Comment by wolverine876 | Hacker News Reader

Comment by wolverine876 | Hacker News Reader

Random number generation is a tool not just for crypto, but for human psychology. There are applications for random, psuedo-random, unpredictable, and 'uncontrolled' number generation. (These are my terminology and concepts. Did I leave out some other property? Has someone actually studied this question?)

Imagine it's dinner time and you want to randomly choose a restaurant, so you roll a die. Let's say you know the die isn't truly random; I guess you probably don't care. Let's say you know it's not really even psuedo-random (by whatever standard that's defined); do you care? Let's say it's just unpredictable - significantly biased, but you don't know the bias - do you care? Let's say I told you what the bias is before you roll, but you are yielding control of the outcome to the dice (which I'm calling 'uncontrolled'). Does that differ from yielding control to another free will, another person? What matters to you here?

Imagine that instead you are deciding whether to buy a house. You can't decide, it's 50-50, let's roll for it! How do the above questions apply?

Dinner is a low-stakes, no-lose situation. The house is a high-stakes, no lose (assuming it legitiately is 50-50) situation.

Imagine a low-stakes, win/lose situation, like a low-stakes game of craps. As long as it's unpredictable, is that fine? What about uncontrolled?

Imagine about a high-stakes game of craps: Honestly, I might still be satisfied with unpredictable (ignoring the risk that someone might cheat and figure out the pattern), or even uncontrolled, if everyone knew the bias.

I might be satisfied with merely uncontrolled for all of those situations, though at a certain level of bias, why roll a die?

I like these divisions!

To boil down the 50/50 one: Imagine your torn between those 2 houses, and your realtor—who also does magic as a hobby—offers you a coin to flip. You ask, "wait, is this a trick coin?"

"Yup!" he replies, "Always lands one way."

"How is that going to help me then!?"

"I got no idea if this is an always-heads coin or an always-tails coin. You see, when they're being minted, each coin randomly plops onto the conveyor before it enters the CBU—"

"—The 'CBU'? What's that?"

"—oh, the Coin Biasing Unit. It's the machine that takes a normal coin and does the proprietary thing that biases it. The coin's orientation as it enters the CBU is the way it'll be biased from then on. As I was saying, the coins enter the CBU randomly, and I've never used this particular one before, so I don't know if it's a Heads coin or a Tails coin."

"... Ok then! Heads I offer on 284 Bayes St, Tails I go with 938 Bernoulli Blvd."

That's great! Come to think of it, drinking games can be 'uncontrolled': 'Watch this CNBC show - every time they use a word starting with 'crypto', we drink!'

Of course, the realtor wants you to buy the house that gives them the higher commission, so, as a hobby magician, your realtor has two coins and flips the one that they know will result in their desired outcome. That whole story about not knowing is just standard misdirection.

Ask the realtor to flip the coins until either HT or TH shows up. Those have equal probabilities, regardless of initial bias.

Not if you do it "streaming", just flipping until you get either pattern. (Suppose T is very rare. Then you'll always start with HHH..., so you'll always get HT.) You have to "chunk" them, considering exactly two flips at a time and using each flip exactly once, to get biases to cancel out.

I've heard people talk about a tough housing market, but this is enough to make me buy an RV instead, and hop from park to park.

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.

Here's a topical example that The Economist showed a few months back https://www.economist.com/graphic-detail/2021/10/11/russian-...

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

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.

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

Your second scheme with mod2 and 5 is still only sensitive to the last digit though.

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.

Concisely: Randomness exists if and only if there is ignorance.

As a DM, if I reach my hand in my bag of unfair chessex dice, make a biased choice of which which biased die I unfairly throw... From my perspective, the odds of a 20 are still 5%, because I don't have good enough memory to know what direction any of those biases go.

If one of my players, who have much less to do than a DM, rolls their same d20 every session, they will eventually pick up on its tendencies and know their die is more likely on average to crit.

If a cheating player understands the velocity of their roll, they can toss in such a way that 20 is much much more likely to appear.

The DM I describe can roll the same die as the player I describe but experience different probabilities because of ignorance. A fair player I describe who rolls their die in the same way as the cheating player I describe is experiencing different probabilities because of ignorance.

Situations we think of as random are just good at quickly spreading ignorance. A tiny change in velocity for the cheating player will spoil his plans, and the dice numbers are spread nearly equally so that this small ignorance about velocity quickly becomes large ignorance about the probability distribution of the result. Knowing half the bits of the seed of a PRNG quickly decays into nearly zero info about it's probability distribution. Knowing the seed of a PRNG precisely and the number of cycles imprecisely quickly becomes worthless, by design.

Dice, PRNGs, other things we think of as random are only different from any other piece of knowledge (future election results, whether the 1000th digit of pi is odd...) in that they are decent at quickly turning what knowledge you have into ignorance.

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