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dechicom Sep 6th, 2018 55 Never
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  1. #! /usr/bin/python
  2. # -*- coding: utf-8 -*-
  3.  
  4. import copy as CO
  5. import bisect as BI
  6. import math as MA
  7. import matplotlib.pyplot as PLT
  8. '''
  9. dice game
  10. copyright 2018 Marc Dechico
  11. this one add matplotlib for visualizing the distri
  12. '''
  13.  
  14. class CountingValueError(ValueError):
  15.     pass
  16.  
  17. def arangements_ie( n, l ):
  18.     """ arrangements_ie ( n,( k1, k2, k3,...) )
  19.    Return the number of possible arrangements of n elements
  20.    with k1, k2,.... elements being indistinguishable.
  21.    """
  22.     a= MA.factorial( n )
  23.     K=0
  24.     for k in l:
  25.         K += k
  26.         if K > n:
  27.             raise CountingValueError ("Can't have k indistinguishable objects taken from n objects if k > n")
  28.         a= a / MA.factorial( k )
  29.     return a
  30. def result(result):
  31.     print "gain\t\tresult"
  32.     for r in result:
  33.         pass
  34.  
  35.  
  36. def storegain(trialgain,trialproba):
  37.     #print "### trial gain:",trialgain,"|proba:",trialproba*100,"%"
  38.     global tp
  39.     global gains
  40.     gains[0].append(trialgain)
  41.     gains[1].append(trialproba)
  42.     tp+=trialproba
  43.     i = BI.bisect_right(totwin,trialgain) -1
  44.     totproba [i] += trialproba
  45.  
  46. def trial(t):
  47.     global g_no
  48.     global g_N
  49.     trialproba = 0.0
  50.     trialgain = 0.0
  51.     for i  in range (g_no):
  52.         k=t[i]
  53.         if k!=0:
  54.             p = gamewin[i][0]
  55.             gain = gamewin[i][1]
  56.             trialgain += gain * k
  57.             proba=MA.pow(p,k)
  58.             if trialproba == 0:
  59.                 trialproba= proba
  60.             else:
  61.                trialproba*= proba
  62.             #print "-- outcome:",i,"|k:",k,"|p:",p,"|totgain:", gain * k
  63.     trialproba*=arangements_ie(g_N,t)
  64.                
  65.     storegain(trialgain, trialproba)
  66.  
  67.  
  68. def callback ( t):
  69.  
  70.     #print t
  71.     #print "."
  72.     global cpt
  73.     cpt+=1
  74.     trial(t)
  75.  
  76. def rec_gen ( co , t ,s ):
  77.     '''
  78.     N: number of experiment still  available
  79.     co: current outcome (position in t )
  80.     t : list of occurence number for each outcome
  81.    '''
  82.    
  83.     for i in xrange ( 0,g_N-s+1 ):
  84.         t[ co ] = i
  85.         ss=s+i
  86.         if ss == g_N :
  87.              callback ( t )
  88.              continue
  89.  
  90.         if  co > 0 :
  91.             t2 = CO.copy ( t )
  92.             rec_gen ( co-1 , t2,ss )
  93.  
  94.     del(t)
  95.     return
  96.  
  97. def gen ( no , N ):
  98.     '''
  99.    no: number outcome  
  100.    N : Number of subsequent experiment (trial of N experiment)
  101.    t : contain the number of occurence for each outcomes
  102.    '''
  103.     global g_no  # number of outcome
  104.     g_no = no
  105.     global g_N  # number of experiment
  106.     g_N = N
  107.     print "===", g_no,g_N
  108.     t = [ 0 ] * no
  109.     rec_gen ( no-1 , t,0 )
  110.  
  111. def plot1(totwin,totproba):
  112.  
  113.     PLT.title("distri")
  114.     PLT.xlabel("win")
  115.     PLT.ylabel("proba")  
  116.    
  117.     PLT.plot(totwin,totproba)
  118.  
  119.     PLT.grid(True)
  120.     PLT.show()
  121.  
  122.  
  123.  
  124.  
  125.  
  126.    
  127. if __name__ == "__main__":
  128.  
  129.     # number of expiriment (how many time I throw the dices)
  130.     N = 100
  131.  
  132.     #list of outcomes  (proba, gain)
  133.     gamewin = [ [1.0/6, 200], [2.0/6, 10], [3.0/6, 0] ]
  134.  
  135.     # game expectation E(X)
  136.     gameexpect= 0
  137.     for g in gamewin:
  138.         gameexpect += g[ 0 ] * g[ 1 ]
  139.     print "Game expectation = ", gameexpect
  140.     # game variance var(X)=E(X²)-E²(X)
  141.     gamevar = 0
  142.     for g in gamewin:
  143.         gamevar +=  MA.pow( g[ 1 ], 2 ) * g[ 0 ]
  144.     gamevar -= MA.pow( gameexpect , 2 )
  145.     print "Game variance = ", gamevar
  146.     print "Game Standard Error =", MA.sqrt(gamevar)
  147.  
  148.     # maxwin after N experiments
  149.     maxwin = 200 * N
  150.    
  151.     print "Maxwin after N throws:", maxwin
  152.     print "Expectation after  N throws:", gameexpect * N
  153.  
  154.     # to have the total gains  we get after N experiments  well distributed in
  155.     #  the result  list [(gains,proba), .... ]  
  156.     totwin = range( 0, int(maxwin), int(maxwin/500))
  157.     totproba = [0.0] * len( totwin )
  158.  
  159.     cpt = 0
  160.     tp=0
  161.     gains=[[],[]]
  162.  
  163.     gen( len(gamewin),N )
  164.     print "cpt",cpt,"tp",tp
  165.     result = zip( totproba, totwin )
  166.  
  167.     # verifying that the calculus are corrects:
  168.     # total probability for all final gains = 1
  169.     print "verify the sum of all probabilty = 1:",sum(totproba)
  170.  
  171.     # game expectation E(Xn) after N throws
  172.     totgameexpect= 0
  173.     for g in result:
  174.         totgameexpect += g[ 0 ] * g[ 1 ]
  175.     print "Game expectation after N throws= ", totgameexpect
  176.     # game variance after N throws var(Xn)=E(Xn²)-E²(Xn)
  177.     totgamevar = 0
  178.     for g in result:
  179.         totgamevar +=  MA.pow( g[ 1 ], 2 ) * g[ 0 ]
  180.     totgamevar -= MA.pow( totgameexpect , 2 )
  181.     print "Game variance N throws = ", totgamevar
  182.     print "Game Standard Error N throws =", MA.sqrt(totgamevar)
  183.  
  184.                      
  185.     #plot1( totwin, totproba )
  186.     plot1( gains[0], gains[1] )
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