Quote from: garlonicon on April 27, 2022, 08:35:41 PM

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You also care that a particular outcome does not affect the next outcome, in other words, that each outcome is independent of all other outcomes.

If you have a stateless function, then it is theoretically possible to get {4,4,4,4,4} result, mentioned above. If you have some kind of state, then you can design your algorithm differently, just to pass some randomness tests. And that will make your outputs more random, but also less resistant to some attacks, because then you can assume that you will never get {4,4,4,4,4}, just because that value will fail some randomness tests. Of course, usually the size of the output will protect you from those attacks, and you will not even notice that potential weakness.

A dice roll should have a 1/6 chance of any given number being chosen. If for example, if a "roll" was a 4, then the chances of the next roll are:
1 - 95%
2 - 1%
3 - 1%
4 - 1%
5 - 1%
6 - 1%

if the previous roll was a 5, each of the above probabilities could be rotated by one index, so the probabilities would be 1, 95, 1, 1, 1, 1%. The probabilities could be similarly rotated for all six numbers.

The above weighting of the dice I believe would still pass randomness tests, because, over many tests, each number would be chosen 1/6 of the time.

Quote from: larry_vw_1955 on April 30, 2022, 01:48:27 AM

Quote from: PrimeNumber7 on April 27, 2022, 06:05:24 PM

If you are using a dice roll to generate a seed, you should care more than just that each outcome has the same probability. You also care that a particular outcome does not affect the next outcome, in other words, that each outcome is independent of all other outcomes.

dice rolls are independent of one another. that's just a fact. the harder thing is for each outcome to have the same probability. but if it's a fair dice then it's probably close enough.

A dice roll *should* be independent of one another. Often times, when someone is generating a private key via "dice rolls" they are actually generating a private key via some kind of simulated dice roll.