Statistics: Coin toss is not fair – Knowledge

A coin toss is an example of a random event: there are two possible outcomes, heads and tails, and both occur with 50 percent probability. At least that’s what we thought so far. But this is not the case, there is an anomaly – and it does not occur due to the rare case in which a coin falls on the edge and does not fall out. What the group led by Dutch mathematician Erik Jan Wagen Makers of the University of Amsterdam has shown experimentally is that the probability that the side that was up before the coin is flipped will be up again after the coin is flipped up is not exactly 50 percent, as one would expect. But it is 50.8 percent. The research group reached this conclusion in an article uploaded to the preprint server Arxiv.

The sheer number of samples shows that a 0.8% deviation does not represent statistical fluctuation. In order to replicate the coin flip experiment enough times, 48 ​​test participants flipped 46 coins of different currencies and values. First, five undergraduate students each performed at least 15,000 coin tosses and recorded the score. Next, 35 volunteers participated in a twelve-hour coin-flipping marathon.. Finally, other participants followed an invitation to flip coins that had been shared on social networks. A total of 350,757 coins were thrown.

The analysis initially showed that the tossed coins landed on one side or the other with approximately the same frequency. In 175,420 tosses, the coins landed on the head side, which corresponds exactly to about 50 percent – so there was no indication of a “head-tail bias,” that is, coins generally landed preferentially on a particular side, for example because Parity. Lateral weight distribution. However, which side was on top at the beginning of the coin toss had an impact on the outcome: that side was likely to be on top again at the end of the coin toss. Experts talk about “same side bias.”

There is a force that is also responsible for making the Earth Egg

This phenomenon is not completely unknown. This was theoretically predicted in 2007: At that time, Stanford mathematician Percy Diaconis, in collaboration with statistician Susan Holmes and mathematician Richard Montgomery, designed a model, which should be able to predict coin tosses in detail. One factor was the so-called initiative. This means that the side of the coin that was up before the flip will turn up again after the flip with a 51 percent probability.

In physics, precession describes a behavior familiar to spinning tops: If a spinning top is pushed slightly, its axis of rotation tilts to the side. As long as the top rotates fast enough, it will not fall; Instead it rotates around the inclined axis of rotation, which in turn rotates around a plumb line. Thus the direction of the rotation axis changes. A wide range of things prevail in nature, not least the Earth. But nuclear spins in human body molecules can also cause them to spin in a tilted manner.

In the case of a coin toss, precession occurs when the coin is not flipped exactly in the middle. Then it stops in the flight phase, this makes it spend a little more time in the original direction and therefore land in the way it was clicked the most. The oscillation of the coin is almost impossible to see with the naked eye – which is exploited by magicians and con artists who can flick the coin so that it does not spin on itself at all, but merely oscillates.

The Wagenmakers-led group now writes that the assumption known as the “DHM model” according to Deaconis, Holmes, and Montgomery has been shown to be correct: The 50.8 percent identified would agree well with the 51 percent predicted by the model. Diaconis wrote in 2007 that it would take at least 250,000 coin tosses to confirm the model experimentally. But clearly he and his companions did not want to get into this problem themselves.

Is the coin flip outdated as a decision-making tool? not necessarily. The result is distorted. But to compensate for this, soccer referees can simply hide the existing side of their coin before tossing it – and before the team captains lining up to pick sides make their choice. There is another difficulty for captains, however: they have to anticipate that the umpire will catch the coin and slap it on the back of the other hand. Then the side that was previously at the bottom is at the top.