Markov chain win rate model

sln.py

#!/usr/bin/env python3

class markov_node:
    def __init__(self, name, outcomes):
        self.name = name
        self.probability = 0.0
        self.incoming_probability = 0.0
        self.outcomes = outcomes
    def push(self):
        for (probability, node) in self.outcomes:
            node.incoming_probability += self.probability * probability
    def collect(self):
        self.probability = self.incoming_probability
        self.incoming_probability = 0.0
    def __str__(self):
        return "%s %.2f" % (self.name, self.probability)

def games_until_streak_expected(win_rate, streak_length):
    loss_node = markov_node("Loss", [])
    success_node = markov_node("%d wins" % streak_length, [])
    success_node.outcomes = [(1.0, success_node)]
    streak_nodes = [success_node]
    for i in range(1, streak_length):
        name = "%d wins" % (streak_length - i)
        new_node = markov_node(name, [(win_rate, streak_nodes[-1]), (1 - win_rate, loss_node)])
        streak_nodes.append(new_node)
    loss_node.probability = 1.0
    loss_node.outcomes = [(win_rate, streak_nodes[-1]), (1 - win_rate, loss_node)]
    streak_nodes.append(loss_node)
    games = 0
    while success_node.probability < 0.5:
        games += 1
        for node in streak_nodes:
            node.push()
        for node in streak_nodes:
            node.collect()
    return games

def run_trial(win_rate, streak_length):
    games = games_until_streak_expected(win_rate, streak_length)
    print("It takes %d games at %s win rate to get a %d game win streak" % (games, "{:.0%}".format(win_rate), streak_length))

if __name__ == '__main__':
    """
    It takes 22715 games at 50% win rate to get a 14 game win streak
    It takes 14637 games at 52% win rate to get a 14 game win streak
    """
    run_trial(.5, 14)
    run_trial(45.0/87, 14)