How is that possible when both outcomes have a probability of exactly 50%?
How did you determine that both outcomes have a probability of exactly 50%?
Fair coins tend to land on the same side they started
51–60 of 277 posts
Re: Fair coins tend to land on the same side they started
#52Earlier quoted context omitted.
What is the physical explanation for this bias?
I would guess it's rather mathematical. Each coinflip has some number of half-flips. Now analyze the distribution of that number. If this distribution were to start at its maximum with 0 half-flips and decay as it increases, summing over the even values (same side up) clearly gives more than summing over the odd values. Now the distribution isn't going to be like that, but I expect that it's generally "front-loaded"…
Yeah, and seeing that the bias occurs only in some people, perhaps it occurs in people who do as little rotation as possible. Not sure if this study has a graph including amount of rotations occurred in general. E.g. you could take all coin flips where 0-5 rotations occurred and compare them to 6-11 rotations.
Re: Fair coins tend to land on the same side they started
#53Re: Fair coins tend to land on the same side they started
#54Based my back-testing of stock market, I found a similar conclusion: if a stock rise yesterday, then today the probability of raise > the probability of fall. P(raise) is about 50.1%, P(fall) is about 49.9%. Vice versa. Having this theory means you can't rely on a single bet, you have to bets many many times to make profit from stock market. Even though I knew that, I am still working as a developer, I wish one day I…
> you have to bets many many times to make profit from stock market
You also have to take into account transaction fees and broker spread. (If you get a great deal on one of these, check the other very carefully!) I'd be quite surprised if the edge on your system is enough to cover those.
Re: Fair coins tend to land on the same side they started
#55Earlier quoted context omitted.
Alert: It's not going to be as simple as this to make money even with large numbers. So don't fret about not having the money and missing some golden opportunity. There are enough actors out there trying to develop complex algorithms to find an edge, and so there wouldn't be any simple edges like this left anywhere as they would be arbitraged away. If there is a simple pattern, it is noticed and traded until the patt…
Has hmate9 pointed out, a simple pattern like the one described can persist indefinitely – but the risk of exploiting it is priced in already.
Yeah, you could find a pattern that wins 99% of the time to yield 1% of what you risk, but you don't consider that there's always 1% odds of losing it all and it's priced in, it just hasn't happened to happen yet, but systems with more precise data have accounted for it.
E.g. something like selling 0dte options sufficiently out of money might seem like a free money hack, but once something unexpected happens you are down to just "who could have possibly foreseen that event to occur, my decision making was solid.".
Re: Fair coins tend to land on the same side they started
#56I 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-Tail sequence.
Edit: The sequence was meant to represent the sequence of head and tail facing up during the rotation. A sequence of [H, T] denotes one full rotation, starting with head. [T, H, T, H] denotes two full rotation, starting with a tail, ends with a head. I didn't mean the result of a flip. So the result of a flip is the final element of the sequence.
Re: Fair coins tend to land on the same side they started
#57How is that possible when both outcomes have a probability of exactly 50%?
An ideal coin flipped by an unbiased super person would have that 50% probability. A real coin flipped by a real human no, as the study shows. Let's consider a spherical cow...
It's simpler: an ideal coin flip is simply assumed to be uniformly distributed, on the basis of there being two possible outcomes and no influence. Where the bias in reality comes from, doesn't matter.
This also happens to be the great divide between frequentists and Bayesians.
Re: Fair coins tend to land on the same side they started
#58I 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…
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Re: Fair coins tend to land on the same side they started
#59Earlier quoted context omitted.
You could read the Diaconis paper?
It is paywalled so I can not. However, I was unaware that they already conducted said experiment. I am now left confused as to why they would not mention such in the abstract, and refer only to natural experiments and second order measurements. I shall aquire the paper and learn why.
Using Google Scholar (1), you can find PDF versions of the paper
(1) https://scholar.google.com/scholar?cluster=16877003867074896...
Re: Fair coins tend to land on the same side they started
#60I 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...