The coin toss. It’s a tradition that dates back at least as far as the Roman Empire. It decided the name of Portland, Ore., which would otherwise have been called Boston. It determined which Wright brother would become the first to take to the air. (It was Wilbur, but his flight crashed, so Orville became the pilot of the first successful flight.) It decides the start of every Super Bowl.
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Now, scientists have determined that the quintessential 50-50 chance isn’t quite 50-50 after all.
That tendency was small and varied between individuals, but it was measurable. A flipped coin has a 50.8 per cent chance of landing on the same side up as when it was flipped, and a 49.2 per cent chance of landing the other way up.
The paper states that the reason for this discrepancy is that when people flip a coin, they introduce a small amount of “precession” or wobble, which causes the coin to spend more of its time in the air with the initial side up. Thus when it comes down, the likelihood of it being same-side-up is a little higher.
This wobble theory had actually been outlined in a 2007 paper, but it had never been accurately measured across so many tosses.
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Earlier scientists had conducted relatively large-scale studies — the paper mentions English mathematician Karl Pearson’s 24,000 flips in the 19th century, and John Kerrich’s 10,000 flips in the 20th, while interned in Nazi-occupied Denmark, no less. Alas, neither man made note of which side the coin started on, or whether a single side was chosen.
Determined to do better, the researchers gathered together 48 people using coins from 46 different currencies to perform 350,757 flips, “a number that — to the best of our knowledge — dwarfs all previous efforts,” they state modestly. The paper contains a link to the raw data and video of the flips, suggesting that the authors may have also stumbled on a possible cure for insomnia.
An important note is that they did not find any evidence of a heads or tails bias in the coin tosses. In other words, a large number of coin tosses will still average out to 50-50, assuming that the starting side is also heads half the time, tails the other. But if you know in advance which side is up at the start, you can calculate a slight advantage.
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Also, the researchers noticed that some of the flippers tended to produce more or fewer same-side-up results, perhaps as a result of their individual style of flipping. But over the large sample, same-side-up was the winner. Heads by a nose, you might say.
“Could future coin-tossers use the same-side bias to their advantage?” the researchers ask? You bet!
Which is to say, if you bet a dollar on a coin toss, winning either $2 or nothing depending on its outcome, you’d be up $19 after a thousand flips. But only if you bet on the starting side up. “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.”
The authors of the paper add that they have no funding to declare, “and conducted this research in their spare time.” That’s almost as impressive as the results of the study.
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