On Sun, May 26, 2013 at 1:38 PM, Steven D'Aprano <steve+comp.lang.pyt...@pearwood.info> wrote: > On Sun, 26 May 2013 03:23:44 +1000, Chris Angelico wrote: > >> Does adding 1 to a random >> number make it less random? It adds determinism to the number; can a >> number be more deterministic while still no less random? >> >> Ah! I know. The answer comes from common sense: > [snip spurious answer] > > I know you're being funny, but in fact adding a constant to a random > variable still leaves it equally random. Adding, multiplying, dividing or > subtracting a constant from a random variable X just shifts the possible > values X can take, it doesn't change the shape of the distribution.
In real numbers, that's correct. However, computers don't work with real numbers, so there's the very, uhh, REAL possibility that some of the entropy will be lost. For instance, multiplying and dividing when working with integers results in truncation, and adding huge numbers to small floats results in precision loss. I was deliberately playing around, but unfortunately there have been many people who've genuinely thought things similar to what I was saying - and then implemented into code. > However, adding two random variables X and Y does change the > distribution. In fact, a very cheap way of simulating an almost normally > distributed random variable is to add up a whole lot of uniformly > distributed random variables. Adding up 12 calls to random.random(), and > subtracting 6, gives you a close approximation to a Gaussian random > variable with mean 0 and standard deviation 1. Yep. The more dice you roll, the more normal the distribution. Which means that d100 is extremely swingy, but 11d10-10 is much less so, and 99d2-98 quite stable. The more randomness you add, the more predictable the result. <quote source="Jubal Early">Does that seem right to you?</quote> ChrisA -- http://mail.python.org/mailman/listinfo/python-list
