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A two-person method to simulate die rolls (2023)

(blog.42yeah.is)
76 points Fraterkes | 2 comments | 05 Dec 25 19:32 UTC | HN request time: 0.021s | source
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AlotOfReading ◴[07 Dec 25 22:36 UTC] No.46186005[source]▶
Another procedure based on a similar problem I worked on with a friend: you both pick positive integers a and b, then add them together to create c. Either sqrt(c) or sqrt(c+1) is irrational and the fractional digits provide your random numbers. If you need a new sequence, you take some digits from the current expansion and sqrt() them again.

Might not be unbiased, but good luck proving it.

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1. crdrost ◴[07 Dec 25 23:20 UTC] No.46186421[source]▶
I'm not entirely sure what algebraic property you would prove with this, but you probably could prove something about it. The issue is that they have repeating continued fraction representations, and large numbers in the continued fraction correspond to very good rational approximations, and so you'd find that a bunch of these chosen at random have pretty good rational approximations, which assuming the denominator is co-prime to 10, probably means that it explores the space of digits too uniformly? Something like that.
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2. AlotOfReading ◴[07 Dec 25 23:29 UTC] No.46186495[source]▶
The approach I was thinking of is that you'd prove normality or the lack thereof, a notoriously open problem for virtually all irrational roots. Continued fractions might be fruitful, but I suspect you'd eventually run one of the many other open problems in that space instead.