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Creating fair dice from random objects

arstechnica.com

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Re: Creating fair dice from random objects

#11

Post by svat »

stevage wrote: post #8
ted_dunning wrote: post #5

Earlier quoted context omitted.

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.

That isn't the title either: the title is “Creating fair dice from random objects”, while what they are responding to may be something like “Creating fair coins from biased coins”. So they're only responding to the “Creating fair _ from _” part of the title. Responding to three out of six words in the title isn't bad I guess.

Re: Creating fair dice from random objects

#12

Post by zzo38computer »

It does not seem to be so useful and practical to use strange shapes for dice; the common shapes, with numbers (or other symbols that are applicable for the game you are playing) on each side, will probably be more useful, anyways. However, it might be interesting.

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.)

Re: Creating fair dice from random objects

#13

Post by gerdesj »

orlp wrote: post #6

How 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…

"arbitrarily" is doing some heavy lifting!

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".

Re: Creating fair dice from random objects

#17

Post by gametorch »

ted_dunning wrote: post #5
gametorch wrote: post #2

the 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.

just providing a comment I thought was interesting and kind of relevant

wasn't trying to hurt anyone or anything

Re: Creating fair dice from random objects

#18

Post by godelski »

pixelpoet wrote: post #4

Hey hey, it's Keenan Crane again :)

For those that don't know, he is a HIGHLY respected researcher and well known for effectively communicating complex topics. He really makes it fun. Often as visually entertaining as 3B1B while diving into more depth. I'd highly recommend people poke through his site and YouTube channel

https://www.cs.cmu.edu/~kmcrane/

https://www.youtube.com/user/keenancrane

https://x.com/keenanisalive?lang=en

Re: Creating fair dice from random objects

#19

Post by ethan_smith »

gametorch wrote: post #2

the 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…

This technique is formally known as the Von Neumann extractor (1951), a foundational concept in randomness extraction.

Re: Creating fair dice from random objects

#20

Post by [deleted] »

ethan_smith wrote: post #19
gametorch wrote: post #2

the 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…

This technique is formally known as the Von Neumann extractor (1951), a foundational concept in randomness extraction.

[deleted]
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