Setup

from itertools import permutations as IP
import math
import matplotlib.pyplot as plt
from matplotlib.ticker import StrMethodFormatter as SMF
import numpy as np
import random
import seaborn as sns

deck = list(range(1,11))

decks = list(IP(deck))

Functions

#How many wins?
def riddler(decks):

    wins = 0
    #Loop through all 10! decks.
    for d in decks:
        
        tot = 0
        #As long as there are cards remaining.
        while len(d) > 0 :
            #Place the top card in your hand and update the deck.
            tot += d[-1]
            d = d[:-1]
            
            #What is the outcome?
            if tot == 21:
                wins += 1
                break
            elif tot > 21:
                break
            else :
                continue
    return(wins)


#For Plot.
def ec1(decks):
    
    #Only scenarios possible.
    wins = {3: 0,
            4: 0,
            5: 0}
    passe = {2: 0,
             3: 0,
             4: 0,
             5: 0,}
    
    #Loop through all 10! decks.
    for d in decks:
        
        tot = 0
        drawn = []
        
        #As long as there are cards remaining.
        while len(d) > 0 :
            #Place the top card in your hand and update the deck.
            tot += d[-1]
            d = d[:-1]
            
            #If you play safe, you will never lose, only pass.                       
            
            #Win, save the count corresponding to the appropriate hand size in dictionary.
            if tot == 21 :
                wins[10 - len(d)] += 1
                break
                
            #Pass, save the count corresponding to the appropriate hand size in dictionary.            
            elif max(d) > 21 - tot :
                passe[10 - len(d)] += 1
                break
            
    return(wins, passe)

    

#Check win combinations.
def ec2(decks):

    wins = {}

    #Loop through all 10! decks.    
    for d in decks:
        
        tot = 0
        hand = []
 
        #As long as there are cards remaining.
        while len(d) > 0 :
            #Place the top card in your hand and update the deck.
            tot += d[-1]
            hand.append(d[-1])
            hand.sort()
            d = d[:-1]
            
            #If you win, what cards are in your hand?
            if tot == 21 :
                if str(hand) in wins.keys():
                    wins[str(hand)] += 1 
                else :
                    wins[str(hand)] = 1
                break
            
            elif max(d) > 21 - tot :
                break
            
    return(wins)

Riddler

riddler(decks)

635040

Extra Credit

dicts = ec1(decks)
print(dicts)

({3: 50400, 4: 21600, 5: 2880}, {2: 1532160, 3: 1562400, 4: 427680, 5: 31680})

wins, passe = dicts

sns.set()
fig = plt.figure(figsize = (15, 8))
ax = fig.add_subplot()

#Title setup.
ax.set_title('Risk Averse, Non-Traditional Blackjack', fontsize = 24)

#X-axis setup.
ax.set_xlabel('Number of Cards in Hand', fontsize = 22)
ax.set_xticks(ticks = range(2,6))
#Y-axis setup.
ax.set_ylabel('Frequency', fontsize = 22)
ax.tick_params(axis = 'both', which = 'major', labelsize = 18)
ax.yaxis.set_major_formatter(SMF('{x:,.0f}'))



#Pass.
bars0 = plt.bar(x = passe.keys(),
                height = np.array(list(passe.values())) + np.array([0] + list(wins.values())),
                color = '#21908CFF',
                width = 1,
                edgecolor = 'grey',
                label = 'Pass')
#Wins.
bars1 = plt.bar(x = wins.keys(),
                height = wins.values(),
                color = '#404688FF',
                width = 1,
                edgecolor = 'grey',
                label = 'Win')

for i in range(4) :
    
    #Pass.
    plt.text(x = bars0[i].get_xy()[0] + 0.45,
             y = bars0[i].get_height() + 25000,
             s = format(int(bars0[i].get_height()), ','),
             ha = 'center',
             size = 'xx-large',
             weight = 'bold',
             c = '#21908CFF',)

    #Wins.
    if i < 3 :
        plt.text(x = bars1[i].get_xy()[0] + 0.45,
                 y = bars1[i].get_height() + 10000,
                 s = format(int(bars1[i].get_height()), ','),
                 ha = 'center',
                 size = 'large',
                 weight = 'bold',
                 c = '#404688FF')


plt.legend(loc = 5,
           fontsize = 'x-large') 
    
fig.savefig("2024.05.24.png", bbox_inches = 'tight')

ec2(decks)

{'[5, 6, 10]': 10080,
 '[4, 7, 10]': 10080,
 '[3, 8, 10]': 10080,
 '[2, 9, 10]': 20160,
 '[2, 4, 5, 10]': 4320,
 '[2, 3, 6, 10]': 4320,
 '[1, 4, 6, 10]': 4320,
 '[1, 3, 7, 10]': 4320,
 '[1, 2, 8, 10]': 4320,
 '[1, 2, 3, 5, 10]': 2880}

Rohan Lewis

2024.05.27