UNO Poker probability check

uno-poker-prob-check.py

import math

def calculate_uno_poker_probabilities():
    """
    Calculates the probabilities of poker hands for a 40-card Uno deck.
    The deck consists of 4 colors (suits) and 10 ranks (0-9).
    A hand is 5 cards.
    """

    # Total number of possible 5-card hands from a 40-card deck
    total_hands = math.comb(40, 5)

    # --- Calculate counts for each hand, from strongest to weakest ---

    # Royal Flush (5-9 of the same color)
    # 1 sequence (5,6,7,8,9) * 4 colors
    royal_flush_count = 1 * 4

    # Straight Flush (any 5 consecutive cards of the same color)
    # Sequences: 0-4, 1-5, 2-6, 3-7, 4-8, 5-9 (6 possible sequences)
    # For each sequence, there are 4 possible colors.
    straight_flush_count = 6 * 4

    # Four of a Kind
    # Choose rank for the 4 cards (10 choices)
    # Choose the 4 cards of that rank (C(4,4)=1)
    # Choose the 1 kicker card from remaining 36 cards
    four_of_a_kind_count = 10 * math.comb(4, 4) * math.comb(36, 1)

    # Full House
    # Choose rank for the triple (10 choices)
    # Choose 3 of 4 cards for the triple (C(4,3))
    # Choose rank for the pair (9 choices remaining)
    # Choose 2 of 4 cards for the pair (C(4,2))
    full_house_count = 10 * math.comb(4, 3) * 9 * math.comb(4, 2)

    # Flush
    # Choose a color (4 choices)
    # Choose 5 cards of that color (from 10 cards) (C(10,5))
    # This count includes straight flushes, so we must subtract them.
    flush_count = 4 * math.comb(10, 5) - straight_flush_count

    # Straight
    # 6 possible sequences (0-4 to 5-9)
    # For each card in the sequence, there are 4 color choices (4^5)
    # This count includes straight flushes, so we must subtract them.
    straight_count = 6 * (4**5) - straight_flush_count

    # Three of a Kind
    # Choose rank for the triple (10 choices)
    # Choose 3 cards of that rank (C(4,3))
    # Choose 2 other ranks for the remaining 2 cards (C(9,2))
    # Choose 1 card from each of those 2 ranks (4*4)
    three_of_a_kind_count = 10 * math.comb(4, 3) * math.comb(9, 2) * 4 * 4

    # Two Pair
    # Choose 2 ranks for the pairs (C(10,2))
    # Choose 2 cards for each pair (C(4,2) * C(4,2))
    # Choose 1 rank for the kicker (8 choices remaining)
    # Choose 1 card for the kicker (4 choices)
    two_pair_count = math.comb(10, 2) * math.comb(4, 2) * math.comb(4, 2) * 8 * 4

    # One Pair
    # Choose rank for the pair (10 choices)
    # Choose 2 cards for the pair (C(4,2))
    # Choose 3 other ranks for the kickers (C(9,3))
    # Choose 1 card from each of those 3 ranks (4*4*4)
    one_pair_count = 10 * math.comb(4, 2) * math.comb(9, 3) * (4**3)

    # High Card
    # Total hands minus all other hands
    all_other_hands = (straight_flush_count + four_of_a_kind_count + full_house_count +
                       flush_count + straight_count + three_of_a_kind_count +
                       two_pair_count + one_pair_count)
    high_card_count = total_hands - all_other_hands

    # --- Store results in a dictionary, including the combined Straight Flush category ---
    hand_counts = {
        "Royal Flush (5-9)": royal_flush_count,
        "Straight Flush (non-royal)": straight_flush_count - royal_flush_count,
        "Four of a Kind": four_of_a_kind_count,
        "Full House": full_house_count,
        "Flush": flush_count,
        "Straight": straight_count,
        "Three of a Kind": three_of_a_kind_count,
        "Two Pair": two_pair_count,
        "One Pair": one_pair_count,
        "High Card": high_card_count
    }

    # --- Print results ---
    print(f"Total possible 5-card hands from a 40-card deck: {total_hands}\n")
    print("{:<28} {:>15} {:>18}".format("Hand Combination", "Count", "Probability (%)"))
    print("-" * 61)
    for hand, count in hand_counts.items():
        probability = (count / total_hands) * 100
        print(f"{hand:<28} {count:>15} {probability:>17.4f}%")

calculate_uno_poker_probabilities()