from argparse import ArgumentParser
import scipy as sp
def fargorate_game_win_probability(rating_a, rating_b):
return 1 / (1 + 2**((rating_b - rating_a)/100))
def race_odds_cdf(n: int, m: int, p: float) -> float:
'''
Args:
n (int): number of successes needed for player A
m (int): number of successes needed for player B
p (float): probability of player A succeeding in a single trial
'''
return sp.stats.nbinom.cdf(k=m, n=n, p=p, loc=1)
def race_odds_summed_pmf(n: int, m: int, p: float) -> float:
'''
Args:
n (int): number of successes needed for player A
m (int): number of successes needed for player B
p (float): probability of player A succeeding in a single trial
'''
return sum(sp.stats.nbinom.pmf(k=i, n=n, p=p) for i in range(m))
def main():
argument_parser = ArgumentParser()
argument_parser.add_argument('--games_a', type=int, required=True, help="number of games A needs to win")
argument_parser.add_argument('--games_b', type=int, required=True, help="number of games B needs to win")
argument_parser.add_argument('--rating_a', type=float, default=0.0, help="Player A's rating")
argument_parser.add_argument('--rating_b', type=float, default=0.0, help="Player B's rating")
args = argument_parser.parse_args()
game_odds = fargorate_game_win_probability(args.rating_a, args.rating_b)
print(f"game_odds:{game_odds:.5f}")
race_odds = race_odds_cdf(args.games_a, args.games_b, game_odds)
print(f"race_odds:{race_odds:.5f}")
race_odds2 = race_odds_summed_pmf(args.games_a, args.games_b, game_odds)
print(f"race_odds2:{race_odds2:.5f}")
if __name__ == '__main__':
main()
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