import random

simulationCount = 100000

counts = {
    '2a': 0,
    '2b': 0,
    '3': 0,
    '4': 0,
    '5': 0,
    '6-2a': 0,
    '6-a/2': 0,
    'EV-relativeToA': 0,
    'EV-relativeToT': 0,
}

def f(key):
    return str(round(counts[key] / simulationCount * 100, 2)) + '%'

for i in range(simulationCount):
    # A person is given two indistinguishable envelopes. One envelope contains twice as much money as the other.
    amounts = [100, 200]

    # The person may pick one envelope and keep whatever amount it contains.
    # They pick one envelope at random.
    # Denote by a the amount in the player's selected envelope.
    # Before they open it they are given a chance to take the other envelope (b) instead.
    random.shuffle(amounts)
    a = amounts[0]
    b = amounts[1]

    # 2) The probability that a is the smaller amount is 1/2, and that it is the larger amount is also 1/2
    if a < b:
        counts['2a'] += 1
    if a > b:
        counts['2b'] += 1

    # 3) The other envelope (b) may contain either 2A or A/2
    if b == 2*a or b == a/2:
        counts['3'] += 1

    # 4) If a is the smaller amount, then the other envelope (b) contains 2a
    if (a < b and b == 2*a) or not a < b:
        counts['4'] += 1

    # 5) If a is the larger amount, then the other envelope (b) contains a/2
    if (a > b and b == a/2) or not a > b:
        counts['5'] += 1

    # 6) The other envelope (b) contains 2a with probability 1/2 and a/2 with probability 1/2
    if (b == 2*a):
        counts['6-2a'] += 1
    if (b == a/2):
        counts['6-a/2'] += 1

    # 7) The expected value of switching from a to b, relative to a, is positive: 0.5*2a + 0.5*a/2 - a = 0.25a
    counts['EV-relativeToA'] += (b/a - 1)

    # ! The expected value of switching from a to b, relative to T, is still zero.
    T = amounts[0] + amounts[1]
    counts['EV-relativeToT'] += (b-a)/T

print('2a: the probability that a is the smaller amount is 50%, observed:', f('2a'))
print('2b: the probability that a is the larger amount is 50%, observed:', f('2b'))
print('3: the other envelope (b) may contain either 2a or a/2, observed:', f('3'))
print('4: if a is the smaller amount, then the other envelope contains 2a, observed:', f('4'))
print('5: if a is the larger amount, then the other envelope contains a/2, observed:', f('5'))
print('6-2a: the other envelope contains 2a with probability 50%, observed:', f('6-2a'))
print('6-a2: the other envelope contains a/2 with probability 50%, observed:', f('6-a/2'))
print('7: the expected value of switching from a to b, relative to a, is +25%, observed:', f('EV-relativeToA'))
print('!: the expected value of switching from a to b, relative to T, is 0%, observed:', f('EV-relativeToT'))