a = [0,0,0,0,0,0,0,0,0,0]
a[5 *(rand + rand)] += 1
=> [28, 60, 96, 151, 171, 168, 146, 96, 63, 21]
What you are referring to here is Benford's Law. Why not simply say that in the title?
Other example - rolling dice with 5 sides signed "6" and one side signed "1" - results will be random, but the resulting distribution won't be uniform.
Uniform distribution is special case of random distribution.
What is a random distribution? I think you meant probability distribution.
I think that the point you're trying to make is that a random variable with a uniform distribution is more "random" than a random variable with a gaussian distribution. The metric you're implying is called entropy, as a uniform distribution is maximally entropic.
After you do study probability (by gambling, by lab work, by quantitative programming, or, least fun, in coursework), you get introduced to the "right questions to ask", like:
"what's the distribution",
"are the samples independent",
"what are you conditioning upon"
For instance, many people don't know that the distribution of the sum of two dice looks very different than just one die. They're both random, but not both uniform. Often people know something's weird, but can't formulate the question because they don't have the language.
Increasing the x would decrease the range of the distribution, while increasing the y would increase the magnitude of the distribution.
I never found something simple enough for what I wanted to apply it to (a game).
(In case anybody is wondering whether I've done the right thing and reported the problem: yes, I have.)
"Random" to mathematicians means the outcome of a probability experiment. If you flip a two-headed coin or roll a one-sided die, and record the results, the results are "random" - random within the set of possible outcomes, according to the function that generates them. So you dutifully record "heads", "heads", "heads" and "1", "1", "1" for your results. It's random!
"Random" for mathematicians inherently means "predictable". There's a known probability distribution.
The word "random" for programmers means something very different. It inherently means "unpredictable". The probability distribution must be flat across the space of possible outcomes. If we are operating in a base-10 system, the chance of any of the next digits occurring must be exactly 1/10.
My prediction is most of the discussion here will be people talking past each other, using different definitions of the word "random".
I think this is the definition for mathematicians as well.
It's just that "random" is a common shortcut for - string comming out of probability experiment - it is very likely that it is random according to Kolmogorov complexity, because most strings are random, and space is very very big.
I think most mathematicians would agree that Probability is a much larger and important branch of mathematics than Kolmogorov-Chaitin complexity, and usually use "random" in its probabilistic meaning.
Thanks for clearing this up.
That's not at all the same as "predictable", but the goal is usually to be able to characterize the phenomenon statistically such that certain properties, such as general location on the number line, can be identified. If such properties cannot be identified, that doesn't make the phenomenon any less random - just less understood and by extension less predictable.
Although I do disagree with the words you used to characterize the differences. While most people use "random" to mean "unpredictable," as you demonstrated, a uniform distribution is just as "predictable" as any other kind of distribution.
I think the real difference is that most people only associate "random" with uniformly random distributions. Since you likely need some formal probability education to be aware of the others, this isn't surprising.
That's the problem with random, you can never be sure: http://www.dilbert.com/dyn/str_strip/000000000/00000000/0000...