Q： 在Python中，一行有N个人头的预期抛硬币次数。为什么不给出正确的答案，但不能给出正确的答案

Question

我正在尝试编写Python代码，看看平均需要抛多少硬币才能得到一行N个头部的序列。在

我感到困惑的是，我的代码生成的答案与网上给出的答案不匹配，例如这里（和许多其他地方）https://math.stackexchange.com/questions/364038/expected-number-of-coin-tosses-to-get-five-consecutive-heads

根据这一点，我需要得到一排人头数的期望投掷次数是：E（1）=2，E（2）=6，E（3）=14，E（4）=30，E（5）=62。但我不知道答案！例如，我得到E（3）=8，而不是14。下面的代码运行以给出答案，但是您可以更改n来测试一行中其他目标数量的头。在

出什么问题了？可能我的代码逻辑中有一些错误，但我承认我不知道它是什么。在

您可以在此处查看、运行和制作我的代码的修改副本：https://trinket.io/python/17154b2cbd

下面是代码本身，在可运行程序之外小饰品.io第页。如果你能帮我找出问题所在，我们将不胜感激！在

非常感谢

拉吉 P、 我能找到的最相关的问题是这个：Monte-Carlo Simulation of expected tosses for two consecutive heads in python 然而，据我所知，这个问题中的代码实际上并不是测试两个连续的头，而是测试以一个head开头的序列，然后在某个稍后，可能是非连续的时间，得到另一个head。在

# Click here to run and/or modify this code:
# https://trinket.io/python/17154b2cbd

import random
# n is  the target number of heads in a row
# Change the value of n, for different target heads-sequences
n = 3  
possible_tosses = [ 'h', 't' ]
num_trials = 1000
target_seq = ['h' for i in range(0,n)]
toss_sequence = []
seq_lengths_rec = []

for trial_num in range(0,num_trials):

    if (trial_num % 100) == 0:
        print 'Trial num', trial_num, 'out of', num_trials
        # (The free version of trinket.io uses Python2)

    target_reached = 0
    toss_num = 0

    while target_reached == 0:

        toss_num += 1
        random.shuffle(possible_tosses)
        this_toss = possible_tosses[0]
        #print([toss_num, this_toss])
        toss_sequence.append(this_toss)
        last_n_tosses = toss_sequence[-n:]
        #print(last_n_tosses)
    if last_n_tosses == target_seq:
        #print('Reached target at toss', toss_num)
        target_reached = 1
        seq_lengths_rec.append(toss_num)

print 'Average', sum(seq_lengths_rec) / len(seq_lengths_rec)

Answer 1

你不会为每个实验重新初始化toss_sequence，所以你用一个预先存在的头部序列开始每个实验，在每个新实验的第一次尝试中有1/2的机会命中目标序列。在

在外部循环中初始化toss_sequence将解决您的问题：

import random
# n is  the target number of heads in a row
# Change the value of n, for different target heads-sequences
n = 4
possible_tosses = [ 'h', 't' ]
num_trials = 1000
target_seq = ['h' for i in range(0,n)]
seq_lengths_rec = []

for trial_num in range(0,num_trials):

    if (trial_num % 100) == 0:
        print('Trial num {} out of {}'.format(trial_num, num_trials))
        # (The free version of trinket.io uses Python2)

    target_reached = 0
    toss_num = 0
    toss_sequence = []

    while target_reached == 0:

        toss_num += 1
        random.shuffle(possible_tosses)
        this_toss = possible_tosses[0]
        #print([toss_num, this_toss])
        toss_sequence.append(this_toss)
        last_n_tosses = toss_sequence[-n:]
        #print(last_n_tosses)
        if last_n_tosses == target_seq:
            #print('Reached target at toss', toss_num)
            target_reached = 1
            seq_lengths_rec.append(toss_num)

print(sum(seq_lengths_rec) / len(seq_lengths_rec))

您可以将代码简化一点，并使其不易出错：

^{pr2}$