If you're forced to pick random numbers between 1 and X in your head, pick instead from a wider range of numbers and then modulo X. Your brain will legitimately have no idea what number you're picking.
e.g. for a range 1-6, pick from 100-250 instead and modulo 6 plus 1.
There are of course brand new biases at play (is your new range cleanly divisible by X?) But it's enough to tamp down the original biases you're worried about
I think you'd be better off taking a small pinch of sand, salt, pepper etc., throwing that on a smooth surface, then counting all the grains and then modulo it (just have the number of grains be >> than the range as in your example). This would reduce a lot of inherent biases, although perhaps introduce others.
At what point do we draw the line and say that these methods are sufficiently random? The task at hand is to come up with a sequence you perceive as random based on the numbers themselves, so adding layers like this seems to go against the concept of the experiment entirely.
How is this different from opening up my JavaScript console and doing Math.random() several times?
This whole experiment has more to do with defining what humans perceive as randomness. Of course, different humans are different. Ramunijan and his 1729 taxi, or a cryptographer studying some (apparently) random string, will keep going when others would not. Interestingly, the same is true for source code, or in the physical realm, looking at the innards of a modern car. It looks random to the layman! But of course it isn't at all.
I'm certainly no expert in randomness generators but the notion has been floating around for awhile that quantum indeterminancy is the best option. Here's a paper on it:
> "The presented above examples clearly show that classic random number generators may be exposed to various attacks, or may have the so-called backdoors. This justifies the need to develop alternative technologies that could replace the classic generators on a large scale. The most promising, because they have a fundamental justification for the randomness in the formalism of quantum mechanics, are quantum random number generators."
This would mean someone asks you to pick a random (integer) number between 0 and 1. That's just a coin flip, there's different/better methods for that.
Sorry, not following you here. How does 16 and 10 sharing a divisor make the mod trick fail? As long as you pick a base that doesn't match the range you're picking within, you should be good to go.
If someone asks me to "pick a random digit in [0x0, 0xF]", then I'll use base-10 as my start. 284. I have no idea which hex digit this will result in after I mod it by 16. It's 0xC, but I didn't know that going into it.
Oh, wait. I think I do see what you're getting at. I would still know if it's even or odd, because 10 and 16 share 2 as a divisor, right?
e.g. for a range 1-6, pick from 100-250 instead and modulo 6 plus 1.
There are of course brand new biases at play (is your new range cleanly divisible by X?) But it's enough to tamp down the original biases you're worried about