Ann's problem

montecarlo.py

from math import comb
import sys
import random

s1, s2, s3, s4 = 10, 11, 12, 13
h = 7
N = s1 + s2 + s3 + s4

def generate_deck():
    deck = s1*[1] + s2*[2] + s3*[3] + s4*[4]
    return deck

def pick_card(deck):
    idx = random.randrange(len(deck))
    return deck.pop(idx)

def sample_is_flush():
    deck = generate_deck()
    hand = []
    for _ in range(h):
        hand.append(pick_card(deck))

    return any(hand.count(suit) >= 5 for suit in [1, 2, 3, 4])

def calc_probability():
    sum_ = 0
    for si in [s1, s2, s3, s4]:
        sum_ += sum(comb(si, k) * comb(N - si, h - k) for k in range(5, h+1))
    return sum_ / comb(N, h)


if __name__ == '__main__':
    samples = int(sys.argv[1])
    flushes = 0
    for n in range(samples):
        flushes += int(sample_is_flush())

    print(f"{flushes} out of {samples} was a flush")
    print(flushes / samples)
    print()
    print("calculation gives probabilty", calc_probability())