I think the game theory inherit here makes it ok for this purpose. You get an advantage being random. You're likely still not going to generate random numbers but at least there's good motivation to be random and that part just becomes part of the game imho (guess what number the opponent calls to maximize your roll).

Of course as others note this is a convoluted mod n process.

Does seem like each person could just secretly write down any number, they are revealed, added and mod 6'd.

Is all this angular difference stuff a fancy way of saying mod 6?

Because you can rig the answer if it's just one person. But if two of you use the method from the post, and both commit to your answers before revealing them, then neither of you can rig it.

Yeah, the only valuable idea here is the angle-one, which is like a modulo, making the approach a primitive LCG, which is a way of generating pseudorandom numbers from seeds.

I'd say the only unbiased and non crappy method here is to feed the 2 participants' numbers into some sorth of hash function.

I think mine from 2017 is a commitment scheme. Certainly is not unique or novel.

https://darkcephas.blogspot.com/2017/07/fair-random-number-g...

If you're worried about someone exiting the protocol, you can use a smart contract to lock their funds so that if they simply exit then they lose all their money.

Bear in mind, the terminal goal doesn't actually require unbiased numbers; the way most TTRPGs work is that you're trying to roll over or under a target number to get a weighted, unpredictable outcome. The idea is that while players (usually) want any given action to succeed, they some of their actions to fail in order to preserve narrative interest, while having their character be better at some things than others.

As such, while randomness is best, the given method is quite sufficient for having fun, and both players can agree that it's fair: they each have equal influence over the result.

If you get all heads or all tails then use the last toss as part of your next set of 3.

E.g. HHHHT -> HHT -> 6

The method proposed is just A - B mod n. The two are entirely equivalent.

Yup

Even without a formal proof you could test it empirically if you generate a large number of samples and run regular tests for pseudorandom number generators. [Edit: a quick test on a million samples and relatively simple RNG tests suggests that this is indeed good enough; maybe worth working out a proof if this hasn't been done already. Edit2: I guess the main problem you'd hit in practice with short sequences of digits would be to avoid accidental recurrences with too short a period, but it should be possible to make it statistically unlikely in practice with enough compute/digits.]

I'm not entirely sure what algebraic property you would prove with this, but you probably could prove something about it. The issue is that they have repeating continued fraction representations, and large numbers in the continued fraction correspond to very good rational approximations, and so you'd find that a bunch of these chosen at random have pretty good rational approximations, which assuming the denominator is co-prime to 10, probably means that it explores the space of digits too uniformly? Something like that.

Can you calculate the digits in your head without help?