Surely a shoe-in for an Ig Nobel

October 16, 2023 6:30 AM

48 people flipped 46 different kinds of coins a total of 350,757 times [PDF] to demonstrate that a flipped coin has a 50.8% chance of landing on the same side it started. This confirms a theoretical result from 2007 [PDF] which took into account precession, which is the fact that "the direction of the axis of rotation changes as the coin goes through its trajectory".

I hope that all the authors can come to the Ig Nobel prize ceremony and be yelled at by a little girl for talking too long.

posted by clawsoon (39 comments total)

"It must be indicative of something besides the redistribution of wealth."
posted by AlonzoMosleyFBI at 6:38 AM on October 16, 2023 [7 favorites]

Perhaps related to the tennis racket theorem?
posted by Brian B. at 6:41 AM on October 16, 2023 [1 favorite]

all these coin flips occurred in the northern hemisphere. i'm not saying coriolis effects definitely biased their results, but they can't be ruled out either
posted by logicpunk at 6:47 AM on October 16, 2023 [8 favorites]

I think this is a pretty big deal? A 0.8% advantage ain't nothing-- if you took every event where a winning coin toss has a psychological (penalty kicks in soccer?) or straight up advantage that bias has definitely caused some upsets.

At least I figure FIFA will have to define how to do a coin-toss in a way to hide the bias, players picking heads/tails before being shown the current state of the coin (though then the ref can influence the result!).

One thing I know is, I'm always going to pick what's face-up if anyone ever asks me going forward.
posted by Static Vagabond at 6:48 AM on October 16, 2023 [5 favorites]

How to they described landing? It it on a table,or something soft, or are they caught? A very quick read didn't answer this, but I can't see that it wouldn't matter. (But my science background is that I once saw Mr. Science on TV....)
posted by cccorlew at 6:51 AM on October 16, 2023 [1 favorite]

The hardest part of this experiment had to have been finding people with enough time and patience to flip a coin thousands of times. I hope at least a modest stipend was offered.
posted by tommasz at 6:52 AM on October 16, 2023

I think this is a pretty big deal? A 0.8% advantage ain't nothing

Indeed, it's a better house edge than the most conservative strategies at craps or blackjack, where casinos can afford to pay many people to stand around to collect it.
posted by Brian B. at 6:57 AM on October 16, 2023 [6 favorites]

I have been explaining statistical significance for years by pointing out that, in order to observe a 1% advantage in a coin flip, you would need to flip the coin about 10,000 times, because statistical power goes like the square root of the number of observations.

This group has done one step better by having fifty-ish independent runs of the 10⁴-scale experiment, a preregistered analysis protocol, and some other careful touches. I haven't read their analysis carefully, but a 10⁶-scale experiment should put their result in 2σ–3σ territory.

If you are in a situation where a 1% advantage is undesirable, just insist that the coin be flipped twice without examining the intermediate result, to dilute the advantage to (1%)² = 0.01%.

I was also amused by the "funding" paragraph.

Top notch science. I approve. (Username is relevant.)
posted by fantabulous timewaster at 7:05 AM on October 16, 2023 [18 favorites]

The "tennis racket theorem" doesn't seem to be relevant, because the symmetry of a well-made coin means it doesn't have three different moments of inertia. Instead, the physics seems to be that the coin spends more of its time in the air with the initial side facing upwards (which I think makes the landing surface irrelevant). The 2007 paper gives the extreme example of a "total cheat coin" which spins like a tossed pizza dough, never flipping even though it's airborne.
posted by fantabulous timewaster at 7:23 AM on October 16, 2023

If you are in a situation where a 1% advantage is undesirable, just insist that the coin be flipped twice without examining the intermediate result, to dilute the advantage to (1%)2 = 0.01%.

Really??
posted by mpark at 7:33 AM on October 16, 2023

the trick is successfully managing to not inspect the intermediate result
posted by bombastic lowercase pronouncements at 7:54 AM on October 16, 2023 [3 favorites]

I guess for this to be wrong, a large number of people would have to cheat on about 1% of their recorded coin flips. Which is some dedication to statistical fraud!

(If they did much more than 1% it would stick out like a sore shumb, or be small relative to total data. So we need people doing 1000s of flips to cheat 10s of times without being caught on video. The cheat could include selecting which videos to share with researchers, however.)
posted by NotAYakk at 8:06 AM on October 16, 2023

It takes a little digging, but you can find some videos on their data page under:

Files->Data->OSF Storage->videos
posted by clawsoon at 8:14 AM on October 16, 2023 [2 favorites]

If you want a fair flip, how about shaking the coin in a cup and dropping it. Much duller than doing everything by hand, but possibly worth it.
posted by Nancy Lebovitz at 8:30 AM on October 16, 2023 [1 favorite]

If you are in a situation where a 1% advantage is undesirable, just insist that the coin be flipped twice without examining the intermediate result, to dilute the advantage to (1%)2 = 0.01%.

