import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import math
from functools import reduce
import random as ran

x = np.random.multinomial(10000, [1/6.]*6, size=1)
type(x)
x[1:[:]]
z = x.tolist()
u = []
for i in z:
    for l in i:
        u.append(l)
N = len(u)
N
y = range(1, N + 1)
plt.bar(y, height = u)
plt.show()
a = np.arrange(3)
x.shape

vec = np.array([1,3,5])
type(vec)
vec * 1/9

mu, sigma = 0, 1 # mean and standard deviation
s = np.random.normal(mu, sigma, 99900)
mu2 = 100
s2 = np.random.normal(mu2, sigma, 100)
sdf = np.append(s, s2)
np.mean(sdf)
np.mean(s)
np.mean(s2)
np.median(sdf)
np.median(s)
np.median(s2)
pop = np.array([1,3,5])
for i in pop:
    print(i)
np.multiply(i for i in pop)
help(np.multiply)
x1 = np.arange(9.0).reshape((3, 3))
x1
np.prod([1,2,3,4])
def gen(n,k):
    if(k==1):
        return [[n]]
    if(n==0):
        return [[0]*k]
    return [ g2 for x in range(n+1) for g2 in [ u+[n-x] for u in gen(x,k-1) ] ]
n, k = 2, 2
possible = gen(n, k)
possible

def mult_function(outcome_list, prob_list):
    n_fac = math.factorial(n)
    outcome_fac_list = []
    prob_out_list = []
    final_prob_list = []
    for i in range(len(outcome_list)):
        outcome_fac_list.append([math.factorial(l) for l in outcome_list[i]])
        prob_out_list.append([prob_list[l]**outcome_list[i][l] for l in range(len(prob_list))])
    for i in range(len(outcome_list)):
        final_prob_list.append([n_fac*np.prod(prob_out_list[i]/np.prod(outcome_fac_list[i]))])
    return n_fac, outcome_fac_list, prob_out_list, final_prob_list


probby = math.factorial(n)*np.prod([1.0, 0.18524475214924618])/np.prod([1, 2])
def n_factorial(outcome_list, prob_list):
    n_fac = math.factorial(n)
    b_fac = []
    b_fac_final = []
    the_list = []
    for i in range(len(outcome_list)):
        temp_list = []
        for sub in outcome_list[i]:
            temp_list.append(math.factorial(sub))
        b_fac.append(temp_list)
        other_temp_list = [prob_list[l]**outcome_list[i][l] for l in range(len(outcome_list[i]))]
        the_list.append(reduce(lambda x,y:x*y,other_temp_list))
    for i_ in range(len(b_fac)):
        temp_list = []
        temp_list.append(reduce(lambda x,y:x*y,b_fac[i_]))
        b_fac_final.append(temp_list)
    for i in range(len(the_list)):
        the_list[i] *=n_fac/b_fac_final[i][0]
    return n_fac, b_fac_final, the_list
r = [0.4,0.6]
s = sum(r)
r = [ i/s for i in r ]
a,b,c = n_factorial(possible,r)
a,b,c,d = mult_function(possible,r)
a
b
c
d
pol = [r[l]**possible[18][l] for l in range(len(possible[0]))]
pol_ = reduce(lambda x,y:x*y, pol)
pol_
sum(c)
r
sum(r)
r[0]**3+r[0]**2*r[1]*3+r[0]*r[1]**2*3+r[1]**3
d = b*c
a
n_fac = math.factorial(len(possible[0]))
n_fac
str(r)
mult_list = pd.DataFrame(
    {'Outcome': possible,
     'Probability': c
    })
mult_list
def prob_of_outcome(outcome_list, prob_list):
    prob_out = []
    for i in outcome_list:
        math.factorial(len(i)) / np.multiply(math.factorial(l) for l in outcome_list[i]) * np.multiply()
plt.figure()
mult_list.plot(kind='barh')
plt.show()

np.sum([2,3,4])


def mult_list(n,k,prob_dist):
    list_of_events = gen(n,k)
    list_of_probs = []
    list_of_real_probs =[]
    list_of_payoffs = []
    for li in list_of_events:
        list_of_probs.append((math.factorial(n)/np.prod([math.factorial(el) for el in li]))*(np.prod([prob_dist[l]**li[l] for l in range(len(prob_dist))])))
        list_of_real_probs.append([round(n*prob_dist[l],2) for l in range(len(prob_dist))])
    for i in range(len(list_of_events)):
        minus = 0
        for l in range(len(list_of_events)):
            if l != i:
                minus += np.sum[(list_of_events[i][pok] - list_of_events[l][pok]) for pok in range(len(list_of_events[i]))]
        list_of_payoffs.append(100 - minus)
    return list_of_events, list_of_probs, list_of_real_probs

np.sum([1,2,3],[2,3,4])