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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
#12About 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…
> but less than that for single-zero roulette (27$).
This reminds me of the casino I was at with a fair roulette. Betting Black/Red and getting a zero meant all bets stayed for the next spin ;)
My winning strategy was to always bet the opposite color of a friend of mine.
Re: Fair coins tend to land on the same side they started
#13[dead]
Re: Fair coins tend to land on the same side they started
#14About 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?
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Re: Fair coins tend to land on the same side they started
#15I would have expected some variance between different currencies and denominations - but maybe that would need a lot more data.
If you read the original Diaconis, Holmes, and Montgomery paper you'll see why it shouldn't depend on this.
There's also the classic Gelman & Nolan https://www.tandfonline.com/doi/abs/10.1198/000313002605 "You Can Load a Die, But You Can't Bias a Coin", in case you're imagining more complex dynamical behavior.
Re: Fair coins tend to land on the same side they started
#16Von 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_...
Re: Fair coins tend to land on the same side they started
#17About 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?
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" in a way that causes a similar effect.
Re: Fair coins tend to land on the same side they started
#18About 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?
It’s in the paper:
> The standard model of coin flipping was extended by Persi Diaconis [12] who proposed that when people flip a ordinary coin, they introduce a small degree of ‘precession’ or wobble—a change in the direction of the axis of rotation throughout the coin’s trajectory. According to the Diaconis model, precession causes the coin to spend more time in the air with the initial side facing up. Consequently, the coin has a higher chance of landing on the same side as it started (i.e., ‘same-side bias’).
[12] Diaconis P, Holmes S, Montgomery R. Dynamical bias in the coin toss. SIAM Review 2007; 49(2): 211–235.
Re: Fair coins tend to land on the same side they started
#19Excellent ig nobel prize contender here
Re: Fair coins tend to land on the same side they started
#20About 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 e…
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 Kelly betting you'll get back to your starting $100 on average in 5000 flips, though. If you can take out a loan of $500 first, you can Kelly bet your way to even much faster, in an expected 700 flips. Whether this is worth the interest on the loan depends on how quickly you can find challengers to bet with.