#-----------------------------------------------------------------------
# LoadedDice.py
#
# Simulates n rolls of 2 loaded 6-sided dice.  Determines the probability 
# that the sum of the two dice is equal to 3.
#
#-----------------------------------------------------------------------
from random import randint, random

n = 1_000_000           # of rolls
sum_eq_3_freq = 0       # number of times the sum is divisible by 3
sum = 0                 # sum of two dice

# dictionary: P[k]=probability of face k (1<=k<=6)
P = {1:.12, 2:.14, 3:.17, 4:.20, 5:.19, 6:.18}

# perform all trials
for i in range(n):

   # throw first die
   x = random() # get a random number in [0.0, 1.0)
   die_1 = 1 if x<P[1] else \
           2 if x<P[1]+P[2] else \
           3 if x<P[1]+P[2]+P[3] else \
           4 if x<P[1]+P[2]+P[3]+P[4] else \
           5 if x<P[1]+P[2]+P[3]+P[4]+P[5] else \
           6

   # throw second die
   y = random() # get a random number in [0.0, 1.0)
   die_2 = 1 if y<P[1] else \
           2 if y<P[1]+P[2] else \
           3 if y<P[1]+P[2]+P[3] else \
           4 if y<P[1]+P[2]+P[3]+P[4] else \
           5 if y<P[1]+P[2]+P[3]+P[4]+P[5] else \
           6

   # compute sum
   sum = die_1 + die_2

   # update frequency
   if sum==3:
      sum_eq_3_freq += 1

# end for

# compute relative frequency of eq_to_3 event
rel_freq = sum_eq_3_freq/n

# print results
print()
print(f"Probabilities: {P}")
print()
print(f"#rolls = {n}")
print()
print(f"relative frequency of sum_eq_3 = {rel_freq},")
print()