> We can prove that in an ideal situation, the die roll will be fair. Assuming both parties can come up with unbiased random numbers ranging from [0;12)...

Doesn't that assumption remove the entire problem though? I thought the whole reason for the method was that people can't easily think of an unbiased random number.

Or put differently, if that's your starting point, what's stopping you from simply doing (A mod 6) + 1?

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?

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.

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.