Fair coins tend to land on the same side they started
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Re: Fair coins tend to land on the same side they started
#2About 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://youtu.be/3xNg51mv-fk?si=o2E3hKa-ReXodOmc) and spent countless hours flipping coins.
In short, we found overwhelming evidence for a "same-side" bias predicted by Diaconis, Holmes, and Montgomery 2007: If you start heads-up, the coin is more likely to land heads-up and vice versa. How large is the bias? In our sample, the mean estimate is 50.8%, CI [50.6%, 50.9%].
We also found considerable variance in the same-side bias between our 48 tossers. The bias varied with a standard deviation of 1.6%, CI [1.2%, 2.0%], in our sample. The variation could be explained by a different degree of "wobbliness" between our tossers.
If you bet a dollar on the outcome of a coin toss 1000 times, knowing the starting position of the coin toss would earn you 19$ on average. This is more than the casino advantage for 6-deck blackjack against an optimal player (5$) but less than that for single-zero roulette (27$).
The manuscript is at arXiv: https://arxiv.org/abs/2310.04153 And the open data, code, and video recordings at OSF: https://osf.io/pxu6r/.
Diaconis, P., Holmes, S., & Montgomery, R. (2007). Dynamical bias in the coin toss. SIAM Review, 49(2), 211-235. https://doi.org/10.1137/S0036144504446436
Re: Fair coins tend to land on the same side they started
#3About 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.
Re: Fair coins tend to land on the same side they started
#4About 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?
Re: Fair coins tend to land on the same side they started
#5Thank you for this. I'll make sure to request a best of 350,757 next time I'm deciding anything by coin toss.
Re: Fair coins tend to land on the same side they started
#6About 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…
This was my intuition in childhood. If you choose tails to be yours and start with tails then catch it, it is most likely to be tails. I came up with this observation myself. Weird.
Re: Fair coins tend to land on the same side they started
#7About 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.
No, not really.
Re: Fair coins tend to land on the same side they started
#8I would have expected some variance between different currencies and denominations - but maybe that would need a lot more data.
Re: Fair coins tend to land on the same side they started
#9About 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…
>If you bet a dollar on the outcome of a coin toss 1000 times, knowing the starting position of the coin toss would earn you 19$ on average. This is more than the casino advantage for 6-deck blackjack against an optimal player (5$) but less than that for single-zero roulette (27$).
This sounds like the plot of a western where a man travels from town to town and gleans a little cash from the local waterhole a little every time. I did the math though, in order to get just the $19, assuming you played a modest 20 times a day, it'd take 10 weeks (not including weekends), and by that point people would definitely figure out your trick. In order to make any profit quickly, you'd have to distribute the strategy, after which your secret would explicitly be out there. Even assuming perfectly honest colleagues, having that many parallel people using the same strategy in the open means that before you turn any real profit, people will find out. It's a fun idea to fantasize about though.
Anyway, cheers on the paper! Pretty cool result that you guys put the effort in in implementing.
Re: Fair coins tend to land on the same side they started
#10About 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…
This was my intuition in childhood. If you choose tails to be yours and start with tails then catch it, it is most likely to be tails. I came up with this observation myself. Weird.
Yeah, I think you were just lucky that your superstition happened to be true.
Trying not to be disrespectful but I don't believe you intuited a 50.8 % bias. So nothing weird going on at all.