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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

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 constructing a fair N-sided die out of any arbitrarily biased die for any N

ted_dunning 1y ago
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.
- gametorch 1y ago
  just providing a comment I thought was interesting and kind of relevant wasn't trying to hurt anyone or anything
- stevage 1y ago
  And yet the person you replied to was quite clear that they are responding to the title.
  - svat 1y ago
    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.
    - ncruces 1y ago
      > and this trivially extends to constructing a fair N-sided die out of any arbitrarily biased die for any N They wrote something interesting, even if it only tangentially matches the topic. Pointing out that it doesn't exactly match the topic also adds to the conversation, I guess, but I think we've now exhausted any interest (so I won't be arguing further).
ethan_smith 1y ago
This technique is formally known as the Von Neumann extractor (1951), a foundational concept in randomness extraction.
- deleted 1y ago
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ted_dunning 1y ago

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.

gametorch 1y ago
just providing a comment I thought was interesting and kind of relevant wasn't trying to hurt anyone or anything
stevage 1y ago
And yet the person you replied to was quite clear that they are responding to the title.
- svat 1y ago
  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.
  - ncruces 1y ago
    > and this trivially extends to constructing a fair N-sided die out of any arbitrarily biased die for any N They wrote something interesting, even if it only tangentially matches the topic. Pointing out that it doesn't exactly match the topic also adds to the conversation, I guess, but I think we've now exhausted any interest (so I won't be arguing further).

ethan_smith 1y ago

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

deleted 1y ago
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