Monte Carlo Simulation and Python 13 - D'Alembert Strategy

Monte Carlo Simulation with Python Playlist: http://www.youtube.com/watch?v=9M_KPXwnrlE&feature=share&list=PLQVvvaa0QuDdhOnp-FnVStDsALpYk2hk0 In this video, we program the D'Alembert Strategy. The D'Alembert betting strategy is a progressive betting strategy that uses increments rather than multiples. In the monte carlo simulation with Python series, we test various betting strategies. A simple 50/50 strategy, a martingale strategy, and the d'alembert strategy. We use the monte carlo simulator to calculate possible paths, as well as to calculate preferred variables to use including wager size, how many wagers, and more. There are many purposes for a monte carlo simulator. Some people use them as a form of brute force to solve complex mathematical equations. A popular example used is to have a monte carlo simulator solve for pi. In our case, we are using the Monte Carlo simulator to account for randomness and the degree of risk associated with a betting strategy. In the world of stock trading and investing, people can use the Monte Carlo simulator to test a given strategy's risk. It used to be very much the case that only performance was considered, for the most part, to decide on a trader's value. Only until recently has the paradigm shifted to consider a strategy's risk more closely. Through this series, you will be able to see just how much random variability can affect the outcome, regardless of how "good" or "bad" a strategy might have been. http://seaofbtc.com http://sentdex.com http://hkinsley.com https://twitter.com/sentdex Bitcoin donations: 1GV7srgR4NJx4vrk7avCmmVQQrqmv87ty6

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1. import random
   import matplotlib
   import matplotlib.pyplot as plt
   import time
   
   lower_bust = 31.235
   higher_profit = 63.208
   
   sampleSize = 100
   startingFunds = 10000
   wagerSize = 100
   wagerCount = 100
   
   def rollDice():
   roll = random.randint(1,100)
   
   if roll == 100:
   #print roll,'roll was 100, you lose. What are tho edds?! Play again!'
   return False
   elif roll <= 50:
   #print roll, 'roll was 1-50, you lose. Play again!'
   return False
   
   elif 100 > roll >= 50:
   #print roll, 'roll was 51-99, you win! * pretty lights flash* Play more!'
   return True
   
   def dAlembert(funds,initial_wager,wager_count):
   global da_busts
   global da_profits
   
   value = funds
   wager = initial_wager
   currentWager = 1
   previousWager = 'win'
   previousWagerAmount = initial_wager
   
   while currentWager <= wager_count:
   if previousWager == 'win':
   if wager == initial_wager:
   pass
   else:
   wager -= initial_wager
   
   print 'current wager:',wager,'value:',value
   
   if rollDice():
   value += wager
   print 'we won, current value:',value
   previousWagerAmount = wager
   else:
   value -= wager
   previousWager = 'loss'
   print 'we lost, current value',value
   previousWagerAmount = wager
   
   if value <= 0:
   da_busts += 1
   break
   
   elif previousWager == 'loss':
   wager = previousWagerAmount + initial_wager
   if (value - wager) <= 0:
   wager = value
   
   print 'lost the last wager, current wager:',wager,'value',value
   
   if rollDice():
   value += wager
   print 'we won, current value:',value
   previousWagerAmount = wager
   previousWager = 'win'
   
   else:
   value -= wager
   print 'we lost, current value:',value
   previousWagerAmount = wager
   
   if value <= 0:
   da_busts += 1
   break
   
   currentWager += 1
   
   if value > funds:
   da_profits += 1
   
   print value
   
   da_profits = 0.0
   da_busts = 0.0
   
   dAlembert(startingFunds,wagerSize,wagerCount)
   
   time.sleep(555555)
   
   def multiple_bettor(funds, initial_wager, wager_count):
   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':
   #print 'we won the last wager, great'
   if rollDice():
   value+=wager
   #print value
   wX.append(currentWager)
   vY.append(value)
   else:
   value -= wager
   previousWager = 'loss'
   #print value
   previousWagerAmount = wager
   wX.append(currentWager)
   vY.append(value)
   if value <= 0:
   #print 'we went broke after'.currentWager,'bets'
   multiple_busts += 1
   break
   
