First, you have to know of a card game called One Handed Solitaire, as reported by Metafilter member ChurchHatesTucker here. CHT’s been on a tear in presenting various card games lately, here’s the other recent posts they’ve made on solitaire card games, with a dungeon crawl flavor: Clear the Dungeon, Tomb of the Four Kings, Scoundrel.

One Handed Solitaire is very simple, and an example of a “zero player game.” There are no decisions to make; winning or losing is completely down to the initial state of the deck. Here are the rules in text:

You start with a shuffled deck of cards. Draw four to form your hand. Your hand is considered to be in sequence, you must keep them in the order drawn. Now:

• If the first and fourth cards are the same suit, discard the second and third cards from your hand out of play. This of course moves the fourth card to be the second card.
• If the first and fourth cards are the same rank, discard the first four cards from your hand.
• If neither of these things are true, draw another card from the deck to the front of your hand. This makes a new first card, and changes which the fourth card is.
• When the deck runs out and you can no longer remove cards, the game is over. If you clear your hand and there’s still cards in the deck you’re not done, draw four more.

Your score (lower is better) is how many cards are in your hand when you run out of deck and can no longer discard cards. The average score is about 13.32 cards left. If you get a score of zero, that is you discard all of the cards from your hand and the deck is empty, you win.

Here are the rules demonstrated by Gather Together Games in a Youtube video (1¾ minutes):

ChurchHatesTucker ran a simulation of 200,000 runs and found the win rate of the game is close to 0.7%. I ran my own simulation, in a Python script, and found that out as well. I’ll put my code at the end of this post. No AI was used in its writing, and permission is not given to use it to train AIs. In fact, that’s true of all the text in this blog.

My first attempt found a win rate of 0.94%, but that turns out to be because I left out the aces from the deck! I tried a run with only 20 cards in the deck the 2-6 of each suit, and the win rate became about 7.5%.

If you want to try yourself, here’s the Python code I used. If you have Python installed, just paste it into a text file, give it the extension .py, and run it. It assumes you’re running it in a Linux or other Unix-like system; if you’re on Windows, you might have to change the “shebang” line at the front to point to where your Python is.

#!/usr/bin/python
import random

def draw(deck):
    if len(deck) > 0:
        return deck.pop(0)
    else:
        return None

def gameend(deck, hand, verbose):
    score = len(hand)
    if verbose >= 1:
        print("Deck exhaused. Final score:",score)
        if score == 0:
            print("Win!")
    if verbose >= 2:
        print("Deck state:",deck)
        print("Hand state:",hand)
    return score

def play(verbose = 0):
    deck = ["2H","3H","4H","5H","6H","7H","8H","9H","TH","JH","QH","KH","AH",
            "2D","3D","4D","5D","6D","7D","8D","9D","TD","JD","QD","KD","AD",
            "2C","3C","4C","5C","6C","7C","8C","9C","TC","JC","QC","KC","AC",
            "2S","3S","4S","5S","6S","7S","8S","9S","TS","JS","QS","KS","AS"]
    hand = []
    random.shuffle(deck)
    for a in range(4):
        hand.append(draw(deck))
    if verbose >= 3:
        print("Game starting--")
    while True:
        if len(hand) < 4:
            drawcard = draw(deck)
            if drawcard == None:
                return gameend(deck, hand, verbose)
            if verbose >= 2:
                print("Drew a",drawcard)
            hand.insert(0, drawcard)
            continue
        cardtop = hand[0]
        cardfourth = hand[3]
        if verbose >= 3:
            print("********: Deck length:",len(deck), "Hand length:",len(hand))
        if verbose >= 2:
            print("CARDS:", cardtop, cardfourth)
        # case 1: if the 1st and 4th cards match suit, discard the second and third cards
        if cardtop[1] == cardfourth[1]:
            d1 = hand.pop(1)
            d2 = hand.pop(1)
            if verbose >= 2:
                print("Discarded",d1,"and",d2)
            continue
        # case 2: if the 1st and 4th cards match rank, discard the top four
        if cardtop[0] == cardfourth[0]:
            d1 = hand.pop(0)
            d2 = hand.pop(0)
            d3 = hand.pop(0)
            d4 = hand.pop(0)
            if verbose >= 2:
                print("Discarded:",d1,d2,d3,d4)
            continue
        # case 3: if neither is true, draw a card
        drawcard = draw(deck)
        if drawcard == None:
            return gameend(deck, hand, verbose)
        else:
            if verbose >= 2:
                print("Drew a card")
            hand.insert(0, drawcard)
        # end of loop

if __name__ == "__main__":
    numgames = 10000000
    wins = 0
    scores = []
    scoresum = 0
    for count in range(numgames):
        score = play(verbose = 0)
        scores.append(score)
        scoresum += score
        if score == 0:
            wins += 1
            #print("A win on game #",count+1)
        if count % 500000 == 0:
            print("Played",count,"games...")
    print("Finished playing",numgames,"games")
    print("Wins:",wins)
    print("Win rate:",wins/numgames)
    print("Total score:",scoresum)
    print("Average score:",scoresum/numgames)
    print("Run compete.")

rodneylives