Thanks for posting your code, but at 178 lines (most of which are either commented out or irrelevent to your question) its a hard slog to work out what you're doing.
And as for the seemingly endless sequence of "Random number ... Value entered", what did information did you think we would get from that? Did you think we would study each and every pair of lines, looking for a pattern? When asking questions about code, it helps to [post a **minimal** example](https://stackoverflow.com/help/minimal-reproducible-example) that we [can easily run](http://sscce.org/). In this case, we can compare the Mersenne Twister PRNG with the operating system's cryptographically strong RNG and see if we get similar results. The beauty of a PRNG like the Mersenne Twister is that it is perfectly repeatable if you know the seed. So if you repeat this *exact* code, you should get the *exact* same output. (Well, almost. Technically only the output of `random.random` is guaranteed not to change from one version to another. But in practice `random.randint` is also very stable.) ```python import random from statistics import mean, stdev random.seed(299) d1 = [random.randint(1, 9) for i in range(100000)] triples = 0 # Count the number of triples. for i in range(len(d1)-3): a, b, c = d1[i:i+3] if a == b == c: triples += 1 print("mean =", mean(d1)) print("stdev =", stdev(d1)) print("runs of three:", triples) ``` If you run that code, the output you get in Python 3.10 should be: ```text mean = 4.99025 stdev = 2.586159666323446 runs of three: 1244 ``` So out of 100000-3 = 99997 groups of three random integers, 1244 or 1.2% are a triplet (a run of three). Now let's compare the same with the OS's cryptographically strong RNG. Because this uses environmental randomness, there's no seed, so we can't replicate the results, but you should usually get something similar. ```python import random from statistics import mean, stdev R2 = random.SystemRandom() d2 = [random.randint(1, 9) for i in range(100000)] triples = 0 # Count the number of triples. for i in range(len(d2)-3): a, b, c = d2[i:i+3] if a == b == c: triples += 1 print("mean =", mean(d2)) print("stdev =", stdev(d2)) print("runs of three:", triples) ``` And output should usually be something like this: ```text mean = 4.99198 stdev = 2.5882045258492763 runs of three: 1228 ``` Virtually no difference. Of course there is a *tiny* chance that you could get something outlandishly unlikely, like a run of fifty thousand 6s in a row. If such a fluke was impossible, it wouldn't be *random*. You can see that there is no significant difference between the Mersenne Twister and the much more expensive crypto-strength SystemRandom. The MT is a **very** vigorously studied PRNG. It has **excellent** statistical properties, without being too expensive to generate random numbers. And it allows replicable results: if you know the seed, you can repeat the output. The only real disadvantage of MT is that it is not secure for cryptographic purposes. (By the way, using `SystemRandom`, I also got 134 runs of four and 14 runs of five.) _______________________________________________ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/OX3OIARPY3CV37M4LX46SFKO7FT2LCPH/ Code of Conduct: http://python.org/psf/codeofconduct/
