monte carlo simulation python

Question

Я хотел бы моделировать семь игр плей-офф серии бейсбола. Скажем, у меня есть вероятность выигрыша для каждой игры в серии. Я хотел бы знать вероятности для каждого возможного результата серии. т.е. TeamA в 4 играх, TeamB в 4 играх, TeamA в 5 играх и т. д.

Это то, что я придумал и, похоже, работает, но я думаю, что это можно было бы сделать лучше.

winPercGM1 = .5 
winPercGM2 = .56 
winPercGM3 = .47 
winPercGM4 = .55 
winPercGM5 = .59 
winPercGM6 = .59 
winPercGM7 = .38 
winPercs = [winPercGM1, winPercGM2, winPercGM3, winPercGM4, winPercGM5, winPercGM6,  winPercGM7] 

def WinSeries(): 
    teamAwins = 0 
    teamBwins = 0 
    for perc in winPercs: 
     if teamAwins == 4:    
      break    
     elif teamBwins == 4:    
      break    
     elif perc > np.random.random(): 
      teamAwins += 1    
     else: 
      teamBwins += 1    
    return teamAwins, teamBwins 

def RunFun(n): 
teamAWins = [] 
teamBWins = [] 
for i in xrange(n): 
    result = WinSeries() 
    teamAWin = result[0] 
    teamBWin = result[1]   
    teamAWins.append(teamAWin) 
    teamBWins.append(teamBWin)  
return teamAWins, teamBWins 


n = 500000 
results = RunFun(n) 

teamAwinSeries = results[0] 
teamBwinSeries = results[1] 

teamBin4 = teamAwinSeries.count(0)/n 
teamBin5 = teamAwinSeries.count(1)/n 
teamBin6 = teamAwinSeries.count(2)/n 
teamBin7 = teamAwinSeries.count(3)/n 
teamAin4 = teamBwinSeries.count(0)/n 
teamAin5 = teamBwinSeries.count(1)/n 
teamAin6 = teamBwinSeries.count(2)/n 
teamAin7 = teamBwinSeries.count(3)/n 

Answer 1

Это можно легко сделать с numpy (Python 2.7)

import numpy as np 

probs = np.array([.5 ,.56 ,.47 ,.55 ,.59 ,.59 ,.38]) 
nsims = 500000 

chance = np.random.uniform(size=(nsims, 7)) 

teamAWins = (chance > probs[None, :]).astype('i4') 
teamBWins = 1 - teamAWins 

teamAwincount = {} 
teamBwincount = {} 
for ngames in range(4, 8): 
    afilt = teamAWins[:, :ngames].sum(axis=1) == 4 
    bfilt = teamBWins[:, :ngames].sum(axis=1) == 4 

    teamAwincount[ngames] = afilt.sum() 
    teamBwincount[ngames] = bfilt.sum() 

    teamAWins = teamAWins[~afilt] 
    teamBWins = teamBWins[~bfilt] 

teamAwinprops = {k : 1. * count/nsims for k, count in teamAwincount.iteritems()} 
teamBwinprops = {k : 1. * count/nsims for k, count in teamBwincount.iteritems()} 

Выход:

>>> sum(teamAwinprops.values()) + sum(teamBwinprops.values()) 
1.0 
>>> teamAwincount 
{4: 26186, 5: 47062, 6: 59222, 7: 95381} 
>>> teamBwincount 
{4: 36187, 5: 79695, 6: 97802, 7: 58465}