# Heads or tails is a fair way to draw lots? Appearances can be deceiving, as is evident after tossing a coin 350,000 times

Place a coin with heads on top of your thumb, then toss it up, and often times it will also land with heads on top. If you start with tails up, it will often land with tails up.

to an experience From the University of Amsterdam, scholars in various countries tossed the coins. This has sometimes happened with entire teams for 12 hours straight, in what is called “Coin toss marathon‘. This allowed statisticians to eventually make their calculations on more than 350,000 tosses of different types of coins.

Result: If the coin starts with a tailspin, there is a 51 percent chance that it will land back in your hand with a tailspin. If your starting position is “head up,” there’s a 51 percent chance you’ll land on your toes again with your head up.

### Percy Deacon

Percy Diaconis once predicted the miraculous outcome. This statistician from Stanford University, among other things, stuck dental floss to the coins so that he could later read from the number of turns of the floss how many turns the coin had made. Diaconis describes how more factors play a role in throwing than just spin speed and upward vertical force. Coins also tend to fluctuate in the air.

“A good magician knows this,” says Erik Jan Wagenmakers, a professor at the University of Amsterdam and one of the authors of the new study. “A magician can toss a coin and catch it with the same side every time. The trick is that such a coin doesn’t tilt, but just swings like tossing a pizza, but you don’t see that with the coin because it’s moving so fast.”

The fluctuation factor is the deciding factor in why coins landing heads, even with a fair toss attempt, often land a little. Wagenmakers: “The difference is minimal.” Diaconis was delighted when we sent him our results: he predicted exactly 51 percent based on the theory. Although he’s the kind of scientist who would also have found it interesting if we had come up with a different percentage.

### “Very strong result”

Kasper Albers, a professor of statistics at the University of Groningen, who was not involved in the new study, speaks of a “very robust design,” with “very strong results.”

The Groningen professor now wonders to what extent lottery is a fair way to draw lots. “Maybe from now on the referee at the halfway point should roll the dice to decide which team can kick or choose which half of the pitch.”

WagonMakers hopes this study will have a chance in the next round of the IG Nobel Prizes, the alternative Nobel Prizes reserved for research that first makes people laugh and then provokes thought. Finally, he points out that all researchers conducted this study in their spare time, without any research funding. “Otherwise the reaction would undoubtedly have been: Are these scientists doing this with my tax money?”

Watch here, for 12 hours straight if you wish, as scientists toss and catch coins.

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