蒙特卡洛—赌博模型笔记

大数定理： 在随机事件的大量重复出现中，往往呈现几乎必然的规律，这个规律即大数定律。通俗说，这个定理就是在试验不变的条件下，重复试验多次，随机事件的频率近似于它的概率。偶然中包含某种必然。

个人理解：蒙特卡洛就是一种根据制定好的规则基于不确定性不断演算得到结果的思想

单倍下注：
每次下注赌注不变，一直赌下去，代码如下

import random
import matplotlib.pyplot as pltdef rollDice():roll = random.randint(1,100)if roll == 100:return Falseelif roll <= 50:return Falseelif 100>roll>50:return Truedef simple_bettor(funds,initial_wager,wager_count):value = funds           # 资金wager = initial_wager   # 赌注wX = []                 # wager XvY = []                 # value YcurrentWager = 1while currentWager <= wager_count:if rollDice():value += wagerwX.append(currentWager)vY.append(value)else:value -= wagerwX.append(currentWager)vY.append(value)currentWager += 1plt.plot(wX,vY)         # 画图# 分类if value<=0:return "broke"elif value<funds:return "lose"elif value>funds:return "win"elif value==funds:return "equal"x = 0
# 赌博人数
people = 100
# funds 赌金
funds = 10000
# 赌注
initial_wager = 100
# 模拟赌博次数
count = 1000num_win = 0
num_lose = 0
num_broke = 0
num_equal = 0while x < people:result = simple_bettor(funds,initial_wager,count)x += 1if result == 'win':num_win += 1elif result == 'lose':num_lose += 1elif result == 'broke':num_broke += 1elif result == 'equal':num_equal += 1print("%d people are betting"%people)
print("people betting %d times"%count)
print("num_win:",num_win)
print("num_lose:",num_lose)
print("num_equal:",num_equal)
print("num_broke:",num_broke)
print("broken rate:",num_broke/people)plt.ylabel("money in hand")
plt.xlabel("betting Count")
plt.show()

结果分析：根据大数定理，单倍下注赌久必输

双倍下注法：
破解大数定理，使用双倍下注
在下注过程中如果输了，则翻倍下注。
比如第一次下注10元输了，则第二轮下注20元
第二轮输了则下注40元。（万一赢了就会把之前输的赚回来）。在资源有限的情况下，这真是个好方法吗？

import random
import matplotlib.pyplot as pltfig = plt.figure(figsize=(10,10))
# 赌博人数
sampleSize = 100
# 赌资
startingFunds = 10000
# 每次赌金
wagerSize = 100
# 赌博次数
wagerCount = 30def rollDice():roll = random.randint(1,100)if roll == 100:return Falseelif roll <= 50:return Falseelif 100>roll>=50:return Truedef double_bettor(funds,initial_wager,wager_count):global double_bustsglobal double_loseglobal double_profitsvalue = funds           # 资金wager = initial_wager   # 赌注wX = []                 # wager XvY = []                 # value YcurrentWager = 1previousWager = 'win'previousWagerAmount = initial_wagerwhile currentWager <= wager_count:if previousWager == 'win':if rollDice():value += wagerwX.append(currentWager)vY.append(value)else:value -= wagerpreviousWager = 'loss'previousWagerAmount = wager     # 前一次赌注wX.append(currentWager)vY.append(value)if value < 0:double_busts += 1breakelif previousWager == 'loss':if rollDice():wager = previousWagerAmount * 2if(value - wager) < 0:          # 钱不够时wager = valuevalue += wagerwager = initial_wagerpreviousWager = 'win'wX.append(currentWager)vY.append(value)else:wager = previousWagerAmount * 2if(value - wager) < 0:wager = valuevalue -= wagerpreviousWager = 'loss'previousWagerAmount = wagerwX.append(currentWager)vY.append(value)if value <= 0:double_busts += 1breakcurrentWager += 1plt.plot(wX,vY)         # 画图# 分类if value>funds:double_profits += 1elif value<funds:double_lose += 1def Print_result():print("总赌金:",startingFunds)print("开始每次赌金:",wagerSize)print("赌博次数:",wagerCount)print("赌钱人数:",sampleSize)print("Doubler Bettor Bust Chances:",(double_busts/sampleSize)*100.00)print("Doubler Bettor Profit Chances:",(double_profits/sampleSize)*100.00)print("Doubler Bettor Lose Chances:",(double_lose/sampleSize)*100.00)x = 0
double_busts = 0.0
double_profits = 0.0
double_lose = 0.0while x < sampleSize:double_bettor(startingFunds,wagerSize,wagerCount)x += 1plt.axhline(0,color='r')
plt.ylabel("Account Value")
plt.xlabel("Wager Count")
Print_result()
plt.show()

