experiment generating coin flips to test kelly criterion

kellycriterion.py

import decimal
import math
import random

from matplotlib import pyplot as plt


def bet(p):
    return random.random() < p


def game(r, p):
    """
    One round of coin flip bet

    r: the amount of the pot that will be wagered on each round
    p: the probability that a coin flip wins, from 0 to 1

    returns: the value of the pot at the end of the game
    """

    # starting value of the pot, this is arbitrary
    pot = 1.0

    i = 0

    while pot > 0.1 and i < 100:
        wager = r * pot

        if bet(p):
            pot += wager / p
        else:
            pot -= wager

        pot = max(pot, 0)
        i += 1
    return pot


def kelly(p, r, num_trials):
    wins = 0
    losses = 0

    pots = []

    for x in range(num_trials):
        # Play one game
        pot = game(r, p)
        # Record logarithm of the result
        pots.append(math.log(pot))

    return sum(pots)

p = 0.6

x_values = list(arange(0, 1, step=0.01))
y_values = []

for r in x_values:
    y_values.append( (r, kelly(p, r, 1000)) )

plt.plot(x_values, y_values)
plt.show()

# optimal value of 'r' (the amount of money you should wager for each coin flip at p=0.6)
# should be around 0.2, or 20%