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?
A die can be biased for two reasons one is intentional means that is created to favor one particular number for cheating purposes. Another one is unintentional like it can happen due to a faulty process while manufacturing and become biased on one side so in both cases the bias is non-random and will likely favor one side but every die can be unique with their bias so if we use 10 different biased dice on multiple rolls then more likely we will see the same combination of number.
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?
Even though it is not entirely possible to find the biased nature of a die, if they can find the noticeable results when rolling a die multiple times then it can be considered as the die is biased towards number 2 so they will incorporate it into the brute forcing process which will reduce the time to crack the result if their guess is right.
So I feel the bias dice can affect the security of seed generation.
What could be the best alternative?
I feel going completely digital can ensure complete randomness and it can be done with the Dice rolling applications built on Pseudorandom Number Generators (PRNGs).