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Easy way to get a fair result from an unfair coin toss: Flip the coin twice in a row, in this case starting with the same side facing up both times, so it's equ
by NameError 2y ago
Easy way to get a fair result from an unfair coin toss: Flip the coin twice in a row, in this case starting with the same side facing up both times, so it's equally unfair for both tosses. If you get heads-heads or tails-tails, discard and start over until you get either heads-tails or tails-heads, which have equal probabilities (so you can say something like HT = "heads" and TH = "tails").
This works even if the coin lands heads 99% of the time, as long as it's consistent (but you'll probably have to flip a bunch of times in that case).
- mankyd 2y agoImportantly - you don't have to know the odds of the coin ahead of time, or which side is more likely. You only need to know that it is consistent.
- IncreasePosts 2y agoThe odds are important to know because if someone gave you a trick coin that always lands on heads, you will be flipping coins until the end of the universe. And I'm sure you have more important things to do than that.
- Vecr 2y agoNah, you can put in a rule to stop. It would be better to know ahead of time, but you don't need to.
- magicalhippo 2y ago> you will be flipping coins until the end of the universe Reminds me of one of my favorite movies, Rosencrantz & Guildenstern Are Dead, which opens with just such a scenario[1]. [1]: https://www.youtube.com/watch?v=RjOqaD5tWB0 https://www.youtube.com/watch?v=RjOqaD5tWB0
- legobmw99 2y agoI’ve seen this attributed to John von Neumann, of all people
- NameError 2y agoIt seems like he did everything! I first heard of Von Neumann in international relations & economics classes as the person who established game theory, then later in CS classes as the creator of mergesort, cellular automata, Von Neumann architecture, etc.
- vonneumannstan 2y agoWait til you hear about what he did in Math and Physics... Very easy to claim he was the most intelligent human to ever live. Or perhaps he was never human... https://en.wikipedia.org/wiki/The_Martians_(scientists) https://en.wikipedia.org/wiki/The_Martians_(scientists)
- EGreg 2y agoI consider LLMs to be the first successful non-von-neumann architecture in many decades
- ant6n 2y agoWhat if consecutive unfair coin flips are not independent?
- FartyMcFarter 2y agoThen it's impossible to trust the coin in the general case. Proof: Imagine the extreme case of the coin containing AI that knows exactly how you use it and how to manipulate each toss result. The coin itself can decide the outcome of your procedure, so it's impossible to trust it to generate randomness.
- lisper 2y agoIt's also impossible to prove that a given coin is not being controlled by an AI. (Or a deity.)
- FartyMcFarter 2y agoYes, which is why you can only trust abstract coins that exist in a formal system which assumes independent tosses :) If you require true randomness without any assumptions this is not the universe for you.
- jjk166 2y agoJust perform the same coin toss in two universes.
- simcop2387 2y agoIf anyone wants to look up why this might work, it's a Whitening transform [0]. I can't find the name of the algorithm itself being describe in the parent but there's more than just that for accomplishing the same thing. 0: https://en.wikipedia.org/wiki/Whitening_transformation https://en.wikipedia.org/wiki/Whitening_transformation
- npsomaratna 2y agoThank you. This was useful to learn.
- aidenn0 2y agoThat's Von Neumann Whitening.
- deleted 2y ago[deleted]
- Aloisius 2y agoEach flip would need to start with the same side up though, if this paper is correct.