Creating fair dice from random objects
arstechnica.com
Creating fair dice from random objects
1–10 of 28 posts
Re: Creating fair dice from random objects
#2the title is a classic quant interview problem
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
Re: Creating fair dice from random objects
#3[deleted]
Re: Creating fair dice from random objects
#4Hey hey, it's Keenan Crane again :)
Re: Creating fair dice from random objects
#5the title is a classic quant interview problem 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 const…
That isn't what the article is about at all. It's not even what the first paragraph is about.
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.
Re: Creating fair dice from random objects
#6How to create a fair coin from an arbitrarily biased coin:
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)
Re: Creating fair dice from random objects
#7How to create a fair coin from an arbitrarily biased coin: 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 (re…
That's cute. intuitively, if two flips give different outcomes, it's fifty/fifty which would be first.
Re: Creating fair dice from random objects
#8the title is a classic quant interview problem 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 const…
That isn't what the article is about at all. It's not even what the first paragraph is about. 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.
And yet the person you replied to was quite clear that they are responding to the title.
Re: Creating fair dice from random objects
#9How to create a fair coin from an arbitrarily biased coin: 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 (re…
Re: Creating fair dice from random objects
#10The question I have is how stable are the probabilities over time? My guess is traditional dice are more physically robust to wear and degrade more gracefully.