playing_cards.py

from random import random
from time import time

from multiprocessing import Pool
import matplotlib.pyplot as plt

def _avg(results):
    return sum(results) / float(len(results))

def _range(results):
    return (min(results), max(results))

def _median(results):
    n = len(results)
    
    if not n % 2:
        return sum(sorted(results)[n//2-1:n//2+1])/float(2)

    return sorted(results)[n//2]

def test(_,cards=52):
    pulls = 0
    found = 0
    odds_to_discover = 1 - found / float(cards)
    while odds_to_discover:
        if odds_to_discover >= random():
            found += 1
            odds_to_discover = 1 - found / float(cards)
        pulls += 1
    return pulls

def threaded_tests(num_threads=4, num_tests=1000):
    results = list()
    pool = Pool(num_threads)

    results = pool.map(
        test,
        xrange(num_tests))

    pool.close();
    pool.join();

    return results

def main():
    num_tests = 10000000
    num_threads = 12

    start = time()
    results = threaded_tests(num_threads=num_threads,num_tests=num_tests)
    end = time() - start

    avg = _avg(results)
    median = _median(results)
    rnge = _range(results)

    print "Num. of trials: %s" % num_tests
    print "Avg. : %s" % avg
    print "Median : %s" % median
    print "Range : [%s - %s]" % rnge
    print "Time (in sec): %s" % end

    plt.hist(results,bins=(rnge[1]-rnge[0]))
    plt.xlabel("Days to collect 52 cards")
    plt.ylabel("Number of tests")
    plt.show()

if __name__ == '__main__':
    main()