N骰子的蒙特卡羅模擬

Question

我正在做這個任務：

你在擲N骰子。 用 Python 編寫一個程序，計算總和大於3N/2且小於9N/2的概率。

我假設我只有 3 個骰子，因為用N骰子制作有點復雜，我嘗試了一些東西，但我不明白如何找到9N/2 > sum > 3N/2的概率

import random
num_throws = 20  # NT
roll_log = [0] * 12  # Generate list for dice roll tallies

for i in range(num_throws):
    # Random integer between 1 and 6 inclusive for each dice
    dice_1 = random.randint(1, 6)
    dice_2 = random.randint(1, 6)
    dice_3 = random.randint(1, 6)

    # Sum the random dice and increment the tally for that particular roll total
    roll_sum = dice_1 + dice_2
    roll_log[roll_sum-1] += 1  # minus 1 because Python is 0-indexed

    for i, tally in enumerate(roll_log):
        roll_prob = float(tally) / num_throws  # Experimental probability of roll
        roll = i + 1  # Since Python lists are 0-indexed
        print('{}: {}/{} = {}'.format(roll, tally, num_throws, roll_prob))
        n = 5
        m = 10

rolls_between = roll_log[n:m-1]  
sum_rolls_between = sum(rolls_between)  
prob_between = float(sum_rolls_between) / num_throws

Answer 1

我修正了第一個答案......不知道是否正確......只是修正了明顯的錯誤......

import random                                                                                       

N = 3                                                                                               
NUM_ROLLS = 10000                                                                                   
UPPER_BOUND = 9 * N / 2                                                                             
LOWER_BOUND = 3 * N / 2                                                                             

counter = 0                                                                                         
for _ in range(NUM_ROLLS):                                                                          
  s = sum([random.randint(1, 6) for _ in range(N)])                                                 
  if s < UPPER_BOUND and s > LOWER_BOUND:                                                           
    counter += 1                                                                                    

prob = 1.0 * counter / NUM_ROLLS                                                                    
print "Upper Bound = ", UPPER_BOUND                                                                 
print "Lower Bound = ", LOWER_BOUND                                                                 
print prob