"""

A Pig Die game is simulated to decide when and where to hold, using MonteCarlo simluations

"""

def pigDie(niter, n):

import pandas as pd

import numpy as np

import random

#We initialize values of our matrix here

iterations = niter

holdn = n

probofn = np.array([0,0,1,2,3,4,5])

probofn [1:len(probofn)] = probofn [1:len(probofn)] + holdn

rownames = ["nzero","n","n+1","n+2", "n+3", "n+4", "n+5"]

colnames = ["Probability"]

probmatrix = np.array([0,0,0,0,0,0,0], dtype=np.float64)

dievalues = [1,2,3,4,5,6]

# (b) Here we run the number of iterations desired and store the values in a table, later broadcasting a division by the number of iterations

for i in range(0, iterations-1):

turnvalue = 0

# (a) The while statement runs a single turn

while turnvalue < holdn:

die = random.sample(dievalues,1)

die = die[0]

if die == 1:

turnvalue = 0

break

else:

turnvalue += np.float64(die)

probmatrix[np.where(probofn == turnvalue)] += np.float64(1)

probmatrix /= np.float64(iterations)

probmatrix = pd.DataFrame(probmatrix, columns = colnames, index = rownames)

print("This is the table for n = ", holdn," and ", iterations, "iterations" )

print(probmatrix)

return(probmatrix)

import pandas as pd

import numpy as np

# we declare the names of our table of hold at "n" scenarios and the probability of results

nrows = ["hold@15","hold@16","hold@17","hold@18","hold@19","hold@20","hold@21","hold@22","hold@23","hold@24","hold@25"]

ncols = ["nzero","n","n+1","n+2", "n+3", "n+4", "n+5"]

colname = ["expectedValue"]

# this "database" table will hold all the probabilities at different hold@n scenarios

database = pd.DataFrame( columns = ncols, index = nrows)

#(e) this loop populates the "database" table

for i in range(0,len(nrows)):

holdn = 15 + i

aux = pigDie(1000000,holdn)

database.iloc[i,:] = list(aux.iloc[:,0])

# this database will be populated with the expected values of the different hold@n scenarios

exValues = pd.DataFrame( columns = colname, index = nrows )

tarray = [0,1,2,3,4,5]

narray = [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]

#this "for" loop broadcasts EACH member of 'narray' into 'tarray' to generate

#the n's -([15,16,17,18,19,20]), then ([16,17,18,19,20,21]) and so on -.

#then each of these vectors is multiplied by their corresponding simulated

#probability in "database", then summed and stored in "exValues"

for m in range(0, len(narray)):

exValues.iloc[m] = np.sum(np.multiply(np.append(0,np.add(narray[m],tarray)), database.iloc[m,:]))

print("This is the expected value tables for each hold@n enunciated")

print(exValues)

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print("This is the expected value tables for each hold@n enunciated")

print(exValues)

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