## Using Monte Carlo to find Best multiple

so we've shown some examples that look promising, but we're unsure about their variables, and we're not sure they wholistically beat doubler. Let's begin to work out that stuff. The question is, can we find a simple variable change where there is both lower risk, and higher profit... and soon, is this the case accross an average of 1 million samples.
```import random
import matplotlib
import matplotlib.pyplot as plt
import time

lower_bust = 31.235
higher_profit = 63.208

# back to 1,000
sampleSize = 1000
startingFunds = 10000
wagerSize = 100
wagerCount = 100

def rollDice():
roll = random.randint(1,100)

if roll == 100:
return False
elif roll <= 50:
return False
elif 100 > roll >= 50:
return True

def multiple_bettor(funds,initial_wager,wager_count):#,color):

global multiple_busts
global multiple_profits

value = funds
wager = initial_wager
wX = []
vY = []
currentWager = 1
previousWager = 'win'
previousWagerAmount = initial_wager

while currentWager <= wager_count:
if previousWager == 'win':
if rollDice():
value += wager
wX.append(currentWager)
vY.append(value)
else:
value -= wager
previousWager = 'loss'
previousWagerAmount = wager
wX.append(currentWager)
vY.append(value)
if value <= 0:
multiple_busts += 1
break
elif previousWager == 'loss':
if rollDice():

#### must change the multiple ####
wager = previousWagerAmount * random_multiple
if (value - wager) <= 0:
wager = value

value += wager
wager = initial_wager
previousWager = 'win'
wX.append(currentWager)
vY.append(value)
else:
wager = previousWagerAmount * random_multiple
if (value - wager) <= 0:
wager = value
value -= wager
previousWager = 'loss'
previousWagerAmount = wager
wX.append(currentWager)
vY.append(value)

if value <= 0:
#change
multiple_busts += 1
break

currentWager += 1

#plt.plot(wX,vY)
#####################
if value > funds:
#change
multiple_profits+=1

def doubler_bettor(funds,initial_wager,wager_count,color):
global doubler_busts
global doubler_profits
value = funds
wager = initial_wager
wX = []
vY = []
currentWager = 1
previousWager = 'win'
previousWagerAmount = initial_wager

while currentWager <= wager_count:
if previousWager == 'win':
if rollDice():
value += wager
wX.append(currentWager)
vY.append(value)
else:
value -= wager
previousWager = 'loss'
previousWagerAmount = wager
wX.append(currentWager)
vY.append(value)
if value < 0:
currentWager += 10000000000000000
doubler_busts += 1
elif previousWager == 'loss':
if rollDice():
wager = previousWagerAmount * 2
if (value - wager) < 0:
wager = value

value += wager
wager = initial_wager
previousWager = 'win'
wX.append(currentWager)
vY.append(value)
else:
wager = previousWagerAmount * 2
if (value - wager) < 0:
wager = value
value -= wager
previousWager = 'loss'
previousWagerAmount = wager
wX.append(currentWager)
vY.append(value)

if value <= 0:
currentWager += 10000000000000000
doubler_busts += 1

currentWager += 1
#plt.plot(wX,vY,color)
#####################
if value > funds:
doubler_profits+=1

def simple_bettor(funds,initial_wager,wager_count,color):
global simple_busts
global simple_profits

value = funds
wager = initial_wager
wX = []
vY = []
currentWager = 1
while currentWager <= wager_count:
if rollDice():
value += wager
wX.append(currentWager)
vY.append(value)
else:
value -= wager
wX.append(currentWager)
vY.append(value)

if value <= 0:
currentWager += 10000000000000000
simple_busts +=1
currentWager += 1
plt.plot(wX,vY,color)
if value > funds:
simple_profits+=1
x = 0

#Doubler Bettor Bust Chances: 84.1457... so anything less than this... aaaand
#Doubler Bettor Profit Chances: 15.6355 ... aaaand better than this.

while x < 10000:

######## move this stuff in here for the maths.
multiple_busts = 0.0
multiple_profits = 0.0
# now we're wanting to do 100 attempts to get a good sample #
multipleSampSize = 100000
currentSample = 1

random_multiple = random.uniform(0.1,10.0)
#random_multiple = 2.00
#print((random_multiple
while currentSample <= multipleSampSize:
multiple_bettor(startingFunds,wagerSize,wagerCount)
currentSample += 1

if ((multiple_busts/multipleSampSize)*100.00 < lower_bust) and ((multiple_profits/multipleSampSize)*100.00 > higher_profit):
print(('#################################################'))
print(('found a winner, the multiple was:',random_multiple))
print(('Lower Bust Rate Than:',lower_bust))
print(('Higher profit rate than:',higher_profit))
print(('Bust Rate:',(multiple_busts/multipleSampSize)*100.00))
print(('Profit Rate:',(multiple_profits/multipleSampSize)*100.00))
print(('#################################################'))
time.sleep(5)
#plt.show()
else:
pass

##        print(('####################################'))
##        print(('To beat:'))
##        print(('Lower Bust Rate Than:',lower_bust))
##        print(('Higher profit rate than:',higher_profit))
##        print(('Bust Rate:',(multiple_busts/multipleSampSize)*100.00))
##        print(('Profit Rate:',(multiple_profits/multipleSampSize)*100.00))
##        print(('####################################'))
##
##        #clears the figure
##        plt.clf()

x+=1
```

The next tutorial: • Monte Carlo Introduction

• Monte Carlo dice Function

• Creating a simple Bettor

• Plotting Results with Matpltolib

• Martingale Strategy

• Bettor Statistics

• More comparison

• Graphing Monte Carlo

• Fixing Debt Issues

• Analyzing Monte Carlo results

• Using Monte Carlo to find Best multiple
• Checking betting results

• D'Alembert Strategy

• 50/50 Odds

• Analysis of D'Alembert

• Comparing Profitability

• Finding best D'Alembert Multiple

• Two dimensional charting monte carlo

• Monte Carlo Simulation and Python

• Labouchere System for Gambling Tested