No matter how you lay out the numbers, a nice hard roll will give you a completely uniform result. The goal here is to make it harder to cheat when you can partially control how the die rolls.
Nobody is pretending there is more entropy than the number of outcomes. What we want is a design that can't be influenced in favor of the roller, even when entropy is a bit low.
Let's design two layouts for a d100. We'll say that you can roll each design two ways. You can roll it properly and get a random number from 1-100, or you can roll it improperly and it will stay within a cluster of 10 numbers, giving you a random number out of that cluster.
The first layout puts similar numbers together. 1-10 are all together, as are 11-20, etc.
The second design is laid out so that every tens digit show up in each cluster, and every ones digit shows up in each cluster.
Both designs can give you equally random numbers. A proper roll gives you a uniform distribution over 100 numbers, and an improper roll gives you a uniform distribution over 10 numbers.
But look at what happens when you apply certain functions to the output. A common use for the d100 might be emulating a d10. If you divide the first die by ten, a proper roll acts like a d10, and an improper roll lets the cheater pick what result they want. With the second die, a proper roll acts like a d10, and an improper roll also acts like a d10.
Fairness is preserved when the imperfections in the randomness don't matter. Your coin method looks like it would be a fair way to pick lottery numbers if it was only used once. But it would be a fair way to pick even or odd indefinitely.
I don't think I'm reading that post wrong! The original poster said " But I wonder if a die that large is even fair." Then the response said it's "fair enough" because even if it only spins part of the way, you'll still get one of a group of dissimilar numbers.
but that's not fair by the definition of what a fair die is. (it has a definition, if you search google you get "In mathematics we say 'fair dice' when we mean that there is an equally likely chance of landing on any face.")
You're basically arguing that dice don't need to be fair. also you completely missed my jab at the NSA breaking RNG's while making them seem "random enough", i.e. getting to quite dissimilar next states while in fact having only a few possible next states.
It's "fair enough" because it gets the important parts right of having a large number of states. Just like your coin flip would get the important parts right if it was used in specific ways.
A coin in the real world isn't fair, because it could land on its side. But it's fair enough.
Statistical sampling doesn't give you guaranteed-accurate results. But the biases cancel out across the metrics you're measuring, so it's good enough.
I didn't ignore your jab at the NSA, but it's pretty weak. The backdoored CSPRNG doesn't give numbers that are worse than any non-backdoored CSPRNG. Depending on your perspective, it can give you uniformly any number, or it can give you only a single number, and the same is true of good algorithms too.
I enjoyed this perspective and it changed my thinking, you've convinced me. It's also unlikely that humans can keep track of the distribution of 120 numbers on a die (in any distribution) so even if the game the cheater is playing is "Pick 20 numbers, then roll. If you roll any of the 20 you win" it is unlikely that they can remember what the die looks like well enough to cheat - except perhaps after massive effort. Fair enough :)
No matter how you lay out the numbers, a nice hard roll will give you a completely uniform result. The goal here is to make it harder to cheat when you can partially control how the die rolls.
Nobody is pretending there is more entropy than the number of outcomes. What we want is a design that can't be influenced in favor of the roller, even when entropy is a bit low.
Let's design two layouts for a d100. We'll say that you can roll each design two ways. You can roll it properly and get a random number from 1-100, or you can roll it improperly and it will stay within a cluster of 10 numbers, giving you a random number out of that cluster.
The first layout puts similar numbers together. 1-10 are all together, as are 11-20, etc.
The second design is laid out so that every tens digit show up in each cluster, and every ones digit shows up in each cluster.
Both designs can give you equally random numbers. A proper roll gives you a uniform distribution over 100 numbers, and an improper roll gives you a uniform distribution over 10 numbers.
But look at what happens when you apply certain functions to the output. A common use for the d100 might be emulating a d10. If you divide the first die by ten, a proper roll acts like a d10, and an improper roll lets the cheater pick what result they want. With the second die, a proper roll acts like a d10, and an improper roll also acts like a d10.
Fairness is preserved when the imperfections in the randomness don't matter. Your coin method looks like it would be a fair way to pick lottery numbers if it was only used once. But it would be a fair way to pick even or odd indefinitely.