An integer. Argument, which led to this returned value, is shortening code a little as in case of checking values which can be returned from this method.

If there has to be definietely any type to be returned, selected by user, I will have to massively rewrite the code of this method, what can one day lead to unpredictable errors.

This method was one of my hardest project to compose. Greatest solution wasn't really easy to find, until "you are good in making a pseudocode". This method opens unseen today vision to probability in code. It exists since my invention, class Tense08Games, to put secrets inside. This invention has been discontinued, but new class Games inside module tense.extensions is planned in further versions of Tense. This method uses both reckon() and abroad() functions, instead of traditional duo range() and len().

Probability is not that seen in real life, still provides a good topic. Sometimes we want to know, when a specific moment will occur, not even knowing when. In games you will see chances of dropping specific items, which are often divided into rarities: common, uncommon, rare, epic, legendary, mythic. These are sorted in order from the most to least probable to drop.

But moving back to method Tense.probability(), it is in my opinion fun method. Basic usage would concern dice roll:

.probability(1, 2, 3, 4, 5, 6)
which is equivalent to random.randint(1, 6) and random.randrange(6) + 1. But what, if we went further, and do the same, but with coin flip? According to the article from Wikipedia, and also video from Reigarw Comparisons Probability Comparison: Rarest Things in the Universe, coin may also land on side, but it is incredibly rare event: it may happen with probability 1 to 6000! So the code below excludes this part:

import random
random.choice((heads, tails))
This will be more probable to allow coin land on side, but omitting really low change of its happening:

random.choice((heads, tails, side))
But class method Tense.probability() solves this issue:

.probability((0, 2), (1, 5999), (2, 5999))
There value 0 equals land on side, other 2 (1 and 2) equal heads and tails. Now a little explanation there: do you see second items in every tuple? Code sums them! That means denominator in probability function in math will be equal: 2 + 5999 + 5999 = 12000. So since we know its denominator, we can easily find probability of dropping every number included as first items in every tuple: value 0 will have 2/12000 (that's right, it is 1/6000!) chance of dropping, meanwhile other 2: 5999/12000 (close to 1/2, 0.49991666666666...). In percents: both heads and tails have chance equally 49.99%, while for side it is extremely low - 0.016%!
Other way to do this is hidden inside optional parameter length, also replacing tuple with other sequences:

.probability({0, 2}, 1, 2, length12000) set
.probability({0: 2}, 1, 2, length12000) dict
.probability([0, 2], 1, 2, length12000) list
This code will suprisingly give 6 more than mere dice roll:

.probability(1, 2, 3, 4, 5, (6, 100))
Denominator there equals 105. If mere integers are provided (not sequences), length is added by 1. 6 will by then have 100/105 (20/21, 95.24%) chance of dropping, meanwhile the rest have 1/105 (0.95%) each.

Since 0.3.26b3 parameter length value can be only in range [1, sys.maxsize] (-1 excluded). If you are unsure, which value sys.maxsize variable returns, it bases on system architecture:

• for systems with 32-bit architecture that value is 2³¹ - 1 (2147483647; 2.147483647e+9)
• for systems with 64-bit architecture that value is 2⁶³ - 1 (9223372036854775807; 9.223372036854775807e+18, like in my case)

However, I consider these as satisfacionary, because this is not like users putting e.g. Tense.probability ((0, int(1e+9) - 1), 1, length = int(1e+9)), what means 1 will be really rare value to drop. Going above sys.maxsize results in an error. This problem can be solved by replacing single list with multidimensional one, however, result may need more time to generate (and it can increase limit to 2¹²⁷ - 1, which equals 170141183460469231731687303715884105727, 1.70141183460469231731687303715 884105728e+38). So make sure you won't go above value from sys.maxsize! This also concerns Tense.probability2() class method.

Due to strict typing you cannot use simple scientific notation without manual cast to an integer.

.probability((0, 2), 1, 2, length12000) OK
.probability((0, 2), 1, 2, length1.2e+4) TypeError: Expected integer or constant 'PROBABILITY_COMPUTE' .probability((0, 2), 1, 2, lengthint(1.2e+4)) OK


Still, you can do lots of things with this method! For example, finally this coin flip we mentioned about before:

coinflip.probability((0, 2), 1, 2, length12000)
if coinflip0:
   .print(Coin landed on side!)
note we can actually do vice versa with these both below
elif coinflip1:
   .print(Coin landed on heads!)
else:
   .print(Coin landed on tails!)