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Fair coins tend to land on the same side they started

arxiv.org

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Re: Fair coins tend to land on the same side they started

#111

Post by SamBam »

helsinkiandrew wrote: post #85

I think you can argue that the experiment wasn't representative of 'normal' coin flips. On average, each flipper in that experiment flipped a coin over 7000 times, after that amount many people will have learned to flip in a comfortable way with less variance between physical action and force they use. I'd imagine that in that case the coin would more likely land with the same orientation. I don't think this would be…

I think this is a great point. One flipper 7000 times is quite different than 7000 flippers one time, if the aim is to see whether there is an underlying bias.

Re: Fair coins tend to land on the same side they started

#112

Post by taway_6PplYu5 »

bob88jg wrote: post #97
098799 wrote: post #84

Earlier quoted context omitted.

Why would you test it? Probability of two heads: p*p Probability of two tails: (1-p)*(1-p) Probability of head followed by tails: p*(1-p) Probability of tails followed by heads: (1-p)*p It's not difficult to notice that if you remove the first two, the last two form a 50/50 distribution

Why would you not - analytical solutions are the rare occurrences might as well approach everything with simulation...

(preface with "in today's world")

Re: Fair coins tend to land on the same side they started

#113

Post by arijun »

mewpmewp2 wrote: post #89
sebzim4500 wrote: post #73

Earlier quoted context omitted.

If you're going to go that way you can skip the coin flip entirely. Just get both of them to write heads or tails on a note and then compare. This technique is used in some crypto projects, except instead of writing on a note you share cryptographic commitments.

But they need to remove the possibility of a psychological guessing game. E.g. Bob could've researched before hand that people are 55% likely to pick heads if they can pick by themselves.

That doesn’t remove the possibility of a psychological guessing game, just makes it more convoluted. If Bob knows Alice will pick first, he can still bias the results.

Re: Fair coins tend to land on the same side they started

#114

Post by sidkshatriya »

098799 wrote: post #84
ChocMontePy wrote: post #69

Earlier quoted context omitted.

If anyone wants to test it, someone wrote a short code that simulates doing that 100,000 times: https://www.techiedelight.com/generate-fair-results-biased-c... The coin is biased to come up TAILS 80% of the time, but using Von Neumann's method in the program I got HEADS 50.035%, TAILS 49.965%.

Why would you test it? Probability of two heads: p*p Probability of two tails: (1-p)*(1-p) Probability of head followed by tails: p*(1-p) Probability of tails followed by heads: (1-p)*p It's not difficult to notice that if you remove the first two, the last two form a 50/50 distribution

The thing about math is that you can do things in multiple ways.

Theory is useful but so is experiment.

Re: Fair coins tend to land on the same side they started

#115

Post by m3kw9 »

jbandela1 wrote: post #16

Von Neumann described a very elegant way to get fair results from a biased coin. 1. Flip the coin twice 2. If you get the same result both times, goto 1 3. Now that you have different results for your pair of flips, use the first element of the pair of flips as your result. https://en.wikipedia.org/wiki/Fair_coin#Fair_results_from_a_...

Flip till I get the side I wanted

Re: Fair coins tend to land on the same side they started

#117

Post by toxik »

098799 wrote: post #84
ChocMontePy wrote: post #69

Earlier quoted context omitted.

If anyone wants to test it, someone wrote a short code that simulates doing that 100,000 times: https://www.techiedelight.com/generate-fair-results-biased-c... The coin is biased to come up TAILS 80% of the time, but using Von Neumann's method in the program I got HEADS 50.035%, TAILS 49.965%.

Why would you test it? Probability of two heads: p*p Probability of two tails: (1-p)*(1-p) Probability of head followed by tails: p*(1-p) Probability of tails followed by heads: (1-p)*p It's not difficult to notice that if you remove the first two, the last two form a 50/50 distribution

I think about it this way

p(th) = p(t) p(h)

p(ht) = p(h) p(t)

Hence p(th) = p(ht) regardless of coin imbalance as long as both events actually will happen. QED.

Re: Fair coins tend to land on the same side they started

#118

Post by kqr »

bob88jg wrote: post #97
098799 wrote: post #84

Earlier quoted context omitted.

Why would you test it? Probability of two heads: p*p Probability of two tails: (1-p)*(1-p) Probability of head followed by tails: p*(1-p) Probability of tails followed by heads: (1-p)*p It's not difficult to notice that if you remove the first two, the last two form a 50/50 distribution

Why would you not - analytical solutions are the rare occurrences might as well approach everything with simulation...

While I agree we should leave the correct answer to simulation, analytical approximations are often surprisingly close and have the benefit of being intuition-building.

Re: Fair coins tend to land on the same side they started

#120

Post by pirates »

aspenmayer wrote: post #71
Philip-J-Fry wrote: post #22

Earlier quoted context omitted.

After reading this the first thought I had was how do you stop people flipping the same way? Like, give me a baton and I could throw it at varying heights and control which side I caught it on. In theory the same applies to coin flipping. You can get quite consistent with your positioning and power. You could probably control for it by making people alternate which side was face up before the flip. That's my intuitio…

Your comment reminded me of two-up. > Two-up is a traditional Australian gambling game, involving a designated "spinner" throwing two coins, usually Australian pennies, into the air. Players bet on whether the coins will both fall with heads (obverse) up, both with tails (reverse) up, or with a head and one a tail (known as "Ewan"). The game is traditionally played in pubs and clubs throughout Australia on Anzac Day,…

Two-up sounds pretty fun. Your comment in turn made me think of Chō-han, which is somewhat similar but involves rolling dice instead of flipping coins. https://en.m.wikipedia.org/wiki/Ch%C5%8D-han
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