Coin flips may not be 50/50 chance - study with 350,757 flips

[underpants]

Coin toss not so random after all, says groundbreaking study

Researchers at the University of Amsterdam recently made a surprising discovery that challenges long-held assumptions about the randomness of coin tossing. After flipping coins over 350,000 times, the largest study of its kind, they found that coins have a slight tendency to land on the same side they started on.

The data showed a small but statistically significant same-side bias of 51%, just slightly higher than the 50% predicted by chance. This subtle yet remarkable finding defies the conventional wisdom that coin flips represent a random and unpredictable 50/50 outcome.

Coins of 46 different currencies were flipped by hand and caught in the palms of 48 student participants to record the landing side. The data collection process required meticulous recording over many months, with flipping sessions videotaped to validate the results.

From the paper:

Could future coin tossers use the same-side bias to their advantage? The magnitude of the observed bias can be illustrated using a betting scenario. If you bet a dollar on the outcome of a coin toss (i.e., paying 1 dollar to enter, and winning either 0 or 2 dollars depending on the outcome) and repeat the bet 1,000 times, knowing the starting position of the coin toss would earn you 19 dollars on average. This is more than the casino advantage for 6 deck blackjack against an optimal-strategy player, where the casino would make 5 dollars on a comparable bet, but less than the casino advantage for single-zero roulette, where the casino would make 27 dollars on average. These considerations lead us to suggest that when coin flips are used for high-stakes decision-making, the starting position of the coin is best concealed.

https://boingboing.net/2023/10/10/coin-toss-not-so-random-after-all-says-groundbreaking-study.html

Link to the study

Fair coins tend to land on the same side they started: Evidence from 350,757 Flips

https://arxiv.org/abs/2310.04153

[LuckyCharms]

1. As a coin collector, this interests me.

I didn't read the article yet, but I'm wondering if it has to do with the distribution of the weight of the metal on the obverse of the coin vs. the reverse.

In other words, I'm wondering if the coins are the same weight and balance on both the front and back.

[underpants]

2. They used 48 different currencies

I heard that on a radio show. Different denominations in each I’m guessing.

[Ferrets are Cool]

4. I dont think so.

The article said that the % was higher for whichever side the coin started.

[LuckyCharms]

15. That still makes me wonder if coins are generally minted with a consistently heavier

side, regardless of the type or denomination.

[Ferrets are Cool]

25. I THINK the heads are heavier.

That is the relevant thought.

[roamer65]

5. Would be interesting to see a study of our present cupronickel clad vs older 90 pct silver coin.

I bet you would be curious as well like me.

[LuckyCharms]

13. I would like to see that as well.

[sl8]

8. The authors say they observed no head/tails bias. nt

[LuckyCharms]

14. Overall, or within each individual coin type that they used?

Sorry, just thinking out loud. Trying to do 50 things at once here. I'll check out the article later.

[sl8]

16. Not sure, I only read the abstract.

Note that they say they observed the difference with some (human) flippers, but not all.

Study (pdf) download link here:

https://arxiv.org/abs/2310.04153

ABSTRACT

Many people have fliipped coins but few have stopped to ponder the statistical and physical intricacies of the process. In a preregistered study we collected350,757coin flips to test the counterintuitive prediction from a physics model of human coin tossing developed by Persi Diaconis. The model asserts that when people flip an ordinary coin, it tends to land on the same side it started – Diaconis estimated the probability of a same-side outcome to be about 51%. Our data lend strong support to this precise prediction: the coins landed on the same side more often than not,Pr(same side) = 0.508, 95% credible interval (CI) [0.506,0.509],BFsame-side bias= 2364. Furthermore, the data revealed considerable between-people variation in the degree of this same-side bias. Our data also conf i rmed the generic prediction that when people flip an ordinary coin—with the initial side-up randomly determined—it is equally likely to land heads or tails: Pr(heads) = 0.500, 95% CI [0.498,0.502], BFheads-tails bias= 0.183. Furthermore, this lack of heads-tails bias does not appear to vary across coins. Our data therefore provide strong evidence that when some (but not all) people flip a fair coin, it tends to land on the same side it started. Our data provide compelling statistical support for Diaconis’ physics model of coin tossing.

[LuckyCharms]

18. Thanks for this. n/t

[no_hypocrisy]

3. In the theory of probability, there are three theories:

When you toss a coin, there is a 50/50 chance of the next toss coming up the same as the first toss.

Or when you toss a coin, the second time, it's random chance that it will be the same as the first toss.

Or when you toss a coin, multiple times, the chances of it will be the same will vary according to the number of times you toss it.

[Cuthbert Allgood]

27. Each coin flip is, in itself, 50/50

Certainly the probability of 10 heads in a row is low, but the odds of heads/tails on that 10th flip is still 50/50 (this study not withstanding). You might want to bet on regression to the mean, but, again, each individual flip is forever and always 50/50.

