squire_sim.py

import random


def sim_game():
    n_cards = 48  # Total number of cards remaining in deck
    n_squires = 4 # Number of squires in deck
    hand_size = 0 # Total cards in hand

    def draw_card():
        nonlocal n_cards, n_squires, hand_size
        # Draw card without replacement
        # randint goes from 0 to n_cards - 1
        if random.randint(0, n_cards) < n_squires:
            n_squires -= 1
            if n_squires == 0:
                return True

        n_cards -= 1
        hand_size += 1

        return False

    # Opening hand. See 5 completely new cards.
    for i in range(5):
        if draw_card():
            return True

    for turn in range(4):
        # Draw a completely new card
        if draw_card():
            return True
       
        # Do Magician
        # How many cards should we mulligan?
        squires_in_hand = 4 - n_squires
        to_mul = hand_size - squires_in_hand

        n_cards += to_mul
        hand_size -= to_mul

        for i in range(to_mul):
            if draw_card():
                return True

    return False


def sim():
    tries = 100000
    successes = 0
    for i in range(tries):
        if sim_game():
            successes += 1

    return successes / tries


if __name__ == "__main__":
    print(sim())