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maths/sum_of_outcomes_for_rolling_n_sided_dice_k_time.py

@@ -3,87 +3,87 @@
 
 def outcome_of_rolling_n_sided_dice_k_time(n_side: int, k_time: int) -> list:
     """
-     The sum of outcomes for rolling an N-sided dice K times.
-
-     This function returns a list. The last two elements are the 
-     range of probability distribution.
-     The range is: 'k_time' to 'k_time*n_side'
-
-     Other elements contain probabilities for getting a summation 
-     from 'k_time' to 'k_time*n_side'.
-
-     Algorithm Explanation:
-
-     1. Explanation of range:
-     When we are rolling a six-sided dice the range becomes
-     1 to 6.
-     While rolling 5 times range becomes 5 to 30.
-     The sum outcomes become 5 when all rolling finds 1.
-     30 happens when all rolling finds 6.
-     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.
-
-     While rolling 2 dice simultaneously,
-     the sum becomes 2 for two 1 outcomes. But the sum becomes
-     3 for two different outcome combinations (1,2) and (2,1).
-     The probability of getting 2 is 1/6.
-     The probability of getting 3 is 2/6
-
-     Link to rolling two 6-sided dice combinations:
-     https://www.thoughtco.com/
-     probabilities-of-rolling-two-dice-3126559
-     That phenomenon is the same as the convolution. 
-
-     The algorithm can be used in playing games or solving 
-     problems where the sum of multiple dice throwing is needed.
-
-
-     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
-     with the sum. The same sum can come in many combinations.
-     Finding all of those combinations and applying Bernoulli
-     is more computationally extensive.
-     
-     I used that method in my paper to draw the distribution
-     Titled: Uncertainty-aware Decisions in Cloud Computing:
-     Foundations and Future Directions
-     Journal: ACM Computing Surveys (CSUR)
-     link: https://dl.acm.org/doi/abs/10.1145/3447583
-     The PDF version of the paper is available on Google Scholar.
-
-
-     >>> import numpy as np
-     >>> outcome_of_rolling_n_sided_dice_k_time(.2,.5)
-     Traceback (most recent call last):
-         ...
-     ValueError: The function only accepts integer values
-     >>> outcome_of_rolling_n_sided_dice_k_time(-1,5)
-     Traceback (most recent call last):
-         ...
-     ValueError: Side count should be more than 1
-     >>> outcome_of_rolling_n_sided_dice_k_time(3,-2)
-     Traceback (most recent call last):
-         ...
-     ValueError: Roll count should be more than 0
-
-     >>> outcome_of_rolling_n_sided_dice_k_time(2,2)
-     [0.25, 0.5, 0.25, 2, 4]
-     >>> outcome_of_rolling_n_sided_dice_k_time(2,4)
-     [0.0625, 0.25, 0.375, 0.25, 0.0625, 4, 8]
-     >>> outcome_of_rolling_n_sided_dice_k_time(4,2)
-     [0.0625, 0.125, 0.1875, 0.25, 0.1875, 0.125, 0.0625, 2, 8]
+    The sum of outcomes for rolling an N-sided dice K times.
+
+    This function returns a list. The last two elements are the
+    range of probability distribution.
+    The range is: 'k_time' to 'k_time*n_side'
+
+    Other elements contain probabilities for getting a summation
+    from 'k_time' to 'k_time*n_side'.
+
+    Algorithm Explanation:
+
+    1. Explanation of range:
+    When we are rolling a six-sided dice the range becomes
+    1 to 6.
+    While rolling 5 times range becomes 5 to 30.
+    The sum outcomes become 5 when all rolling finds 1.
+    30 happens when all rolling finds 6.
+    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.
+
+    While rolling 2 dice simultaneously,
+    the sum becomes 2 for two 1 outcomes. But the sum becomes
+    3 for two different outcome combinations (1,2) and (2,1).
+    The probability of getting 2 is 1/6.
+    The probability of getting 3 is 2/6
+
+    Link to rolling two 6-sided dice combinations:
+    https://www.thoughtco.com/
+    probabilities-of-rolling-two-dice-3126559
+    That phenomenon is the same as the convolution.
+
+    The algorithm can be used in playing games or solving
+    problems where the sum of multiple dice throwing is needed.
+
+
+    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
+    with the sum. The same sum can come in many combinations.
+    Finding all of those combinations and applying Bernoulli
+    is more computationally extensive.
+
+    I used that method in my paper to draw the distribution
+    Titled: Uncertainty-aware Decisions in Cloud Computing:
+    Foundations and Future Directions
+    Journal: ACM Computing Surveys (CSUR)
+    link: https://dl.acm.org/doi/abs/10.1145/3447583
+    The PDF version of the paper is available on Google Scholar.
+
+
+    >>> import numpy as np
+    >>> outcome_of_rolling_n_sided_dice_k_time(.2,.5)
+    Traceback (most recent call last):
+        ...
+    ValueError: The function only accepts integer values
+    >>> outcome_of_rolling_n_sided_dice_k_time(-1,5)
+    Traceback (most recent call last):
+        ...
+    ValueError: Side count should be more than 1
+    >>> outcome_of_rolling_n_sided_dice_k_time(3,-2)
+    Traceback (most recent call last):
+        ...
+    ValueError: Roll count should be more than 0
+
+    >>> outcome_of_rolling_n_sided_dice_k_time(2,2)
+    [0.25, 0.5, 0.25, 2, 4]
+    >>> outcome_of_rolling_n_sided_dice_k_time(2,4)
+    [0.0625, 0.25, 0.375, 0.25, 0.0625, 4, 8]
+    >>> outcome_of_rolling_n_sided_dice_k_time(4,2)
+    [0.0625, 0.125, 0.1875, 0.25, 0.1875, 0.125, 0.0625, 2, 8]
 
     """
 
@@ -103,10 +103,10 @@ def outcome_of_rolling_n_sided_dice_k_time(n_side: int, k_time: int) -> list:
     while iter1 < k_time:
         prob_dist = np.convolve(prob_dist, dist_step)
         iter1 = iter1 + 1
-        
+
     prob_list = list(prob_dist)
     prob_list.append(k_time)
-    prob_list.append(k_time*n_side)
+    prob_list.append(k_time * n_side)
 
     return prob_list