Calculate star gaining rate based on the deck win rate

hearthstone.py

# WR 45.34% is enough to keep your ground.
# WR 50% gains 0.125 stars per battle on average.


def get_streak_points(num_wins):
    if num_wins < 3:
        return num_wins
    return num_wins * 2 - 2


def get_point_rate(win_rate):
    if win_rate == 0:
        return -1
    if win_rate == 1:
        return 2
    assert 0 < win_rate < 1
    lose_streak_len = 0
    lose_streak_points = 0
    win_streak_len = 0
    win_streak_points = 0
    avg_len = 0

    probability = 1  # To move to next step.
    while probability >= 0.0001:
        lose_streak_len += 1
        lose_streak_points += probability * win_rate * get_streak_points(
            -lose_streak_len
        )
        probability *= 1 - win_rate
    else:
        lose_streak_points += probability * get_streak_points(
            -(lose_streak_len + 1)
        )

    probability = 1  # To move to next step.
    while probability >= 0.0001:
        win_streak_len += 1
        win_streak_points += probability * (1 - win_rate) * get_streak_points(
            win_streak_len
        )
        avg_len += probability * (1 - win_rate) * win_streak_len
        probability *= win_rate
    else:
        win_streak_points += probability * get_streak_points(
            win_streak_len + 1
        )
        avg_len += probability * (win_streak_len + 1)

    point_rate = (win_streak_points + lose_streak_points) / (
        avg_len - lose_streak_points
    )
    print(
        f'Avg lose streak {-lose_streak_points:.3f}'
        f' gives {lose_streak_points:.3f} points.'
        f'\nAvg win streak {avg_len:.3f} gives {win_streak_points:.3f} points.'
        f'\nTotal {win_streak_points + lose_streak_points:.3f} points'
        f' for {avg_len - lose_streak_points:.3f} games'
        f', or {point_rate:.3f} points per game.'
    )
    return point_rate