Computing the best ratio of lotus to recall among lotus-recall-only decks

lotus_and_recall_deck.py

"""
Script discussed in
https://youtu.be/s5ud06udqT0
"""

import random


NUM_GAME_SIMS = 10 ** 7

Lotus = 'Lotus'
Recall = 'Recall'
DECK_SIZE = 60
NUM_CARDS_STARTING_HAND = 7

REQUIRED_RECALLS_TO_WIN = 18  # roof of (DECK_SIZE - NUM_CARDS_STARTING_HAND) / 3


class Game:
    def __init__(self, num_of_recalls):
        self.num_of_recalls = num_of_recalls
        self.num_of_lotuses = DECK_SIZE  - num_of_recalls

    def draw(self, num_cards):
        for _ in range(num_cards):
            if self.deck[0] == Recall:
                self.recalls_in_hand += 1
            else:
                self.mana_pool += 3
            self.deck = self.deck[1:]

    def play_recall(self):
        self.mana_pool -= 1
        self.recalls_in_hand -= 1
        self.draw(3)

    def run(self):
        self.deck = self.num_of_recalls * [Recall] + self.num_of_lotuses * [Lotus]
        self.recalls_in_hand = 0
        self.mana_pool = 0

        # Get starting hand
        for num_starting_hand in range(NUM_CARDS_STARTING_HAND + 1)[::-1]:
            if num_starting_hand == 1:
                return 1  # Too many mulligans, first turn kill not possibly anymore

            random.shuffle(self.deck)
            potential_hand = self.deck[:num_starting_hand]
            if Lotus in potential_hand and Recall in potential_hand:
                self.draw(num_starting_hand)
                break  # At least one recall and one lotus => good to go

        while len(self.deck) >= 3:
            if self.recalls_in_hand == 0 or self.mana_pool == 0:
                return 1  # Out of recalls or out of mana

            self.play_recall()
            if self.recalls_in_hand >= REQUIRED_RECALLS_TO_WIN and self.mana_pool >= REQUIRED_RECALLS_TO_WIN:
                return 0  # Win

        return 1  # Milled yourself to death (TODO: This assumes 53 cards at start and not more (from potential mulligan))


for num_recalls in (36, 37, 38, 39, 40):
    game = Game(num_recalls)
    fails = 0
    for _ in range(NUM_GAME_SIMS):
        fails += game.run()

    percent = "{:3.3f}".format(100 * fails / NUM_GAME_SIMS)
    print(f"Simulated {NUM_GAME_SIMS} games starting with {num_recalls} recalls. Fails: {fails}, or {percent} %")

exit("Done.")


"""
num_recalls = 10000
Simulated 10000 games starting with 23 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 24 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 25 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 26 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 27 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 28 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 29 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 30 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 31 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 32 recalls. Fails: 9999, or 99.990 %
Simulated 10000 games starting with 33 recalls. Fails: 9982, or 99.820 %
Simulated 10000 games starting with 34 recalls. Fails: 9780, or 97.800 %
Simulated 10000 games starting with 35 recalls. Fails: 7793, or 77.930 %
Simulated 10000 games starting with 36 recalls. Fails: 3120, or 31.200 %
Simulated 10000 games starting with 37 recalls. Fails: 10, or 0.100 %
Simulated 10000 games starting with 38 recalls. Fails: 13, or 0.130 %
Simulated 10000 games starting with 39 recalls. Fails: 17, or 0.170 %
Simulated 10000 games starting with 40 recalls. Fails: 23, or 0.230 %
Simulated 10000 games starting with 41 recalls. Fails: 43, or 0.430 %
Simulated 10000 games starting with 42 recalls. Fails: 66, or 0.660 %
Simulated 10000 games starting with 43 recalls. Fails: 107, or 1.070 %
Simulated 10000 games starting with 44 recalls. Fails: 148, or 1.480 %
Simulated 10000 games starting with 45 recalls. Fails: 192, or 1.920 %
Simulated 10000 games starting with 46 recalls. Fails: 323, or 3.230 %
Simulated 10000 games starting with 47 recalls. Fails: 682, or 6.820 %
Simulated 10000 games starting with 48 recalls. Fails: 2524, or 25.240 %
Simulated 10000 games starting with 49 recalls. Fails: 7823, or 78.230 %
Simulated 10000 games starting with 50 recalls. Fails: 9738, or 97.380 %
Simulated 10000 games starting with 51 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 52 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 53 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 54 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 55 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 56 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 57 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 58 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 59 recalls. Fails: 10000, or 100.000 %
Simulated 10000 games starting with 60 recalls. Fails: 10000, or 100.000 %

num_recalls = 10000000
Simulated 10000000 games starting with 36 recalls. Fails: 3186269, or 31.863 %
Simulated 10000000 games starting with 37 recalls. Fails: 11688, or 0.117 %
Simulated 10000000 games starting with 38 recalls. Fails: 13387, or 0.134 %
"""