Itertools to create a list and work out probability

Question

I am trying to work out the probability of 'Susie' winning a match.

Probability of 'Susie' winning a game = 0.837
Probability of 'Bob' winning a game = 0.163

If the first person to win n games wins a match, what is the smallest value of n such that Susie has a better than 0.9 chance of winning the match?

So far I have this code:

import itertools

W = 0.837
L = 0.163
for product in itertools.product(['W','L'], repeat=3): #3=number of games
    print product

Which prints:

('W', 'W', 'W')
('W', 'W', 'L')
('W', 'L', 'W')
('W', 'L', 'L')
('L', 'W', 'W')
('L', 'W', 'L')
('L', 'L', 'W')
('L', 'L', 'L')

I then want to use these results to work out the probability of 'Susie' winning the match overall.

I have worked out this problem on paper, the more games played, the more chance there is of 'Susie' winning the match.

Answer 1

You can use a dictionary for probabilities:

import itertools
import operator

probabilities = {'W':0.837, 'L':0.163}

for product in itertools.product(['W','L'], repeat=3): #3=number of games
    p = reduce(operator.mul,
               [probabilities[p] for p in product])
    print product, ":", p

The reduce function accumulates all elements of a list using function given in the first argument - here we accumulate them by multiplying.

This gives you probabilities of each event sequence. From this you can easily choose which one is "Susie winning a match", and sum the probabilities. One possibility to do this is:

import itertools
import operator

probabilities = {'W':0.837, 'L':0.163}

winProbability = 0
for product in itertools.product(['W','L'], repeat=3): #3=number of games
    p = reduce(operator.mul,
               [probabilities[p] for p in product])

    if product.count('W') > 1: #works only for 3 games
        winProbability += p
        print "Susie wins:", product, "with probability:", p
    else:
        print "Susie looses:", product, "with probability:", p

print "Total probability of Susie winning:", winProbability 

The condition works only for 3 games, but I'm really leaving this one to you - it's easy to generalize this for n games :)