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Second solution in Clear category for Probably Dice by colinmcnicholl
import math
def nCr(n, r):
f = math.factorial
return f(n) // f(r) // f(n - r)
def probability(dice_number, sides, target):
k_max = math.floor((target - dice_number) / sides)
prefix = 1 / (sides ** dice_number)
prob = 0
k = 0
for k in range(k_max + 1):
try:
res = ((-1)**k * nCr(dice_number, k)
* nCr(target - sides * k - 1, dice_number - 1))
prob += res
except ValueError:
print("factorial not defined for negative values")
return round(prefix * prob, 4)
if __name__ == '__main__':
#These are only used for self-checking and are not necessary for auto-testing
def almost_equal(checked, correct, significant_digits=4):
precision = 0.1 ** significant_digits
return correct - precision < checked < correct + precision
assert(almost_equal(probability(2, 6, 3), 0.0556)), "Basic example"
assert(almost_equal(probability(2, 6, 4), 0.0833)), "More points"
assert(almost_equal(probability(2, 6, 7), 0.1667)), "Maximum for two 6-sided dice"
assert(almost_equal(probability(2, 3, 5), 0.2222)), "Small dice"
assert(almost_equal(probability(2, 3, 7), 0.0000)), "Never!"
assert(almost_equal(probability(3, 6, 7), 0.0694)), "Three dice"
assert(almost_equal(probability(10, 10, 50), 0.0375)), "Many dice, many sides"
Feb. 7, 2019
