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

(blog.42yeah.is)
76 points Fraterkes | 3 comments | 05 Dec 25 19:32 UTC | HN request time: 0s | 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. pama ◴[07 Dec 25 23:58 UTC] No.46186711[source]▶
Even without a formal proof you could test it empirically if you generate a large number of samples and run regular tests for pseudorandom number generators. [Edit: a quick test on a million samples and relatively simple RNG tests suggests that this is indeed good enough; maybe worth working out a proof if this hasn't been done already. Edit2: I guess the main problem you'd hit in practice with short sequences of digits would be to avoid accidental recurrences with too short a period, but it should be possible to make it statistically unlikely in practice with enough compute/digits.]
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2. AlotOfReading ◴[08 Dec 25 02:30 UTC] No.46187657[source]▶
Passes dieharder and PractRand, so it's pretty dang good.
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3. pama ◴[08 Dec 25 03:11 UTC] No.46187884[source]▶
Yeah I like the simplicity and power of it. You might want to tackle the math and write it up.