import numpy as np import numpy.random as rand import matplotlib.pyplot as plt

set_Doors = [1,2,3] # for reference # let 1 be our first choice # if thats correct # Then monty will reveal 2 or 3 # if not # he will reveal 1 or the door without the prize (1 or 2 || 1 or 3) # we arbitrarily labeled the doors 1,2,3 so we can solve for an initial guess of 1 and the odds will be the same no matter which door we actualy open first def montyHallSim(N=10,change = False): ''' Input number of runs (N) and a boolean representing if we writs doors (change). Output numpy array of wins (1), and losses (0). ''' resultArray = [] # 1 for win, 0 for lose for _ in range(N): choice = 1 truePrize = rand.randint(1,4) if truePrize == choice: # if prize behind first choice, randomly reveal one of the other 2 doors reveal = rand.randint(2,4) else: # if prize not behind chosen door, reveal the remaining door reveal = 6/(choice*truePrize) if change: # only change the choice to non-revealed door if strat set to True choice = 6/(choice*reveal) else: pass if choice == truePrize: # Check if we won! resultArray.append(1) else: # Check if we lost ): resultArray.append(0) return np.array(resultArray) runs = 10000 # Run simulatiom results_strat1 = montyHallSim(runs) results_strat2 = montyHallSim(runs,change = True) # Calculate the odds we experienced percent_correct_strat1 = np.count_nonzero(results_strat1)/len(results_strat1) percent_correct_strat2 = np.count_nonzero(results_strat2)/len(results_strat2) # Display results print("After",runs,"games we observe") print("Strat 1 odds:",np.around(percent_correct_strat1*100,0),"%") print("Strat 2 odds:",np.around(percent_correct_strat2*100,0),"%")