Experimental mathematics for November 2011 London MathsJam

envelope_choice.py

#!/usr/bin/env python
"""This piece of experimental mathematics came out of a discussion at the November 2011
London MathsJam sparked by a Google Plus post from Randall Munroe https://plus.google.com/111588569124648292310/posts/dv9Fi45h91T

Code by @axiomsofchoice with help from other MathsJam attendees, including @Samuel_Hansen
"""

import random

n_trials = 1000000

def genpair(n,val_i):
    choice = random.gauss(mu=0.0, sigma=1.0)
    if choice > 0:
        return (n,2*n)
    else:
        return (n,n/2)

def random_tuple_item(first,second):
    choice = random.gauss(mu=0.0, sigma=1.0)
    if choice > 0:
        return first
    else:
        return second

first_car_val = 10

examples = [genpair(first_car_val,i) for i in range(n_trials)]

#card_sum = reduce(lambda x, y: x+y, [for examples)


#print "Example: ", examples

chosen_cards = [random_tuple_item(i,j) for i,j in examples]

#print "Card choices: ", chosen_cards

print "Sum of example second card for %s trials: %s" % (n_trials, reduce(lambda x, y: x+y, chosen_cards) / n_trials)