This topic has probably been covered many times, but I have a few questions I want to address.
As an intro, we can use dice to generate a seed phrase. Bitcoin hardware wallets/signing devices such as Coldcard or Seedsigner allow you to input the results of 50/99/x number of rolls and convert that into a seed.
A big danger of using dice rolls is if the dice are biased and more likely to land on one or multiple numbers. It affects the randomness, hence the security of your seed and Bitcoin. A truly unique dice roll is one where each outcome is equally likely. If one or more numbers have a greater chance to land on top, that is obviously not the case. It limits the keyspace from where the seed is generated, making brute forcing easier. Surely not easy enough, but easier.
A couple of questions:
In what ways are dice biased? Is the bias random?
For instance, am I more likely to roll a 2 than any other numbers on dice #1 and a 3 on dice #2?
Are dice manipulated on purpose, and if so, manipulated to achieve what results (rolls)? Or is the bias a result of low-quality production? If they are not manipulated on purpose, and the bias is random for each dice, wouldn't it even out if I have multiple dice (10, for instance) and roll them as many times as possible? If each dice is biased to a different number, can we really talk about a significant loss of randomness in the final result?
To take this further, how could someone take advantage of the bias in my dice to bruteforce my seed without knowing what that bias is? Even if 8/10 of my dice are biased and only 2 produce near-perfect results, wouldn't you need to know the exact bias to brute force my seed? If my thinking is correct, having knowledge of this bias would be essential for whoever or whatever is trying to hack my seed phrase because, based on the results alone, you can't possibly know that one of my dice has a tendency to roll a 2. In theory, if I throw 10 dice in the air, biased or unbiased, they could all show the result 2. Very unlikely, but still possible. How would the attacker differentiate the biased from the unbiased rolls?
As a way to mitigate bias, it's better to use different types of dice from different manufacturers, sizes, etc. Although I can't possibly see all dice from manufacturer #1 as being biased to the same number and the dice from manufacturer #2 to a different number. It must be a random bias.
When we are on the subject of manually testing a die, it's very difficult to discover a slight bias. Obviously, if every second roll lands on the same number and you rolled it hundreds of times, it's enough proof that something is wrong. If all numbers appear in what seems to be a random fashion, it isn't easy to come to a conclusion. Randomness means that the number 5 could be rolled 1/10 times. But even if you roll it 7/10 times, we can't talk about bias if you don't get approximately the same number of unexpected results after dozens and hundreds of attempts.
