odds.py

from random import choice
from decimal import Decimal

stats = [0] * 100

def advance(n, f):
    return n * (1+f)


def backoff(n, f):
    return n * (1-f)


def solve(n):
    return Decimal((1 - n) / n)


def play():
    n = Decimal(0.00000001)
    success = False
    for i in range(100):
        f = solve(n)
        n = choice((advance, backoff))(n, f)
        if n == 1 and not success:
            success = True
            stats[i] += 1
            # print(f"got there in {i} turns")
    # print(f"game ended, value is {n}")
    return n == 1


def check_odds(n):
    wins = 0
    losses = 0
    for i in range(n):
        if play():
            wins += 1
        else:
            losses += 1
    print(f"observed odds over {n} tries {wins}/{n} = {wins/n}")


def display_stats():
    norm = max(stats)
    scale = 100 / norm
    print(stats)
    for i, s in enumerate(stats):
        print(f"{i:2d} {'=' * int(s * scale)}")

if __name__ == '__main__':
    check_odds(100_000)
    display_stats()