How to simulate the Monty Hall \"Let\'s Make A Deal\" probability problem in Sta

Question

How to simulate the Monty Hall "Let's Make A Deal" probability problem in Stata? There is programming code available for Matlab but I am interested in how to do it in Stata. Any help?

Explanation / Answer

#!/usr/bin/env python3 """Simulate the Monty Hall problem. """ import argparse, random def simulate(num_doors, switch, verbose): """(int, bool): bool Carry out the game for one contestant. If 'switch' is True, the contestant will switch their chosen door when offered the chance. Returns a Boolean value telling whether the simulated contestant won. """ # Doors are numbered from 0 up to num_doors-1 (inclusive). # Randomly choose the door hiding the prize. winning_door = random.randint(0, num_doors-1) if verbose: print('Prize is behind door {}'.format(winning_door+1)) # The contestant picks a random door, too. choice = random.randint(0, num_doors-1) if verbose: print('Contestant chooses door {}'.format(choice+1)) # The host opens all but two doors. closed_doors = list(range(num_doors)) while len(closed_doors) > 2: # Randomly choose a door to open. door_to_remove = random.choice(closed_doors) # The host will never open the winning door, or the door # chosen by the contestant. if door_to_remove == winning_door or door_to_remove == choice: continue # Remove the door from the list of closed doors. closed_doors.remove(door_to_remove) if verbose: print('Host opens door {}'.format(door_to_remove+1)) # There are always two doors remaining. assert len(closed_doors) == 2 # Does the contestant want to switch their choice? if switch: if verbose: print('Contestant switches from door {} '.format(choice+1), end='') # There are two closed doors left. The contestant will never # choose the same door, so we'll remove that door as a choice. available_doors = list(closed_doors) # Make a copy of the list. available_doors.remove(choice) # Change choice to the only door available. choice = available_doors.pop() if verbose: print('to {}'.format(choice+1)) # Did the contestant win? won = (choice == winning_door) if verbose: if won: print('Contestant WON', end=' ') else: print('Contestant LOST', end=' ') return won def main(): # Get command-line arguments parser = argparse.ArgumentParser( description='simulate the Monty Hall problem') parser.add_argument('--doors', default=3, type=int, metavar='int', help='number of doors offered to the contestant') parser.add_argument('--trials', default=10000, type=int, metavar='int', help='number of trials to perform') parser.add_argument('--verbose', default=False, action='store_true', help='display the results of each trial') args = parser.parse_args() print('Simulating {} trials...'.format(args.trials)) # Carry out the trials winning_non_switchers = 0 winning_switchers = 0 for i in range(args.trials): # First, do a trial where the contestant never switches. won = simulate(args.doors, switch=False, verbose=args.verbose) if won: winning_non_switchers += 1 # Next, try one where the contestant switches. won = simulate(args.doors, switch=True, verbose=args.verbose) if won: winning_switchers += 1 print(' Switching won {0:5} times out of {1} ({2}% of the time)'.format( winning_switchers, args.trials, (winning_switchers / args.trials * 100 ) )) print('Not switching won {0:5} times out of {1} ({2}% of the time)'.format( winning_non_switchers, args.trials, (winning_non_switchers / args.trials * 100 ) )) if __name__ == '__main__': main()

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