#Creates a list of all 1,296 dice rolls for 4 dice.
#Creates a list of the corresponding 6 sums for each of the 1,296 rolls.
all_dice = []
all_sums = []
for d0 in range(1, 7) :
    for d1 in range(1, 7) :
        for d2 in range(1, 7) :
            for d3 in range(1, 7) :
                all_dice.append((d0, d1, d2, d3))
                all_sums.append((d0+d1,
                             d0+d2,
                             d0+d3,
                             d1+d2,
                             d1+d3,
                             d2+d3))

                
                
#Takes a number between 2 - 12 and removes any of the sums that contains that number.
#Returns the modified list of sums.
def removeSums(n, list_of_sums):
    new_sums = []
    for sums in list_of_sums:
        if n not in sums:
            new_sums.append(sums)
    
    return(new_sums)

#For each of the sums of two dice, 2 - 12, 
#how many of the 1296 dice rolls does it exist in?
#This loop returns a dictionary of the sum and the count.

sum_count = dict()
for s in range(2, 13):
    
    sum_count[s] = 1296 - len(removeSums(s, all_sums))
    
sum_count

#For each of the sums of two dice, 2 - 12, 
#how many times does it exist in the 1296 dice rolls?
#This loop returns a dictionary of the sum and the count.

all_sums_flat = [s for sums in all_sums for s in sums] 

all_sums_count = {}
for s in all_sums_flat:
    
    if s not in all_sums_count.keys():
        all_sums_count[s] = 1
    else:
        all_sums_count[s] += 1
        
all_sums_count

#For each of the 330 combinations of 4 dice sums, 
#this loop returns a dictionary of the quadruple and the number of winning possibilities. 
remaining = dict()
for s1 in range(2, 10):
    for s2 in range(s1+1, 11):
        for s3 in range(s2+1, 12):
            for s4 in range(s3+1, 13):
                remaining[(s1, s2, s3, s4)] = 1296 - len(removeSums(s1, removeSums(s2, removeSums(s3, removeSums(s4, all_sums)))))

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


#Plot.
sns.set()
fig = plt.figure(figsize = (14, 8))
ax = fig.add_subplot()

#Histogram.


#Change first and last color.
N, bins, patches = ax.hist(x = remaining.values(),
         #Number of bins.
         bins = 15*np.arange(35)+774 ,
         align = "mid")

for i in range(0,1):
    patches[i].set_facecolor('#481567')
for i in range(1, len(patches)-2):    
    patches[i].set_facecolor('#2D708E')
for i in range(len(patches)-2, len(patches)):
    patches[i].set_facecolor('#3CBB75')


#Title.
ax.set_title("Distribution of 330 Sums Choice Possibilities and Dice Rolls Won", fontsize = 24)

#Axes.
ax.set_xlabel("Dice Rolls Won", fontsize = 18)
ax.set_ylabel("Number of Sum Choices", fontsize = 18)
ax.tick_params(axis = 'both', labelsize = 16)

#Min text.
ax.annotate('Minimum Winnings: 774',
            xy = (750, 4),
            xytext = (750, 4),
            fontsize = 18,
            fontweight = 'bold',
            color = '#481567');
ax.annotate('Sums: 2, 3, 11, 12',
            xy = (770, 2.5),
            xytext = (770, 2.5),
            fontsize = 18,
            fontweight = 'bold',
            color = '#481567');
#Max text.
ax.annotate('Maximum Winnings: 1264',
            xy = (1150, 4),
            xytext = (1150, 4),
            fontsize = 18,
            fontweight = 'bold',
            color = '#3CBB75');
ax.annotate('Sums: 4, 6, 8, 10',
            xy = (1175, 2.5),
            xytext = (1175, 2.5),
            fontsize = 18,
            fontweight = 'bold',
            color = '#3CBB75');

fig.savefig("2022.03.11 Classic1.png")

for key in remaining.keys():
    if remaining[key] > 1237:
        print(key, remaining[key])

(2, 6, 8, 10) 1246
(4, 6, 7, 9) 1238
(4, 6, 8, 10) 1264
(4, 6, 8, 12) 1246
(5, 7, 8, 10) 1238

Rohan Lewis

2022.03.14