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February 24, 2025 12:37
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| import itertools | |
| NDICES = 8 | |
| def value(final_cfg, threshold=21): | |
| v = sum([(i + 1) * n for (i, n) in enumerate(final_cfg)]) | |
| # At least one worm. | |
| if final_cfg[5] > 0: | |
| return int(v >= threshold) | |
| else: | |
| return 0.0 | |
| draws = [] | |
| for ndices in range(NDICES + 1): | |
| ndraws = 6 ** ndices | |
| _draws = {} | |
| for draw in itertools.product(range(6), repeat=ndices): | |
| cnts = [0] * 6 | |
| for d in draw: | |
| cnts[d] += 1 | |
| cnts = tuple(cnts) | |
| _draws[cnts] = _draws.get(cnts, 0) + 1 | |
| draws.append(_draws) | |
| print(draws[0]) | |
| print(draws[1]) | |
| for d in draws: | |
| print(sum(d.values())) | |
| THRESHOLDS = [21] | |
| for threshold in THRESHOLDS: | |
| cache = {} | |
| def dp(cfg): | |
| key = tuple(cfg) | |
| if key in cache: | |
| return cache[key] | |
| # Stop now | |
| res = value(cfg, threshold=threshold) | |
| dice_left = NDICES - sum(cfg) | |
| can_continue = dice_left > 0 and sum([int(c > 0) for c in cfg]) < 6 | |
| if can_continue: | |
| exp = 0.0 | |
| ndraws = 0 | |
| for (draw, draw_cnt) in draws[dice_left].items(): | |
| # select | |
| tmp = 0 | |
| for picked_value in range(6): | |
| # Cannot pick a value that was already picked. | |
| if cfg[picked_value] > 0 or draw[picked_value] == 0: | |
| continue | |
| cfg[picked_value] += draw[picked_value] | |
| _dp = dp(cfg) | |
| tmp = max(tmp, _dp) | |
| cfg[picked_value] -= draw[picked_value] | |
| exp += draw_cnt * tmp | |
| ndraws += draw_cnt | |
| exp /= ndraws | |
| res = max(res, exp) | |
| cache[key] = res | |
| return res | |
| print(threshold, dp([0] * 6)) | |
| # Starting from 1 dice showing a 6 | |
| print(dp([0, 0, 0, 0, 0, 1])) | |
| # Starting from 2 dices showing a 6 | |
| print(dp([0, 0, 0, 0, 0, 2])) | |
| # Starting from 1 dice showing a 5 | |
| print(dp([0, 0, 0, 0, 1, 0])) | |
| print(dp([0, 0, 0, 0, 2, 0])) | |
| print(dp([0, 0, 0, 0, 3, 0])) | |
| print(dp([0, 0, 0, 1, 0, 0])) | |
| print(dp([0, 0, 0, 2, 0, 0])) | |
| print(dp([0, 0, 0, 3, 0, 0])) | |
| print(dp([0, 0, 0, 4, 0, 0])) |
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