import math
import numpy as np
import pandas as pd
import random
import seaborn as sns
x = np.array([[3/8],
[1/16],
[9/16]])
y = np.array([[1, 0, 3/8],
[0, 1, 1/16],
[0, 0, 9/16]])
a = y@x
for i in range(10000) :
a = y@a
a
array([[8.57142857e-001],
[1.42857143e-001],
[4.94065646e-324]])
x = np.array([[24/256],
[40/256],
[144/256],
[48/256]])
y = np.array([[1, 0, 1/8, 3/32],
[0, 1, 1/8, 5/32],
[0, 0, 5/8, 9/16],
[0, 0, 1/8, 3/16]])
a = y@x
for i in range(10000) :
a = y@a
a
array([[4.5e-001],
[5.5e-001],
[4.9e-324],
[0.0e+000]])
def monteCarlo(rolls):
wins = 0
losses = 0
#Roll 4 dice.
for roll in range(rolls):
#Inititate.
dice = [random.randrange(1, 5, 1),
random.randrange(1, 5, 1),
random.randrange(1, 5, 1),
random.randrange(1, 5, 1)]
#Place in bins until all are unique or all are duplicate.
outcome = updateDice(dice)
if outcome == "win":
wins += 1
else:
losses += 1
return(wins, losses)
#Returns "win" or "loss" depending on if all dice are in unique or all dice are duplicates
def updateDice(dice):
#Frequency of dice numbers.
freq = {}
for r in dice :
if r in freq.keys():
freq[r] += 1
else :
freq[r] = 1
#Place dice in unique and duplicate bins.
unique = []
duplicate = []
for f in freq:
if freq[f] == 1:
unique.append(f)
elif freq[f] > 1:
for i in range(freq[f]):
duplicate.append(f)
#All are unique.
if len(unique) == 4:
return("win")
#All are duplicate.
elif len(duplicate) == 4:
return("loss")
#Reroll duplicates.
else :
newdice = unique.copy()
for d in duplicate:
newdice.append(random.randrange(1, 5, 1))
return(updateDice(newdice))
monteCarlo(10000000)
(4496805, 5503195)