mc_hothand.py

from random import random
from collections import Counter

def randbits(n, p):
    i = 0
    while i<n:
        yield random() < p
        i += 1

def mc_hothand(trials, p):
    d={1:{0:0,1:0},0:{0:0,1:0}}
    lastbit=0
    for nextbit in randbits(trials, p):
        d[lastbit][nextbit] += 1
        lastbit = nextbit
    if d[1][0]+d[1][1]:
        return float(d[1][1])/float(d[1][0]+d[1][1])
    return 0.0 # short runs will sometimes yield a division by zero.
    
def hothand_asymptote():
    return [sum([mc_hothand(n,0.5) for i in xrange(1000)])/1000.0 for n in xrange(4,100)]
    
def hothand(p=0.5, trials=3):
    lastbit = random() < p
    wins = 0
    for i in xrange(trials):
        nextbit = random() < p
        if nextbit != lastbit:
            wins += 1
        lastbit = nextbit
    return wins

def test_hothand(p,n):
    a = Counter([hothand(p,n) for i in xrange(1000)])
    return (a[0]*-3)+(a[1]*-1)+a[2]+(3*a[3])

Coded when I read the intro to http://www.wsj.com/articles/the-hot-hand-debate-gets-flipped-on-its-head-1443465711