50 authors in a paper about flipping coins?
Blind guess, it's cheaper and easier to recruit volunteers to flip a coin 7000 times if you promise them credit on the paper.
You are absolutely right :)
Fair coins tend to land on the same side they started
81–90 of 277 posts
Re: Fair coins tend to land on the same side they started
#82Von 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_...
ok but if the coin tends to land as starting then
1. starting from heads
2. flip heads
3. flip heads
4. starting from heads
5. flip heads
6. flip tails
take 5 = heads?
heads should still be more likely to occur than tails under this scenario, although, Zeno-like, with decreasing likelihood approaching zero over time?
on edit: of course Von Neumann's process has more restrictions, leading closer to fairness.
Re: Fair coins tend to land on the same side they started
#83About a year ago, we embarked on a quest to answer one of the most intriguing questions: If you flip a fair coin and catch it in hand, what's the probability it lands on the same side it started? Today, we are finally ready to share the results. Thanks to my friends, collaborators, and even strangers from the internet, we collected flippin 350,757 coin flips. We ran several "Coin Tossing Marathons" (e.g., https://you…
It becomes clear why there's a same-side bias when watching the video: https://www.youtube.com/watch?v=3xNg51mv-fk
These are fairly gentle coin tosses; barely going a foot into the air!
When I think of a coin toss, I think high and spinning fast (like the ones before sports games, where the coin goes into the air and lands on the ground, usually rolls a short way, and is collected on whatever side it landed). I would guess the 50.8% same-side bias would be much closer to 50% if the coins were tossed this way in the experiment.
Re: Fair coins tend to land on the same side they started
#84Von 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_...
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
Re: Fair coins tend to land on the same side they started
#85I 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 true if someone flipped without practice.
Re: Fair coins tend to land on the same side they started
#86Von 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_...
That's really cool. The key insight is that "The reason this process produces a fair result is that the probability of getting heads and then tails must be the same as the probability of getting tails and then heads, as the coin is not changing its bias between flips and the two flips are independent." So you have to make sure you always start with the same side up.
Re: Fair coins tend to land on the same side they started
#87Earlier quoted context omitted.
Make a deal with all the banks or systems that can print money that would allow you to take an infinite loan from them. Then just double the bet every time you lose. If they can print money, why not infinitely as you will always pay it back anyway, so you don't have to worry about introducing inflation. There will always be a point when you can just burn the money that you temporarily introduced.
...from where does the money come that you pay back? Even if you have an unlimited stake, your winnings will be constrained by the counterparty eventually.
Right, I forgot, you also need someone willing to take those bets. So I think what you should do is make bets against multiple casinos/institutions where you can develop an algorithm that will find you an optimal method of betting for reasonable 50/50 results, if it makes easier to think. So for example at some point you might want to go to a casino and put the max bet on a single number in roulette, but do it enough times that you would have 50% odds of winning.
Once that is exhausted, you would have to become more creative, like trying powerball enough times, but I'm not sure how good the odds are there vs the reward. Maybe that wouldn't ever work.
Actually, I forgot. You can just play with highly leveraged options. It's not infinite yet, but come back to me until you've multiplied enough times that even options are not enough.
Forget everything I said before, just play with options and automated algorithm to buy more. And post here once you can't buy any higher cost options, and we'll figure something out together.
Re: Fair coins tend to land on the same side they started
#88Earlier 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
Some of us suck at math.
Re: Fair coins tend to land on the same side they started
#89Earlier quoted context omitted.
> That's amazing, but I guess it won't help when the person can choose the bias? Alice writes on a piece of paper whether to use the result from the first or the second coin, Bob flips the coins however he likes, then once there are two different sides of the coins up, Alice turns over the paper and reveals to Bob which coin contains the result. Though I guess that unnecessarily complicates the procedure – maybe Alic…
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.
Re: Fair coins tend to land on the same side they started
#90Thank you for this. I'll make sure to request a best of 350,757 next time I'm deciding anything by coin toss.
It’s 50.8% bias, so you only need to do best of 1015!