Scientists Just Proved Coin Tosses Are Flawed Using 350,757 Coin Flips

Everything you knew about coin flipping is wrong.

In 2007 a paper by Diaconis-Holmes-Montgomery developed a theoretical model of coin flipping and suggested human coin flipping results in a bias towards showing the same side. Just now, researchers conducted perhaps the largest coin flipping experiment in history by flipping coins 350,757 times and they confirmed this bias exists.

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

Images Creative Commons BY or public domain
Diaconis, Persi, Susan Holmes, and Richard Montgomery. "Dynamical bias in the coin toss." SIAM review 49.2 (2007): 211-235.
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[pierrecurie]

I recall reading many years ago that most coins do have a bias because heads/tails are not perfectly symmetrical, with 1 side slightly heavier. However, this bias appears at the 1 part in 10k-100k level, so is completely drowned out by the same side bias.

[robertzarfas]

I spent weeks in middle school practicing flipping a coin to make it look like it was flipping when it reality it was just spinning while remaining with the same face up. It worked about 60% of the time. Won a lot of bets.

[bosstowndynamics]

A note on coin flip strategy - some people routinely flip the coin upside down (usually catching the coin and then slapping it face down on the back of their other hand) - in that case you should bet on the opposite side instead

[efi]

You can make the coin toss a little more complicated to ensure that it's fair:
Flip the coin two times. If it shows heads-tails, you win. If it shows tails-heads, your opponent wins. If it shows the same side twice in a row, repeat the process. That way, whatever the probability p of heads is, your chance of winning is p*(1-p), while your opponent's chance is (1-p)*p.

[heitortremor]

Very important for when I go on a coin flipping marathon competition with my friend

[Lord_Skeptic]

It is the 50/50/90 rule.
If you have a 50/50 chance of getting something right there is a 90% chance you will get it wrong.

[JLvatron]

This proves the fairest way to decide is
“Paper, Rock, Scissors!”
From Ernest Goes to Camp

[Pufferfish_Pond]

And here I was thinking the bias would be from the two sides not using the same amount of metal for the patterns and therefore being weighted

[JoeyTM]

2:18
"So how do we decide whether to start heads up or tails up?"
"Iunno, let's flip a coin."

[DownDance]

Tossing a coin digitally is practically also not really random, but probably not foreseeable for a normal human

[jamesfunk]

The coin tosses I've seen for NFL games are not caught in the hand. The coin lands on the turf, and the referee looks at it and announces the result.

[Ima-hoot]

I’ve been flipping a coin with more than 51% success on same side for years ! Introduce even more horizontal spin by not flipping directly up !

[torbtrick]

start with heads up, then flip. if it’s heads, leave it heads up then flip again, if (the first flip) is tails, turn it heads up then flip. if the first flip is heads and the second flip is tails, side A wins, if the first flip is tails and second flip is heads, side B wins. any other scenario and you restart from scratch.

[alastairchestnutt]

The way that coins are tossed here is that they are tossed, caught and then turned over onto the back of the hand. That would give a bias to the opposite side.

[napoearth]

Why is this surprising. No coin is perfectly balanced, and they're not being tossed in a vacuum and with identical force.

[philrobson]

You can’t bias a coin but the side of bread with the jam and peanut butter usually falls jam side down.

[SvdSinner]

I'm still waiting for the coin flipping study that flips enough coins to have at least one coin land on its edge and balance there.

[PringoOrSomething]

I’ve noticed that when I flip a coin I always get it to land on the same side

[multiwebinc]

When I flip a coin, I catch it in one hand and then flip it onto the back of the other hand, so the bias would actually be the other way.

[kimsmoke]

A coin toss depends statistically on the center of mass relative to the geometric center plane.