⭐ Merited by ETFbitcoin (1)
If the number 1 is 25%
If the probability of having '1' is 25%, and 15% for each other, each dice roll will produce 2.67 bits of entropy. This means that you would have sufficient entropy with 48 dice rolls. That post and calculation of yours you linked to is way above my understanding. All I can see is the final result in bits of entropy (without knowing if your calculation is ok) showing more than what a 12-word seed has.
All you need to know is that we have an equation that tells us how entropy bits are worked out. These units define how unpredictable an event is. For example, a dice that gives '1' 99% of the time generates a lot less entropy bits in each roll than a completely unbiased. In that post you linked to above, you demonstrated that even a biased dice produces enough entropy with a big number of rolls. If that is true, the dice would have to be awfully biased to only produce 99 bits to the point you can see it with the naked eye.
Correct. It would need to be so awful, that you could feel it's improper for generating entropy. A dice that generates 128 bits in 99 rolls, which are necessary for a Bitcoin seed phrase, generates 1.29 bits per roll. Imagine that even a dice that rolls '1' 75% of the time (and 5% for each other result) gives more than 1.39 bits of entropy. And to give you a picture, these would be potential results from such a flawed dice:
Code:
Try #1: 1111111663111111111111213115161161111161531111411141111211111141111111111121111511111111113111112121
Try #2: 6111431111121115141251111461611141111111113111111111113211321312111612111311131111111133611311112111
Try #3: 1511511111111111115121161221311151533111111111111111111112211111111111111112131151111111112111311161
Try #2: 6111431111121115141251111461611141111111113111111111113211321312111612111311131111111133611311112111
Try #3: 1511511111111111115121161221311151533111111111111111111112211111111111111112131151111111112111311161
I think everyone could notice they're using a bad dice in such a case.