Monty Hall in my coin toss?
posted by asnider at 8:49 AM on October 16, 2023 [1 favorite]

Could someone ELI5 why exactly this happens?
posted by gottabefunky at 9:34 AM on October 16, 2023

It seems to be a bias introduced by the conventional mechanics of flipping. As mentioned above, the extreme case is a tossed pizza that doesn't flip at all.

I agree with Nancy above that shaking the coin in a cup should eliminate that type of bias.
posted by SaltySalticid at 9:51 AM on October 16, 2023

This is a lot more flips (and probably better controlled) than a previous attempt during World War II, where they only flipped 10,000 times.
posted by Mogur at 9:57 AM on October 16, 2023

If you were bored as a kid in the pre-internet age, you might know it is not that hard to control the outcome of a flip with pretty good accuracy. (This is with a decent sized coin, the classic "toss and catch" flip, and once you've done four or five in a row.) Better than 51%.

I found a write up of one pretty relaxed study here. I don't think this approach is especially interesting, and con men have better ways to rig a toss.

Still, I'd be a little skeptical of the methodology where each person flips thousands of times, except they have a theoretical explanation that precedes the experiment. So I'm going to assume decent experimental technique.

I think this is a pretty big deal? A 0.8% advantage ain't nothing-- if you took every event where a winning coin toss has a psychological (penalty kicks in soccer?) or straight up advantage that bias has definitely caused some upsets.

Obviously it's huge if you could get someone to run a coin flipping game thousands of times in a row and you knew which side it was starting on. You could eventually break the bank.

In the real world things we use coin flips for, like who gets to ride shotgun or who kicks off in overtime in American football, you're dealing with other levels of randomization: Who gets to call the toss, whether they know this trick, whether they know which side up it starts on, etc.

I tried to estimate this for the NFL overtime kick, which has a pretty big impact (maybe 60/40) on who wins the game. Back of the envelope, if everyone used this strategy on every toss, it might have helped the visiting team win one extra game in the last 25 years.
posted by mark k at 10:04 AM on October 16, 2023 [5 favorites]

On the actual benefits of making large amounts of money from small anomalies, see the story of Joseph Jagger, "the man who broke the bank at Monte Carlo". (Snopes, Wikipedia). A story from the 19th century of a failed textile mill owner sat around a casino for months looking for the actual frequency numbers came up on a specific roulette wheel, then made millions (in today's dollar.)
posted by mark k at 10:14 AM on October 16, 2023 [3 favorites]

This is a great argument for making slightly biased coins, one for each side, to restore the expected value. Just don't get the two coins mixed up at experiments.
posted by They sucked his brains out! at 11:30 AM on October 16, 2023

For people asking about the double-flip, the advantage is diluted whether or not you examine the intermediate result, it's just that you don't want to examine it so that people don't get Big Mad if they called the intermediate result but not the final one. Unless probability is even more scary magic than I realize.
posted by Justinian at 1:31 PM on October 16, 2023 [1 favorite]

(Also you could obviously flip the coin more than twice. Every time you flip it dilutes another two orders of magnitude. After a third flip it's basically non-existent in practical terms.)
posted by Justinian at 1:41 PM on October 16, 2023

> For people asking about the double-flip, the advantage is diluted whether or not you examine the intermediate result, it's just that you don't want to examine it so that people don't get Big Mad if they called the intermediate result but not the final one.

oh, derp, yeah, you’re right. the person calling heads or tails calls before the first flip, so it doesn’t matter if they see the coin between the two flips. color me embarrassed
posted by bombastic lowercase pronouncements at 1:43 PM on October 16, 2023

It seems to be a bias introduced by the conventional mechanics of flipping. As mentioned above, the extreme case is a tossed pizza that doesn't flip at all.

Sort of? From the original theoretical paper, they seem to be working with a "large initial velocity and large rate of spin, a vigorous flip, caught in the hand without bouncing."

Makes sense that the math would be different if the coin were a pizza and the flip was a drop. It's an odd example of a "coin flip" though!

Also a bit biased in its own way. Everyone knows a dropped pizza will land sauce side down 100% of the time.

Which in turn reminds me of John Sladek's proposal to get levitation by strapping a piece of buttered toast (butter side up) to the backs of cats.
posted by mark k at 1:47 PM on October 16, 2023 [1 favorite]

I assume the thing the double-flip advocates aren't quite saying explicitly must be that the second toss is meant to use however the first one lands as the starting-position for the second toss (which...isn't necessarily the case when coins are caught in the palm, but tossed from the thumb, but I guess could be enforced as long as someone is looking at the first result and making sure it matches the second's starting position).

