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Fair coins tend to land on the side they started (2023)

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Re: Fair coins tend to land on the side they started (2023)

#41

Post by NameError »

legobmw99 wrote: post #31
NameError wrote: post #20

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 coi…

I’ve seen this attributed to John von Neumann, of all people

It 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.

Re: Fair coins tend to land on the side they started (2023)

#42

Post by FartyMcFarter »

ant6n wrote: post #34
NameError wrote: post #20

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 coi…

What if consecutive unfair coin flips are not independent?

Then 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.

Re: Fair coins tend to land on the side they started (2023)

#43

Post by pugets »

swayvil wrote: post #28
Vecr wrote: post #14

Earlier quoted context omitted.

How good are you at Bayesian statistics, conditionalization, and understanding various biases? The simulation here should be good (it's better than mine).

Next you'll cite Bible verse.

“We toss the coin, but it is the Lord who controls its decision.” - Proverbs 16:33 (TLB)

Re: Fair coins tend to land on the side they started (2023)

#44

Post by Vecr »

TremendousJudge wrote: post #40
cgag wrote: post #24

I wouldn't be surprised if there is something to it, but I suspected they didn't use legitimate coin flips (because it seems like a large amount of people can't really flip a coin), and looking at the videos confirms it, at least for the flips done by Bartos: https://osf.io/6a5hy/ They're very low RPM and very low time in the air. Nothing I would accept for any decision worth flipping a coin for.

This was my first objection as well. However, if most people flip coins like that, then the measurements are valid -- the conclusions are about what average people will do, not a perfect mechanical coin flip. Otherwise you're falling in the no true coin flip fallacy.

Yeah, if I'm actually forced to use a coin instead of a computer system, I try to ping the thing off the ceiling and at least one wall (not in that order). Hitting various other things is a benefit, not a downside.

Re: Fair coins tend to land on the side they started (2023)

#45

Post by IncreasePosts »

mankyd wrote: post #29
NameError wrote: post #20

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 coi…

Importantly - 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.

The 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.

Re: Fair coins tend to land on the side they started (2023)

#46

Post by lisper »

FartyMcFarter wrote: post #42
ant6n wrote: post #34

Earlier quoted context omitted.

What if consecutive unfair coin flips are not independent?

Then 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.

It's also impossible to prove that a given coin is not being controlled by an AI. (Or a deity.)

Re: Fair coins tend to land on the side they started (2023)

#47

Post by vonneumannstan »

NameError wrote: post #41
legobmw99 wrote: post #31

Earlier quoted context omitted.

I’ve seen this attributed to John von Neumann, of all people

It 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.

Wait 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)

Re: Fair coins tend to land on the side they started (2023)

#48

Post by Vecr »

IncreasePosts wrote: post #45
mankyd wrote: post #29

Earlier quoted context omitted.

Importantly - 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.

The 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.

Nah, you can put in a rule to stop. It would be better to know ahead of time, but you don't need to.

Re: Fair coins tend to land on the side they started (2023)

#49

Post by magicalhippo »

IncreasePosts wrote: post #45
mankyd wrote: post #29

Earlier quoted context omitted.

Importantly - 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.

The 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.

> 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

Re: Fair coins tend to land on the side they started (2023)

#50

Post by FartyMcFarter »

lisper wrote: post #46
FartyMcFarter wrote: post #42

Earlier quoted context omitted.

Then 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.

It's also impossible to prove that a given coin is not being controlled by an AI. (Or a deity.)

Yes, 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.

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