Posted by epipolar 2 days ago
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.)
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)
Needless to say, p * (1 - p) and (1 - p) * p have an equal probability, so if we don't reject our two tosses, we have a fair outcome.I'm not sure that two concurrent harmonious answers constitutes a "fixed" coin or a diagnosis of a fixed coin.
This scheme will be rubbish with a one sided coin ie the limit for "arbitrary fixed coin".
2. the person who achieves this is the winner.
https://www.cs.cmu.edu/~kmcrane/
https://archimedes-lab.org/2021/07/15/amazing-roman-rock-cry...
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
What they are doing is designing physical shapes that will have a specified probability of falling in different positions.
What you are talking about is post processing a biased random signal to get a less biased signal.
wasn't trying to hurt anyone or anything