Or am I missing some counter-intuitive statistics nuance here?
posted by nobody at 1:54 PM on October 16, 2023

If my intuition about it is correct, you don't have to make sure the starting position of the second toss is the same as the result of the first toss, you just have to do the switch from catching the first toss to throwing the second toss in a non-biasing fashion. The easiest way would be to decide how you want to transfer the coin in advance and do it that way every time. It doesn't matter if that results in the starting position for the second toss being the same as the first toss or opposite that of the first toss as long as its the same every time.

I think it would also work if it was random as to whether it was the same or opposite but humans are very bad at doing randomness so better not to try.
posted by Justinian at 2:14 PM on October 16, 2023 [1 favorite]

I think that's actually a pretty good argument for not looking at the intermediate result even if theoretically it shouldn't matter. If you have no idea what the intermediate result is you can't subconsciously bias it.
posted by Justinian at 2:19 PM on October 16, 2023

fantabulous timewaster, get back here! We need an explanation!
posted by mpark at 3:26 PM on October 16, 2023

Fun read! "Wobbly tosser" sounds like an insult from a 70s British crime movie.
posted by Gorgik at 3:30 PM on October 16, 2023 [1 favorite]

The hardest part of this experiment had to have been finding people with enough time and patience to flip a coin thousands of times. I hope at least a modest stipend was offered.

Every one of the flippers, I kid you not, was made a co-author of this paper! All 50 of them!

Per:

For all but the last four positions, the authorship order aligns with the number of coin flips contributed.

And this is their only reward:

Funding

The authors have no funding to declare, and conducted this research in their spare time

You should really read the whole thing, it's chock full of gems

We collected data in three different settings using the same standardized protocol. First, a group of five bachelor students
each collected at least 15,000 coin flips as a part of their bachelor thesis project, contributing 75,036 coin flips in total.
Second, we organized a series of on-site “coin flipping marathons” where 35 people spent up to 12 hours coin-flipping
(see e.g., https://www.youtube.com/watch?v=3xNg51mv-fk for a video recording of one of the events),
contributing a total of 203,440 coin flips.3 Third, we issued a call for collaboration via Twitter, which resulted in an
additional seven people contributing a total of 72,281 coin flips

posted by 3j0hn at 4:22 PM on October 16, 2023

It's clear what they mean by bachelor above but I want to believe it meant unmarried because only unmarried losers had time to do this.
posted by Justinian at 4:41 PM on October 16, 2023

I think this is a pretty big deal? A 0.8% advantage ain't nothing

I immediately thought of applying to two-up, but the coins are flipped from a set starting position (one heads, on tails), so there's no real advantage that I can see.
posted by pompomtom at 5:09 PM on October 16, 2023

Can someone with more than a freshman level of stats tell me what this means?

A preregistered Bayesian informed binomial hypothesis test indicates extreme evidence in favor of the same-side bias predicted by the D-H-M model, BFsame-side bias = 1.71 × 10¹⁷. A similar (not-preregistered) analysis yields moderate evidence against the presence of a heads-tails bias, BFheads-tails bias = 0.168.

It sounds like they basically flipped a coin and got lucky with which analysis got run? Like if they'd pre-registered the alternate analysis no one would believe the paper? That can't be right though.
posted by mark k at 6:10 PM on October 16, 2023

It sounds like they basically flipped a coin and got lucky with which analysis got run? Like if they'd pre-registered the alternate analysis no one would believe the paper? That can't be right though.

The pre-registered analysis is for same-side bias, while the not-preregistered analysis is for heads-tails bias. I think what they're trying to say is that both analyses lead to the conclusion that there's a same-side bias but not a heads-tails bias.
posted by clawsoon at 6:15 PM on October 16, 2023 [1 favorite]

Thanks! I misread the point of that line.
posted by mark k at 6:42 PM on October 16, 2023 [1 favorite]

If you want to eliminate all bias, including any intrinsic bias in the coin itself, you can use the "Von Neumann randomness extractor":

From the same starting configuration each time (e.g., always starting with heads up for each flip), flip a coin twice in a row. If the flips are different, take the first flip. Otherwise, start over.

This works because regardless of what the actual probability is of H vs. T, the sequences HT and TH are equally likely (unlike HH and TT). Note that you must always flip in groups of two! So if your first two flips are HH, you need to totally discard those results and flip two whole new times. Note also that the more biased your coin is, the more flipping you'll expect to do before getting a result.
posted by Pyry at 8:51 PM on October 16, 2023 [12 favorites]

A 0.8% advantage ain't nothing-- if you took every event where a winning coin toss has a psychological (penalty kicks in soccer?) or straight up advantage that bias has definitely caused some upsets.

As others have hinted, hiding or randomizing the starting position should alleviate that.

I still think <300k flips sounds a couple orders of magnitude too small to draw conclusions, but I’m no numberwang.
posted by aspersioncast at 9:55 AM on October 17, 2023

Pyry, that's a great trick.
posted by fantabulous timewaster at 5:18 PM on October 17, 2023