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One thing I like about the psychology of random is you can tell what numbers are true random vs what numbers are human generated if you know what to look for. F

One thing I like about the psychology of random is you can tell what numbers are true random vs what numbers are human generated if you know what to look for. For instance humans will avoid closeness (1 next to 2) and runs (1 next to 1 again). They will also usually avoid starting with the lowest and highest number in the range (asking for random numbers between 0 and 10 will almost never result in the first number being 0 or 10). If they are aware of this and try to compensate they’ll start creating patterns that give them away.

Morizero 5y ago
Here's a topical example that The Economist showed a few months back https://www.economist.com/graphic-detail/2021/10/11/russian-elections-once-again-had-a-suspiciously-neat-result https://www.economist.com/graphic-detail/2021/10/11/russian-...
wolverine876 5y ago
I remember a securities market-fixing scam was discovered years ago because the numbers were not random but (in hindsight) obviously human-created.
zamadatix 5y ago
I wonder what PRNGs there are that are reasonably easy enough to do in your head but can give better randomness than a person trying to be random normally.
- Cogito 5y ago
  Modular arithmetic can work, but you need to be a little bit careful. If you want a number from 0-10 then modulo 11 works perfectly (as long as you pick a number well outside any 11 times table you have memorised). This is because it's relatively easy to pick a number without immediately knowing what the mod 11 version of it will be. For 1-10 you could do mod 10, but that's too easy to cheat. Instead you can take you initial guess n, and multiply (n mod 5) + 1 by (n mod 2) + 1. For example 42 -> ((42 mod 5) + 1) x ((42 mod 2) + 1) = 3 x 1 = 3; 43 -> 4 x 2 = 8. This second scheme works because we're using a factorisation of the length of our intial range of guesses, and then multiplying the answers. We add 1 because 0s make multiplying boring (and we want 1-10 in any case). There will still be bias, especially if you've used the scheme before. With the mod5 mod2 scheme the biggest bias is that you only get a 1 if the original guess is congruent to 0 mod 10. A way to avoid that bias, which unfortunately introduces another bias, is to do a two modulo steps. Start with a biggish number, and then do your final one. This is harder to do in your head and makes some final guesses more likely, but only a bit. So for example, do final guess = (n mod 19) mod 10 + 1. 19 is easyish to calculated because you find the closest multiple of 20, workout that mod 19, and add any leftovers to it. 42 mod 19 = 40 mod 19 + 2 = 2 + 2 = 4 (42 mod 19) mod 10 + 1 = 4 mod 10 + 1 = 5
  - unholiness 5y ago
    Your second scheme with mod2 and 5 is still only sensitive to the last digit though.
    - Cogito 5y ago
      Ahh you’re of course correct, might still be useful if you don’t memorise the mapping. I should have gone with my gut and generated the first 100 with each scheme to look at what the distribution looks like. Mod 19 scheme feels like it should be decent but it gives 10 half the probability of any other number. I did find a quick fix that may still be simple enough: take the number mod 19, and add the last digit of the original number. Now take the last digit of the sum, and add 1. So new guess = 1 + (n mod 19 + n mod 10) mod 10. Doing a quick simulation there is no obvious bias.

Morizero 5y ago

Here's a topical example that The Economist showed a few months back https://www.economist.com/graphic-detail/2021/10/11/russian-elections-once-again-had-a-suspiciously-neat-result https://www.economist.com/graphic-detail/2021/10/11/russian-...

wolverine876 5y ago

I remember a securities market-fixing scam was discovered years ago because the numbers were not random but (in hindsight) obviously human-created.

zamadatix 5y ago

I wonder what PRNGs there are that are reasonably easy enough to do in your head but can give better randomness than a person trying to be random normally.

Cogito 5y ago
Modular arithmetic can work, but you need to be a little bit careful. If you want a number from 0-10 then modulo 11 works perfectly (as long as you pick a number well outside any 11 times table you have memorised). This is because it's relatively easy to pick a number without immediately knowing what the mod 11 version of it will be. For 1-10 you could do mod 10, but that's too easy to cheat. Instead you can take you initial guess n, and multiply (n mod 5) + 1 by (n mod 2) + 1. For example 42 -> ((42 mod 5) + 1) x ((42 mod 2) + 1) = 3 x 1 = 3; 43 -> 4 x 2 = 8. This second scheme works because we're using a factorisation of the length of our intial range of guesses, and then multiplying the answers. We add 1 because 0s make multiplying boring (and we want 1-10 in any case). There will still be bias, especially if you've used the scheme before. With the mod5 mod2 scheme the biggest bias is that you only get a 1 if the original guess is congruent to 0 mod 10. A way to avoid that bias, which unfortunately introduces another bias, is to do a two modulo steps. Start with a biggish number, and then do your final one. This is harder to do in your head and makes some final guesses more likely, but only a bit. So for example, do final guess = (n mod 19) mod 10 + 1. 19 is easyish to calculated because you find the closest multiple of 20, workout that mod 19, and add any leftovers to it. 42 mod 19 = 40 mod 19 + 2 = 2 + 2 = 4 (42 mod 19) mod 10 + 1 = 4 mod 10 + 1 = 5
- unholiness 5y ago
  Your second scheme with mod2 and 5 is still only sensitive to the last digit though.
  - Cogito 5y ago
    Ahh you’re of course correct, might still be useful if you don’t memorise the mapping. I should have gone with my gut and generated the first 100 with each scheme to look at what the distribution looks like. Mod 19 scheme feels like it should be decent but it gives 10 half the probability of any other number. I did find a quick fix that may still be simple enough: take the number mod 19, and add the last digit of the original number. Now take the last digit of the sum, and add 1. So new guess = 1 + (n mod 19 + n mod 10) mod 10. Doing a quick simulation there is no obvious bias.