   elif previousWager == 'loss':
   #print 'we lost the last one, so we will be smart and double'
   if rollDice():
   wager = previousWagerAmount * random_multiple
   if (value - wager) < 0:
   wager = value
   #print 'we won',wager
   value += wager
   #print value
   wager = initial_wager
   previousWager = 'win'
   wX.append(currentWager)
   vY.append(value)
   else:
   wager = previousWagerAmount * random_multiple
   if (value - wager) < 0:
   wager = value
   #print 'we lost',wager
   value -= wager
   previousWagerAmount = wager
   wX.append(currentWager)
   vY.append(value)
   if value <= 0:
   #print 'we went broke after',currentWager,'bets'
   multiple_busts += 1
   break
   
   #print value
   previousWager = 'loss'
   
   currentWager += 1
   
   #print value
   #plt.plot(wX,vY,color)
   if value > funds:
   multiple_profits += 1
   
   def doubler_bettor(funds, initial_wager, wager_count, color):
   value = funds
   wager = initial_wager
   global doubler_busts
   global doubler_profits
   wX = []
   vY = []
   
   currentWager = 1
   previousWager = 'win'
   previousWagerAmount = initial_wager
   
   while currentWager <= wager_count:
   if previousWager == 'win':
   #print 'we won the last wager, great'
   if rollDice():
   value+=wager
   #print value
   wX.append(currentWager)
   vY.append(value)
   else:
   value -= wager
   previousWager = 'loss'
   #print value
   previousWagerAmount = wager
   wX.append(currentWager)
   vY.append(value)
   if value <= 0:
   #print 'we went broke after'.currentWager,'bets'
   doubler_busts += 1
   break
   
   elif previousWager == 'loss':
   #print 'we lost the last one, so we will be smart and double'
   if rollDice():
   wager = previousWagerAmount * 2
   
   if (value - wager) < 0:
   wager = value
   #print 'we won',wager
   value += wager
   #print value
   wager = initial_wager
   previousWager = 'win'
   wX.append(currentWager)
   vY.append(value)
   else:
   wager = previousWagerAmount * 2
   if (value - wager) < 0:
   wager = value
   #print 'we lost',wager
   value -= wager
   previousWagerAmount = wager
   wX.append(currentWager)
   vY.append(value)
   if value <= 0:
   #print 'we went broke after',currentWager,'bets'
   doubler_busts += 1
   break
   
   #print value
   previousWager = 'loss'
   
   currentWager += 1
   
   #print value
   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)
   
   currentWager += 1
   
   if value <= 0:
   value = 0
   simple_busts+=1
   #print 'Funds:', value
   
   plt.plot(wX,vY,color)
   if value > funds:
   value = 0
   simple_profits+=1
   
   while True:
   multiple_busts = 0.0
   multiple_profits = 0.0
   
   multipleSampSize = 100000
   currentSample = 1
   
   random_multiple = random.uniform(0.1,10.0)
   
   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 to beat',lower_bust
   print 'Higher profit rate to beat:', higher_profit
   print 'bust rate:',(multiple_busts/multipleSampSize)*100.00
   print 'Profit rate:',(multiple_profits/multipleSampSize)*100.00
   print '############'
   
   else:
   pass
   '''print '############'
   print 'Found a loser, the multiple was', random_multiple
   print 'Lower bust to beat',lower_bust
   print 'Higher profit rate to beat:', higher_profit
   print 'bust rate:',(multiple_busts/multipleSampSize)*100.00
   print 'Profit rate:',(multiple_profits/multipleSampSize)*100.00
   print '############'''
2. peeked here and there again on this series, and it seems what you are accomplishing with a randomized simulation can be accomplished analytically in a cleaner way with probability distributions.
   
   The only real utility of Monte Carlo that I know of is multi dimensional integration with more than something like 7 degrees of freedom if i recall correctly... or when the domain is too weird.
3. Roulette det not have a 50/50 chance. It's 18/37 so even worse than your roll dice function.