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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?
About 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…
What is the physical explanation for this bias?
You could probably control for it by making people alternate which side was face up before the flip.
That's my intuition anyway.
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_...
This 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?
Can someone who has access to a precision robot and controlled environment please check; if one applies the same force on the coin in flipping, with it landing on a (soft) surface at the same height it - will it land the same side every time.
Based 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…
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_...
Because according to the study the person can choose the bias by choosing which side start up.
So if the person wants tails based on what you've said, they should always
1. Do the first throw starting tails up.
2. If the first one is tails, then they now want to start second one heads up.
3. If the first one is heads, they will want to try and get heads again to dismiss the results. So they will do heads up.
So assuming for example that they have an ability to control bias 75% vs 25%.
Then there would be 75% chance of getting first as tails. After that 75% chance of getting heads.
So they will have 56.25% chance of getting it right the first 2 rounds.
The worst case for them would be if they get heads first (25% chance), and then are unable to get heads again. Which would be another 25% chance so 6.25% odds to lose with the first round.
So 56.25% chance of winning the first round of 2, or 6.25% losing and 37.5% of having to try again.
And I think the odds would converge at somewhere around 90% to 10%. I didn't do full calculations here, but overall it seems this strategy would increase the bias even more.