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is3ka1/shoot_the_dragons_gate.py

Created December 16, 2023 16:55
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  1. is3ka1 revised this gist Dec 16, 2023. No changes.
  2. is3ka1 created this gist Dec 16, 2023.
    73 changes: 73 additions & 0 deletions shoot_the_dragons_gate.py
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    #!/usr/bin/env python3

    import matplotlib.pyplot as plt
    import seaborn as sns
    import numpy as np


    def calculate_probabilities(card1, card2, num_decks=1):
    deck = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13] * int(4 * num_decks)

    deck.remove(card1)
    deck.remove(card2)

    is_pair = card1 == card2

    if is_pair:
    higher_cards = [card for card in deck if card > card1]
    lower_cards = [card for card in deck if card < card1]
    collision_cards = [card for card in deck if card == card1]

    higher_prob = len(higher_cards) / len(deck)
    lower_prob = len(lower_cards) / len(deck)
    collision_prob = len(collision_cards) / len(deck)
    print('higher_prob: ', higher_prob)
    print('lower_prob: ', lower_prob)
    print('collision_prob: ', collision_prob)

    higher_expected_value = higher_prob * 1 - collision_prob * 3 - lower_prob * 1
    lower_expected_value = lower_prob * 1 - collision_prob * 3 - higher_prob * 1

    return {'higher': (higher_prob, higher_expected_value), 'lower': (lower_prob, lower_expected_value)}

    else:
    lower = min(card1, card2)
    upper = max(card1, card2)
    winning_cards = [card for card in deck if lower < card < upper]
    collision_cards = [card for card in deck if card == lower or card == upper]

    win_probability = len(winning_cards) / len(deck)
    collision_probability = len(collision_cards) / len(deck)
    print('win_probability: ', win_probability)
    print('collision_probability: ', collision_probability)

    expected_value = win_probability * 1 - collision_probability * 2 - (1 - win_probability - collision_probability) * 1
    return {'between': (win_probability, expected_value)}

    def choose_best_strategy_probabilities(card1, card2, num_decks=1):
    probabilities = calculate_probabilities(card1, card2, num_decks)
    print('probabilities: ', probabilities)
    if 'between' in probabilities:
    return probabilities['between']
    elif probabilities['higher'][1] > probabilities['lower'][1]:
    return probabilities['higher']
    else:
    return probabilities['lower']

    def plot_probabilities_with_hotmap(num_decks=1):
    expectations = np.zeros((13, 13))
    for i in range(13):
    for j in range(13):
    probabilities = choose_best_strategy_probabilities(i + 1, j + 1, num_decks)
    expectations[i, j] = probabilities[1]

    plt.figure(figsize=(10, 10))

    # flip the expectations matrix by y-axis to align with the card values
    expectations = np.flipud(expectations)
    ax = sns.heatmap(expectations, annot=True, fmt='.2f', cmap='coolwarm', center=0,
    xticklabels=['A', '2', '3', '4', '5', '6', '7', '8', '9', '10', 'J', 'Q', 'K'],
    yticklabels=['K', 'Q', 'J', '10', '9', '8', '7', '6', '5', '4', '3', '2', 'A'],
    )
    ax.set(xlabel='Card 1', ylabel='Card 2', title=f'Expectation Values Distribution for Dragon Gate Game with {num_decks} Deck{"s" if num_decks > 1 else ""}')
    plt.show()