In football matches, a coin toss is often used to decide who will take the kick-off. And on the face of it, that’s pretty fair.
Since coins have two sides and you add a random element (flipping and catching the coin), you assume that the one you choose has a 50/50 chance of landing. But researchers crunched the numbers by examining 350,757 coin tosses and found that wasn’t the case. So, it is possible to turn the odds in your favor, even if they are very small.
According to a team led by American mathematician Persi Diaconis, when you toss a coin you add a small amount of wobble to it.
Of the smaller number of coin tosses recorded and analyzed, Diaconis found that coins landed on the side they were tossed about 51 percent of the time. The team hired 48 people to flip 350,757 coins from 46 different currencies and found that overall the coin had a 50.8 percent probability of landing on the side it was tossed.
When they looked deeper into the data, they found that coin toss patterns varied widely across people, with some showing a strong same-party bias and others showing none at all.
We also found considerable variance in the same-side bias between our 48 tossers. The bias varied with a standard deviation of 1.6%, CI [1.2%, 2.0%], in our sample. The variation could be explained by a different degree of "wobbliness" between our tossers.
— František Bartoš (@BartosFra) October 9, 2023
Percentage margins may not seem like much, but they can lead to an advantage over time.
“The magnitude of the observed bias can be demonstrated using a betting scenario,” the team explains in their discussion. If you bet a dollar on the outcome of the coin toss (that is, you pay $1 to enter and win $0 or $2, depending on the outcome) and repeat the bet 1,000 times, knowing the starting position of the coin toss will earn you an average of $19.
Of course, the results of this research are quite controversial. But it might still be useful to keep it in a corner of your mind…
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