the basic idea is that, because multiplication commutes, probability of A then B is the same as probability of B then A, so long as they are independent events (rolling objects typically meets this criteria)

so instead of using just A or just B, which might neither have 0.5 probability, you only count "A then B" and "B then A" as rolls

and this trivially extends to constructing a fair N-sided die out of any arbitrarily biased die for any N

1. Toss the coin and remember the answer.

2. Toss the coin again, if it is different from your previous toss then your result from #1 is fair. Otherwise, go back to step 1.

If p is the probability of getting heads, there are four possible outcomes with their associated probabilities:

    TT -> (1 - p)^2   (rejected)
    HT -> p * (1 - p)
    TH -> (1 - p) * p
    TT -> p^2         (rejected)

Another reason to use dice for tabletop games is so that the game can be played without the use of a computer.

When I play GURPS, I generally use different dice with each dice roll in order to try to mitigate some of the bias. (I don't know quite how much effective this really is, though.)

https://archimedes-lab.org/2021/07/15/amazing-roman-rock-cry...