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First solution in Uncategorized category for Probably Dice by Rounin
probs = dict()
def probability(dice_number, sides, target):
if str([dice_number, sides, target]) in probs:
return probs[str([dice_number, sides, target])]
elif target == 0 and dice_number == 0:
return 1
elif target == 0 and dice_number == 0:
return 0
elif target > (sides*dice_number):
return 0
odds = 0
for roll in range(1, min(target, sides)+1):
odds += probability(dice_number-1, sides, target-roll)
probs[str([dice_number, sides, target])] = odds/sides
return odds/sides
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"
July 29, 2017