50 authors in a paper about flipping coins?
Fair coins tend to land on the same side they started
61–70 of 277 posts
Re: Fair coins tend to land on the same side they started
#62Earlier quoted context omitted.
The upshot is that as long as you only stake $1 at a time, you're unlikely to lose more than $50. On the other hand, /if/ you do, you'll have to play for 6000 more flips until you can be fairly certain that you're even again. What's worse is if, after having lost $50, you're down to your last $50, there's almost a 1/5 chance you'll blow all of it trying to recover if you wager $1 each time. If you grow wise and start…
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.
Re: Fair coins tend to land on the same side they started
#63I always tell people that result of coin flip is highly start state dependent. Imagine a sequence of H(ead), T(ail), H, T, H, T, ... if the sequence starts with H first, in no way can the number of T exceed that of H, but the number of H might be 1 greater that that of T. I never tested my self, but I hypothesize that the propability will be more skewed if the number of revolutions is less, i.e. having a shorter Head…
Can you toss a coin without it flipping at least once (changing state)? I find it quite unlikely to happen, so if the starting state was H, your sequence will be THTH...
I can't quite define what counts as start of sequence. Maybe a sequence should always have at least one element, and toss straight up is allowed. But if some flipping is mandatory, then the start of sequence would mean the other side of the coin. All I could deduce before this paper is the probabilty of coin flip is skewed.
Re: Fair coins tend to land on the same side they started
#64Von 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_...
I love the math/stats history around gambling-related things, thanks for mentioning this. This method assumes the flipper can't introduce bias. ET Jaynes in his book Probability Theory also mentions that it is easy to learn to flip a fair coin in such a way that the result can be predetermined. I searched a tiny bit for this but couldn't find what he was referring to though.
Lots of practice, use your thumb to hit the edge of the coin to give you more control, aim for a specific spot so you use the same amount of force and control the amount of times it flips. You can also use a surface that absorbs more so the coin is less likely to flip after hitting it.
Re: Fair coins tend to land on the same side they started
#65About 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…
Fun that you're showing your own work. Since this is your work, it could have Show HN in the title; I guess.
If there isn't a product one can try, it's not a Show HN material.
Re: Fair coins tend to land on the same side they started
#66I think the sporting approach of letting the coin drop to the ground rather than catching it is the answer to avoid bias in coin tossing.
Not neccessarily because spinning and bouncing coins are often much more biased then flipped coins. (Unequal weight distribution on the side can bias a spinned coin while it doesn not bias a flipped coin. There are a couple of studies on it too.)
Re: Fair coins tend to land on the same side they started
#67Von 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_...
I love the math/stats history around gambling-related things, thanks for mentioning this. This method assumes the flipper can't introduce bias. ET Jaynes in his book Probability Theory also mentions that it is easy to learn to flip a fair coin in such a way that the result can be predetermined. I searched a tiny bit for this but couldn't find what he was referring to though.
I’ve heard that, with many hours of practice, dedicated amateurs and many famous magicians are able to do this kind of thing. I wouldn’t call it sleight of hand, but it is similar, although it may fall under that category broadly. I’m not a domain expert but I was taught some simple coin tricks as a child by my artist mom’s artist friend who ran the local frame shop. I never tried or thought to try to favor the coin flip or introduce bias, but it’s definitely a skill that can be acquired.
Re: Fair coins tend to land on the same side they started
#68Earlier 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.
The Federal Reserve. They can print money arbitrarily.
Re: Fair coins tend to land on the same side they started
#69Von 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%.
Re: Fair coins tend to land on the same side they started
#70This is incredibly puzzling. Is there a minimum number of rotations per coin flip to consider it valid? If looks like the bias was not evenly distributed across people. How did you protect your experiment from skilled bad actors who could influence the data with a few bad/skilled flips? Did strangers on the internet fare any differently than in-person attempts from trusted people?
We told people that the coin has to flip at least once (which would bias it for the opposite site). Whenever instructing people, I tried to explaining that the coin flip should look like you were trying to determine an outcome of a bet.
You can find the complete experimental protocol here: https://osf.io/hkv8p
Also, I wish I had (any) budget to hire proffesional skilled tossers haha.