结果分析：
初看貌似是个好方法，真是这样？
可见随着次数的增多，破产率猛增

两种方法联合演示：

import random
import matplotlib.pyplot as pltfig = plt.figure(figsize=(10,10))
# 赌博人数
sampleSize = 100
# 赌资
startingFunds = 10000
# 每次赌金
wagerSize = 100
# 赌博次数
wagerCount = 30000def rollDice():roll = random.randint(1,100)if roll == 100:return Falseelif roll <= 50:return Falseelif 100>roll>=50:return Truedef double_bettor(funds,initial_wager,wager_count,color):global double_bustsglobal double_profitsvalue = funds           # 资金wager = initial_wager   # 赌注wX = []                 # wager XvY = []                 # value YcurrentWager = 1previousWager = 'win'previousWagerAmount = initial_wager# 开始下注while currentWager <= wager_count:if previousWager == 'win':if rollDice():value += wagerwX.append(currentWager)vY.append(value)else:value -= wagerpreviousWager = 'loss'previousWagerAmount = wager     # 前一次赌注wX.append(currentWager)vY.append(value)if value < 0:double_busts += 1breakelif previousWager == 'loss':if rollDice():wager = previousWagerAmount * 2if(value - wager) < 0:          # 钱不够时wager = valuevalue += wagerwager = initial_wagerpreviousWager = 'win'wX.append(currentWager)vY.append(value)else:wager = previousWagerAmount * 2if(value - wager) < 0:wager = valuevalue -= wagerpreviousWager = 'loss'previousWagerAmount = wagerwX.append(currentWager)vY.append(value)if value <= 0:double_busts += 1breakcurrentWager += 1plt.plot(wX,vY,color)         # 画图# 分类if value>funds:double_profits += 1def simple_bettor(funds,initial_wager,wager_count,color):global simple_bustsglobal simple_profitsvalue = funds           # 资金wager = initial_wager   # 赌注wX = []                 # wager XvY = []                 # value YcurrentWager = 1# 开始下注while currentWager <= wager_count:if rollDice():value += wagerwX.append(currentWager)vY.append(value)else:value -= wagerwX.append(currentWager)vY.append(value)if value <= 0:simple_busts += 1breakcurrentWager += 1plt.plot(wX,vY,color)         # 画图# 分类if value > funds:simple_profits += 1def Print_result():print("总赌金:",startingFunds)print("开始每次赌金:",wagerSize)print("赌博次数:",wagerCount)print("赌钱人数:",sampleSize)print("Double Bettor Bust Chances:",(double_busts/sampleSize)*100.00)print("Simple Bettor Bust Chances:",(simple_busts/sampleSize)*100.00)print("Double Bettor Profit Chances:",(double_profits/sampleSize)*100.00)print("Simple Bettor Profit Chances:",(simple_profits/sampleSize)*100.00)x = 0
# 双倍下注法
double_busts = 0.0
double_profits = 0.0
# 单倍下注法
simple_profits = 0.0
simple_busts = 0.0while x < sampleSize:double_bettor(startingFunds,wagerSize,wagerCount,'c')simple_bettor(startingFunds, wagerSize, wagerCount,'k')x += 1plt.axhline(0,color='r')
plt.ylabel("Account Value")
plt.xlabel("Wager Count")
Print_result()
plt.show()

运行结果：
当赌博次数很大时，双倍下注破产率大于单倍下注法，但不管怎么说，100个人中赢的人很少，所以珍爱生命远离赌博。

模型小白，望大佬批评指点。
参考：https://www.bilibili.com/video/BV17D4y1o7J2?from=search&seid=15046903514947720514

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