Fair coins tend to land on the side they started (2023)
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Fair coins tend to land on the side they started (2023)
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Re: Fair coins tend to land on the side they started (2023)
#2There's a nice presentation of the paper here https://www.youtube.com/watch?v=-QjgvbvFoQA
In essence the effect comes from "precession" - the tendency of the flip to not be purely vertical but to have some wobble/angular momentum which causes it to flip in such a way as to spend longer on one side than the other. Depending on the technique this will have a greater or lesser effect on the fairness of the coin toss, ranging from about p_same = 0.508 for the best technique to one person in the study actually exhibiting 0.6 over a large sample which is staggeringly unlikely if the toss was purely fair. In the extreme, it shows in the video a magician doing a trick toss using precession that looks as if it's flipping but does not in fact change sides at all, purely rotating in the plane of the coin and wobbling a bit.
The video is quite a nice one for setting out how hypothesis testing works.
Re: Fair coins tend to land on the side they started (2023)
#3I am curious how this changes if we condition on it flipping in the air at least once. Can we think of this result as a mixture distribution of a fair 50/50 chance of it flips at least once, and a delta function that is 100% at the side it started on, if not flipped at all?
Re: Fair coins tend to land on the side they started (2023)
#4This is clearly the law of conservation of reality at work.
Likewise, when you hear a word for the first time suddenly you hear it five times in a row. Or if you see somebody once you suddenly start running into them all over the place.
It's because it's cheaper to repeat past realities than to create new ones.
Re: Fair coins tend to land on the side they started (2023)
#5Winner of the 2024 Ig Nobel prize in probability [1]. A nice read as well!
Re: Fair coins tend to land on the side they started (2023)
#6This is clearly the law of conservation of reality at work. Likewise, when you hear a word for the first time suddenly you hear it five times in a row. Or if you see somebody once you suddenly start running into them all over the place. It's because it's cheaper to repeat past realities than to create new ones.
I don't think that's true, isn't this tested in a way to obviate that psychological effect? I've done coin-flipping in computer simulations and that doesn't happen. (And yes it was a bit more realistic vs a single element, multiple linked elements flip more realistically. No air resistance simulation though.)
Re: Fair coins tend to land on the side they started (2023)
#7This is clearly the law of conservation of reality at work. Likewise, when you hear a word for the first time suddenly you hear it five times in a row. Or if you see somebody once you suddenly start running into them all over the place. It's because it's cheaper to repeat past realities than to create new ones.
Or how when you look for something it always ends up in the last place you look, if it weren't there would have been some number of places you looked that were completely unnecessary.
Re: Fair coins tend to land on the side they started (2023)
#8There's a nice presentation of the paper here https://www.youtube.com/watch?v=-QjgvbvFoQA In essence the effect comes from "precession" - the tendency of the flip to not be purely vertical but to have some wobble/angular momentum which causes it to flip in such a way as to spend longer on one side than the other. Depending on the technique this will have a greater or lesser effect on the fairness of the coin toss, ra…
link to the "wobble flip" trick
https://youtu.be/-QjgvbvFoQA?t=325
Re: Fair coins tend to land on the side they started (2023)
#9you shouldn't bet on it though
Re: Fair coins tend to land on the side they started (2023)
#10This is clearly the law of conservation of reality at work. Likewise, when you hear a word for the first time suddenly you hear it five times in a row. Or if you see somebody once you suddenly start running into them all over the place. It's because it's cheaper to repeat past realities than to create new ones.
I don't think that's true, isn't this tested in a way to obviate that psychological effect? I've done coin-flipping in computer simulations and that doesn't happen. (And yes it was a bit more realistic vs a single element, multiple linked elements flip more realistically. No air resistance simulation though.)
Oh sure, let's doubt the evidence of our senses in favor of convention. That's good science.