Hearthstone Legendary

hs_legendary.py

import random

n_runs = 100000

stars_needed_from_25_to_legendary = 10+15+20+25+25
stars_above_which_no_bonus_is_awarded = stars_needed_from_25_to_legendary-25
max_games = 20000

def stars_to_rank(stars):
    ranks_gained = 0
    if stars <= 10:
        ranks_gained = stars / 2
    elif stars <= 25:
        ranks_gained = 5 + (stars-10) / 3
    elif stars <= 45:
        ranks_gained = 10 + (stars-25) / 4
    else:
        ranks_gained = 15 + (stars-45) / 5
    return 25 - ranks_gained

for win_rate in range(100,49,-1):
    win_rate = win_rate / 100.0
    n_legendary_runs = 0
    n_total_games = 0
    n_total_max_stars = 0
    for runs in range(n_runs):
        legendary = False
        games_played = 0
        won_last_game = False
        won_second_last_game = False
        stars = 0
        max_stars = 0
        while not legendary and games_played < max_games:
            win = random.random() < win_rate
            if win:
                if won_last_game and won_second_last_game and stars < stars_above_which_no_bonus_is_awarded:
                    stars += 2
                else:
                    stars += 1
            else:
                stars = max(0, stars - 1)
            max_stars = max(stars, max_stars)
            legendary = stars >= stars_needed_from_25_to_legendary
            won_second_last_game = won_last_game
            won_last_game = win
            games_played += 1
#        print ("Win rate: {}, Games played: {}, stars: {}".format(win_rate, games_played, stars))
        n_legendary_runs += legendary
        n_total_games += games_played
        n_total_max_stars += max_stars
    print ("Win rate: {:.0%}, Most Stars: {}, Higest Rank: {}, Legendary chance: {}, Games played: {}".format(win_rate, n_total_max_stars / n_runs, stars_to_rank(n_total_max_stars / n_runs), float(n_legendary_runs) / n_runs, n_total_games / n_runs))

hs_legendary_output.txt

Win rate: 100%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 61
Win rate: 99%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 62
Win rate: 98%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 63
Win rate: 97%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 65
Win rate: 96%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 66
Win rate: 95%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 68
Win rate: 94%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 70
Win rate: 93%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 71
Win rate: 92%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 73
Win rate: 91%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 75
Win rate: 90%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 77
Win rate: 89%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 79
Win rate: 88%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 82
Win rate: 87%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 84
Win rate: 86%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 87
Win rate: 85%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 89
Win rate: 84%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 92
Win rate: 83%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 95
Win rate: 82%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 98
Win rate: 81%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 101
Win rate: 80%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 105
Win rate: 79%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 108
Win rate: 78%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 112
Win rate: 77%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 117
Win rate: 76%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 121
Win rate: 75%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 126
Win rate: 74%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 131
Win rate: 73%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 137
Win rate: 72%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 142
Win rate: 71%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 149
Win rate: 70%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 156
Win rate: 69%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 164
Win rate: 68%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 172
Win rate: 67%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 182
Win rate: 66%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 192
Win rate: 65%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 203
Win rate: 64%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 216
Win rate: 63%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 231
Win rate: 62%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 247
Win rate: 61%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 266
Win rate: 60%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 287
Win rate: 59%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 313
Win rate: 58%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 344
Win rate: 57%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 379
Win rate: 56%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 426
Win rate: 55%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 483
Win rate: 54%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 560
Win rate: 53%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 663
Win rate: 52%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 813
Win rate: 51%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 1048
Win rate: 50%, Most Stars: 95, Higest Rank: 0, Legendary chance: 1.0, Games played: 1440