The Monty Hall Problem
I had the same issue, being unconvinced about it, and so I wrote a similar program in Python. (Yeah, I'm a productive guy at work.)
import random pot_goat = "GOAT" pot_car = "CAR" pots = pot_goat, pot_car door_a = "DOOR A" door_b = "DOOR B" door_c = "DOOR C" doors = door_a, door_b, door_c player_nonswitch = "PLAYER NS" player_switch = "PLAYER SW" player_repick = "PLAYER RP" players = player_nonswitch, player_switch, player_repick def make_round(): door_pots = dict((door, pot_goat) for door in doors) door_pots[random.choice(doors)] = pot_car return door_pots stats = dict((player, dict((pot, 0) for pot in pots)) for player in players) num_rounds = 10 ** 7 for round_num in xrange(num_rounds): if (round_num % (10 ** 5)) == 0: print "Round #%d (%.2f%%)" % (round_num, float(round_num) / num_rounds * 100) door_pots = make_round() for player in players: # First the contestant gets to choose from all three doors. choice = random.choice(doors) # Then, the host reveals a door which has a goat behind it which the # contestant didn't choose, asking if the contestant wants to remake # the door choice. goats = [d for (d, p) in door_pots.iteritems() if p == pot_goat and d != choice] reveal_door = random.choice(goats) remaining_doors = [d for d in doors if d != reveal_door] if player == player_repick: # Contestant just picks randomly, blindfolded. choice = random.choice(remaining_doors) elif player == player_switch: # Contestant does want to switch, and so chooses again from the # remaining doors. choice = [d for d in remaining_doors if d != choice] stats[player][door_pots[choice]] += 1 for player, player_pots in stats.iteritems(): goats, cars = player_pots[pot_goat], player_pots[pot_car] cars_amount = float(cars) / (goats + cars) * 100 print "%s: %d goats, %d cars - %.2f%% cars" % (player, goats, cars, cars_amount)
PLAYER NS: 6665086 goats, 3334914 cars - 33.35% cars PLAYER SW: 3333893 goats, 6666107 cars - 66.66% cars PLAYER RP: 5001588 goats, 4998412 cars - 49.98% cars
PLAYER NS is the non-switching player,
PLAYER SW switches, and
PLAYER RP just randomly chooses again.
I can't explain this at all.
simples3 0.3 released!
Just released simples3 version 0.3.
This release adds support for generating those nice only-valid-until-some-time URLs (expiring URLs.) Thanks to Pavel Repin for that.
Otherwise mostly bugfixes and cosmetic changes (non-API breaking.)
simples3 0.3-r2. on PyPI or just
sudo easy_install -U simples3 as usual.