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Monty Carlo Simulation with Python

A method to visualize outcomes and risks of any decision. Let's start with a simple gambling experiment.

1 - 50 house wins! 51 - 99 you win! - 100 house wins! Let's rolls a dice with 100 sides and see the effects of this.

import random

# Create a function which rolls the dice. 
def rollDice():
    roll = random.randint(1, 100) 
    if roll == 100:
        return False
    elif roll <= 50:
        return False
    elif 100 > roll > 50:
        return True

# Create a better (a person placing bets on the dice roll
def simple_bettor(funds, initial_wager, wager_count):
    value = funds
    wager = initial_wager
    
    currentWager = 1
    
    while currentWager <= wager_count:
        if rollDice():
            value += wager
        else:
            value -= wager
        currentWager += 1
    
    if value <= 0:
        value = 'broke'
        
    print('Funds: ', value)
   

# Let's see some results while a 10 players play 10,000 games starting with $10,000 and betting $100 a game
number_of_bettors = 10
while number_of_bettors > 0:
    simple_bettor(10000, 100, 10000)
    number_of_bettors -= 1

Funds:  3600
Funds:  broke
Funds:  broke
Funds:  10600
Funds:  broke
Funds:  broke
Funds:  broke
Funds:  broke
Funds:  broke
Funds:  19200

Though many of our betters ended up broke we can map their progress throughout the games being played

import matplotlib.pyplot as plt

# Create a better (a person placing bets on the dice roll
def simple_bettor_plotter(funds, initial_wager, wager_count):
    value = funds
    wager = initial_wager
    
    # For plotting purposes
    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)
        currentWager += 1
    
    if value <= 0:
        value = 'broke'
        
    plt.plot(wX, vY)

# Let's plot 10 betters playing 10,000 games.
plt.figure(figsize=(20,10))
number_of_bettors = 10
while number_of_bettors > 0:
    simple_bettor_plotter(10000, 100, 10000)
    number_of_bettors -= 1
plt.ylabel('Account Value')
plt.xlabel('Wager Count')
plt.show()

Doubling on a loss strategy (Martingale Strategy)

def doubler_bettor(funds, initial_wager, wager_count):
    broke_count = 0
    value = funds
    wager = initial_wager
    
    # For plotting purposes
    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:
                    broke_count += 1
                    break
        elif previousWager == 'loss':
            if rollDice():
                wager = previousWagerAmount * 2
                value += wager
                wager = initial_wager
                previousWager = 'win'
                wX.append(currentWager)
                vY.append(value)
            else:
                wager = previousWagerAmount * 2
                value -= wager
                if value < 0:
                    broke_count += 1
                    break
                previousWager = 'loss'
                previousWagerAmount = wager
                
                wX.append(currentWager)
                vY.append(value)

                    
        currentWager += 1
    plt.plot(wX, vY)

# Let's plot 10 betters playing 1000 games while double betting.
plt.figure(figsize=(20,10))
number_of_double_bettors = 10
while number_of_double_bettors > 0:
    doubler_bettor(10000, 100, 1000)
    number_of_double_bettors -= 1
plt.ylabel('Account Value')
plt.xlabel('Wager Count')
plt.show()

The majority of people will go broke using the double or nothing strategy.

# Let's plot 10 betters playing 10,000 games while double betting.
plt.figure(figsize=(20,10))
number_of_double_bettors = 10
while number_of_double_bettors > 0:
    doubler_bettor(10000, 100, 10000)
    number_of_double_bettors -= 1
plt.ylabel('Account Value')
plt.xlabel('Wager Count')
plt.show()

When attempting to use the Martingale double strategy we can see that nobody get's anywhere near being able to complete 10,000 games. All go broke after <2000 games.