from random import random

class Horse(object):
    def __init__(self, name, pos, frate):
        self.name = name
        self.pos = pos
        self.frate = frate

    def __str__(self):
        return self.name

def run_race():
    stable = []
    for i in range(20):
        x = Horse(str(i + 1), 0, .52 + (i * .02))
        stable.append(x)
    winners = []
    while True:
        for horse in stable:
            x = random()
            if x <= horse.frate:
                horse.pos += 1
            else:
                horse.pos -= 1
            if horse.pos == 200:
                winners.append(horse.name)
        if len(winners) > 0:
            break
    return winners

def run_a_lot(times):
    races = {}
    odds = []
    for i in range(times):
        y = run_race()
        for winner in y:
            try:
                races[winner] += 1
            except KeyError:
                races[winner] = 1
    times = float(times)
    for key in races:
        odds.append((key, races[key] / times))
    return odds

print run_a_lot(500000)
print run_a_lot(500000)
print run_a_lot(1000000)