_dice*s)+1):
        The_distribution[count] = ProbofEachNum(num_of_dice,s,each_possible_number)
        count += 1
    return list(The_range),list(The_distribution)