[Bettie]

6. Nice to see something light

around here.

Thanks for the break.

[underpants]

21. ❤️

I know nice been trying find some lighter but not Lounge stuff to post in GD.
https://www.democraticunderground.com/100218349391

I haven’t watched 2 minutes of news at home this week. I’m sorry for everyone involved but I don’t need to see it.

[Amishman]

7. My guess is it's a slight tendency to flip coins to a consistent height

With a similar rotation

[Hugin]

10. I haven't looked at the study yet...

To see if they were controlling for that condition.

On it’s face (pun intended) you could be correct. To get consistent results then there must be something consistent in the process.

Sometimes the simplest questions are the most difficult to answer. Like why a bicycle tends to remain upright when rolled forward. They have done experiments on that controlling every variable they can think of including centripetal forces and atmospheric interactions and there’s still no clear answer.

[Wednesdays]

20. In the case of the bicycle,

my guess is it's the same reason why a gyroscope stays upright. A bicycle has two large "gyroscopes" on it. It stays upright as long as it's rolling, and when the rolling ebbs, that's when it falls over.

[whopis01]

37. It the gyroscopic effect

But trying to explain why a gyroscope stays upright and resists motion is fairly complicated. And gyroscopes are fairly simple when it comes to rotating bodies because of their design, putting the majority of the mass into the rotating ring.

It gets even weirder when you have different mass distributions. Like this T shaped handle on the space station:

?si=XULx_n43N2n-kJDH

[Renew Deal]

9. Were different flipping techniques found to be more random?

[sl8]

19. Presumably. They report that it varied among the human flippers. nt

[edhopper]

11. It means coins are not perfectly weighted

between heads and tales.

[Cuthbert Allgood]

28. That's not what the study tested.

I had to do with which side was facing up pre-flip. There was no heads/tails bias.

[edhopper]

34. thanks

didn't read the whole thing.

[Old Crank]

12. I think it has more to do with the distance travelled

If you could flip a coin so that it turns over for 10 full rotations, Or any other full rotation number. it will land on the side it started on. If I were to care that I flipped a coin exactly the same way every time I would be able to have one side come up most of the time.
Which is why you probably want a neutral third party flipping teh coin if it is a meaning full decision.

[Disaffected]

22. That's the crux of the matter.

Last edited Wed Oct 11, 2023, 02:54 PM - Edit history (1)

It depends on the speed of rotation when flipped and the time the coin is in the air which determine whether it flips a full or half rotation before landing. That still doesn't explain though why the same side up seems to be slightly favoured.

Was any explanation offered?

[muriel_volestrangler]

31. Probably not about speed; a physical model had already predicted this, due to precession

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’). Based on a modest number of empirical observations (featuring coins with ribbons attached and
high-frame-rate video recordings) Diaconis [12] measured the off-axis rotations in typical human flips. Based on these
observations, the Diaconis model predicted that a coin flip should land on the same side as it started with a probability
of approximately 51%, just a fraction higher than chance

And there was significant variation by person flipping - from 0.487 'same side' to 0.601. It'd be interesting to check their methods, and if the most 'biased' had their thumb in a different position.

[Disaffected]

32. Very nice - thank you!

It would also be interesting to devise an automated coin flipping machine with random spin rates and duration. I expect then, the results would be also pretty much random.

[whopis01]

36. That's not the reason for the bias

If you had a machine that flipped it precisely the same way each time, I agree that distance would be the dominant factor. However these flips were done by people and a lot of different people, which should effectively randomize the distance travelled.


What they found was the bias is because when you flip a coin, you don’t rotate it exactly around a single axis. It rotates mostly around one axis, but has a slight precession around another axis. That causes it to spend slightly more time with the original side facing up.

[Iggo]

17. Yeah, but what if you flip them in a vacuum, huh?

Oh, wait…

[keithbvadu2]

23. Not enough sample size? Need more flips to get closer to 50/50?

[milestogo]

24. We have to appeal all those NFL games.

[Old Crank]

26. And all the World cup games that went to penalties

There are two flips there. First for goal choice and second for who kicks first.
The mechanic for that will have the ref hide the coin before the flip. Or as I used to do have it called in the air..

[underpants]

29. No air calls in the NFL anymore

There have been more than a couple instances in which Ref thought a player called heads but didn’t. They call it. Then it gets flipped. Yeah, they messed up flipping a coin.

[Disaffected]

33. How would calling it in the air help?

[Cuthbert Allgood]

30. "Tails never fails." Randy Moss

Lifelong Vikings fan, and I think about this clip a lot.
https://www.facebook.com/watch/?v=474710893809465

[hunter]

35. Never let a magician flip your coins or shuffle your cards.

They can do much better than 51%.

That's all I'm going to say.