import random

parameters = [(7, 3),
              (7, 4),
              (7, 5),
              (8, 3),
              (8, 4),
              (8, 5),
             ]

num_trials = 100000

for N, n in parameters:
    stay_wins = 0
    switch_wins = 0

    for t in range(num_trials):
        doors = set(range(N))
    
        prize = random.sample(doors, 1)
        first_pick = random.sample(doors, 1)

        openable_doors = doors - set(prize + first_pick)
        opened = random.sample(openable_doors, n)

        switchable_doors = doors - set(opened + first_pick)
        switched_pick = random.sample(switchable_doors, 1)
    
        if prize == first_pick:
            stay_wins += 1
        if prize == switched_pick:
            switch_wins += 1

    ratio = float(switch_wins) / stay_wins
    theoretical_ratio = float(N - 1) / (N - n - 1) 
    print 'N={0}, n={1}\t {2} {3} {4:.3f} {5:.3f}'.format(N,
                                                          n,
                                                          switch_wins,
                                                          stay_wins,
                                                          ratio,
                                                          theoretical_ratio,
                                                         )