import numpy as np import pandas as pd import matplotlib.pyplot as plt # this generates a dataframe showing all the possible arragements of items behind the door possibility_1 = ['goat', 'goat', 'prize'] possibility_2 = ['goat', 'prize', 'goat'] possibility_3 = ['prize', 'goat', 'goat'] df = pd.DataFrame([possibility_1, possibility_2, possibility_3], columns = ['door_1', 'door_2', 'door_3']) df.index = ['possibility 1:','possibility 2:', 'possibility 3:'] print('\n\nHere are all the possible arrangements of the items behind the doors:') display(df) # this generates an output that shows all possible outcomes for all possible choices doors = np.arange(1,4) for door in doors: door_choice = door print('\n\n####################################################################################################################\n') print('If you chose door number', door, ':\n') if door_choice == 1: door_choice = 'door_1' elif door_choice == 2: door_choice = 'door_2' elif door_choice == 3: door_choice = 'door_3' for i in np.arange(len(df)): if df[door_choice].iloc[i] == 'goat': print('\nIf you chose '+str(door_choice)+', and possibility '+str(i+1)+' was true, you would have WON if you had SWITCHED, and LOST if you had STAYED.') if df[door_choice].iloc[i] == 'prize': print('\nIf you chose '+str(door_choice)+', and possibility '+str(i+1)+' was true, you would have LOST if you had SWITCHED, and WON if you had STAYED.')

display(df)

# setting the number of iterations for the simulation n_iters = 10000 # creating arrays to store the outcomes of three different strategies: always switching, never switching and randomly switching always_switch_outcomes = np.array([]) never_switch_outcomes = np.array([]) random_switch_outcomes = np.array([]) # running thousands of trials to see which strategy is most effective for i in np.arange(n_iters): df = pd.DataFrame([possibility_1, possibility_2, possibility_3], columns = ['door_1', 'door_2', 'door_3']) df.index = ['possibility 1:','possibility 2:', 'possibility 3:'] # randomly deciding the arrangement of items behind the doors state_of_the_world = df.loc[np.random.choice(df.index)] # picking a first door at random first_choice = np.random.choice(state_of_the_world.index) # opening the remaining door which has a goat behind it remaining = state_of_the_world.index[state_of_the_world.index != first_choice] remaining = np.random.permutation(remaining) for r in remaining: if state_of_the_world.loc[r] == 'goat': state_of_the_world.loc[r] = 'goat (open)' break # choosing to switch or stay based on the three strategies not_open = state_of_the_world[state_of_the_world != 'goat (open)'] switcher_outcome = not_open.loc[not_open.index[not_open.index !=first_choice][0]] stayer_outcome = state_of_the_world.loc[first_choice] random_outcome = np.random.choice(state_of_the_world[state_of_the_world != 'goat (open)']) # recording the outcome for each strategy always_switch_outcomes = np.append(always_switch_outcomes,switcher_outcome) never_switch_outcomes = np.append(never_switch_outcomes,stayer_outcome) random_switch_outcomes = np.append(random_switch_outcomes,random_outcome) # calculating the proportion of wins for each strategy prop_wins_always_switch = np.count_nonzero(always_switch_outcomes == 'prize')/len(always_switch_outcomes) prop_wins_never_switch = np.count_nonzero(never_switch_outcomes == 'prize')/len(never_switch_outcomes) prop_wins_random_switch = np.count_nonzero(random_switch_outcomes == 'prize')/len(random_switch_outcomes) # plotting the outcomes of the simulation plt.figure(figsize = (10,4)) plt.title('% of wins for 3 different strategies over '+str(n_iters)+' Monty Hall trials') plt.bar(['Always Switch', 'Never Switch', 'Randomly Switch',], [prop_wins_always_switch*100, prop_wins_never_switch*100, prop_wins_random_switch*100], color = ['red', 'black', 'cyan']) plt.xlabel('Strategy') plt.ylabel('% of wins') plt.show() print('There were '+str(n_iters)+' trials.\n') print('The "Always Switch" strategy won the prize on', prop_wins_always_switch*100,'% of the trials.\n') print('The "Never Switch" strategy won the prize on', prop_wins_never_switch*100,'% of the trials.\n') print('The "Randomly Switch" strategy won the prize on', prop_wins_random_switch*100,'% of the trials.\n')