Created
December 11, 2016 13:58
-
-
Save weatherspud/f8755d176a68e177e84e15bd2f862c06 to your computer and use it in GitHub Desktop.
approximate a fireball roll with two dice
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
#!/usr/bin/env python3.5 | |
import math | |
die = 6 | |
mean = sum(range(1, die + 1)) / die | |
variance = sum([i * i for i in range(1, die + 1)]) / die - mean ** 2 | |
max_roll = 30 | |
for n in range(1, max_roll + 1): | |
best_diff = None | |
best_b = None | |
for b in range(0, math.ceil(math.sqrt(n - 1)) + 2): | |
if n % 2 == b % 2: | |
continue | |
diff = abs(b**2 + 1 - n) | |
actual_sd = math.sqrt(n * variance) | |
approx_sd = math.sqrt(b * b * variance + variance) | |
# print('DEBUG n: {} b: {}: diff: {}'.format(n, b, diff)) | |
if best_diff is None or diff < best_diff: | |
best_b = b | |
best_diff = diff | |
best_actual_sd = actual_sd | |
best_approx_sd = approx_sd | |
a = int(mean * (n - best_b - 1)) | |
sd_change = best_approx_sd - best_actual_sd | |
print(u'{}d6: {} + d6 × {} + d6'.format(n, | |
a, | |
best_b)) |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment