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maths/sum_of_outcomes_for_rolling_n_sided_dice_k_time.py

@@ -3,15 +3,15 @@
 def outcome_of_rolling_n_sided_dice_k_time(n_side: int, k_time: int) -> list:
     """
    Sum of outcomes for rolling an N-sided dice K times.
-   
+
    This function returns a list. The first element is an array.
    That array contains indexes.
    The second element is another array.
    That array contains probabilities for getting each index values
    as the sum of obtained side values.
 
     Algorithm Explanation:
-    
+
     1. Explanation of range:
     When we are rolling a six-sided dice the range becomes
     1 to 6.
@@ -21,28 +21,28 @@ def outcome_of_rolling_n_sided_dice_k_time(n_side: int, k_time: int) -> list:
     1 is the minimum and 6 is the maximum of side values
     for a 6 sided dice. Therefore, the range is 5 to 30.
     Therefore, the range is k to n*k.
-    
+
     2. Explanation of probability distribution:
     Say we are rolling a six-sided dice 2 times.
     for 0 roll, the outcome is 0 with probability 1.
     For the first roll, the outcome is 1 to 6 equally distributed.
-    
+
     For the second roll, each previous outcome (1-6) will face
     an addition from the second rolling (1-6).
     If the first outcome is (known) 3, then the probability of
     getting each of 4 to 9 will be 1/6.
-    
+
     The sum becomes 2 for two 1 outcomes. But the sum becomes
     3 for two outcomes (1,2) and (2,1).
-    
+
     Link:
     https://www.thoughtco.com/
     probabilities-of-rolling-two-dice-3126559
-    
+
     That phenomenon is the same as the convolution. However, the
     index position is different. Therefore, we adjust the index.
-    
-    
+
+
     NB: a) We are assuming a fair dice
     b) Bernoulli's theory works with getting the probability of
     exactly 3 sixes while rolling 5 times. It does not work directly
@@ -51,7 +51,7 @@ def outcome_of_rolling_n_sided_dice_k_time(n_side: int, k_time: int) -> list:
     is more computationally extensive.
     c) The algorithm can be used in playing games where the sum of
     multiple dice throwing is needed.
-    
+
     I used that method in my paper to draw the distribution
     Titled: Uncertainty-aware Decisions in Cloud Computing:
     Foundations and Future Directions
@@ -78,28 +78,28 @@ def outcome_of_rolling_n_sided_dice_k_time(n_side: int, k_time: int) -> list:
     ([2, 3, 4], [0.25, 0.5, 0.25])
     >>> outcome_of_rolling_n_sided_dice_k_time(2,4)
     ([4, 5, 6, 7, 8], [0.0625, 0.25, 0.375, 0.25, 0.0625])
-    
+
     """
-    
+
     if n_side != int(n_side) or k_time != int(k_time):
         raise ValueError("The function only accepts integer values")
     if n_side < 2:
         raise ValueError("Side count should be more than 1")
     if  k_time < 1:
         raise ValueError("Roll count should be more than 0")
     if k_time > 100 or n_side > 100:
-        raise ValueError("Limited to 100 sides or rolling to 
+        raise ValueError("Limited to 100 sides or rolling to
         avoid memory issues")
-        
+
     probability_distribution = 1
     distribution_step = np.ones(n_side)/n_side
-    
+
     iter1 = 0
     while iter1 < k_time:
         probability_distribution =
         np.convolve(probability_distribution, distribution_step)
         iter1 = iter1+1
-    
+
     index = list(range(k_time,k_time*n_side+1))
     return index, list(probability_distribution)