import random
import math


def game(first):
    first_wins = 0
    for i in range(first):
        if random.random() >= 0.5:
            first_wins += 1

    first_wins *= 2

    second = 2*first
    second_wins = 0
    for i in range(second):
        if random.random() >= 0.5:
            second_wins += 1

    if first_wins == second_wins:
        return 0
    elif first_wins > second_wins:
        return 1
    return 2


def main():
    n = 10
    iterations = 100000
    results = [0, 0, 0]
    for i in range(iterations):
        results[game(n)] += 1

    print("Simulacija")
    print(f"Nerijeseno: {results[0]/iterations}")
    print(f"Prvi: {results[1]/iterations}")
    print(f"Drugi: {results[1]/iterations}")
    print()

    sum = 0
    for i in range(0, n+1):
        sum += math.comb(n, i) * math.comb(2*n, 2*i)
    draw = sum / 2**(3*n)
    win = (1 - draw) / 2
    print("Izracun")
    print(f"Nerijeseno: {draw}")
    print(f"Prvi: {win}")
    print(f"Drugi: {win}")


if __name__ == "__main__":
    main()