Add Monte Carlo dice simulation algorithm (TheAlgorithms#1759)

* Implement basic dice simulation

* Add tests to throw_dice

* Fix comment

* Add type hints

* Add additional comments

* Update monte_carlo_dice.py

Co-authored-by: Christian Clauss <cclauss@me.com>

Author: naviji

maths/monte_carlo_dice.py

@@ -0,0 +1,45 @@
+import random
+from typing import List
+
+class Dice:
+    NUM_SIDES = 6
+
+    def __init__(self):
+        """ Initialize a six sided dice """
+        self.sides = list(range(1, Dice.NUM_SIDES + 1))
+
+    def roll(self):
+        return random.choice(self.sides)
+
+    def _str_(self):
+        return "Fair Dice"
+
+
+def throw_dice(num_throws: int, num_dice: int=2) -> List[float]:
+    """
+    Return probability list of all possible sums when throwing dice.
+
+    >>> random.seed(0)
+    >>> throw_dice(10, 1)
+    [10.0, 0.0, 30.0, 50.0, 10.0, 0.0]
+    >>> throw_dice(100, 1)
+    [19.0, 17.0, 17.0, 11.0, 23.0, 13.0]
+    >>> throw_dice(1000, 1)
+    [18.8, 15.5, 16.3, 17.6, 14.2, 17.6]
+    >>> throw_dice(10000, 1)
+    [16.35, 16.89, 16.93, 16.6, 16.52, 16.71]
+    >>> throw_dice(10000, 2)
+    [2.74, 5.6, 7.99, 11.26, 13.92, 16.7, 14.44, 10.63, 8.05, 5.92, 2.75]
+    """
+    dices = [Dice() for i in range(num_dice)]
+    count_of_sum = [0] * (len(dices) * Dice.NUM_SIDES + 1)
+    for i in range(num_throws):
+        count_of_sum[sum([dice.roll() for dice in dices])] += 1
+    probability = [round((count * 100) / num_throws, 2) for count in count_of_sum]
+    return probability[num_dice:]  # remove probability of sums that never appear
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()