In the launch of the coin, is it better to choose head or cross? If we take a coin and launch it in the air, we expect them to come out head or cross with the same probability: 50 and 50. This, however, It is not entirely true. A recent study showed that it is more likely that comes out the same face that was found upward At the time of launch. For example, if when we made the launch of the coin, the face on the top was head, it will be slightly more likely to come out. The chances, therefore, would not be 50 and 50, but 51 and 49 in favor of the “starting” face. The experiment involved 48 people who have launched several coins for a total of 350 757 launch. The research is so absurd that it has earned theIG Nobela satirical prize awarded annually to celebrate the most unusual results in scientific research.
Launch of the coin: because the face upwards is important
The launch of the coin, known as “Head or cross”the most direct and common way to decide between two options has been centuries. The two contenders choose one face each – head and cross – the coin is launched and the verdict is accepted. The name of this method derives from depictions ancient engraved On coins: a head on the one hand (usually that of a sovereign) and one cross on the other. Just for its apparent impartiality, Making “head or cross” is the most used technique to choose between two equivalent options. Over time, several studies have analyzed the probability of exit of each side of the coin and in general have confirmed that the launch of a coin it is fair, If the coin is not made up.
In the 2007, However, a mathematical of the Stanford University and former illusionist, lost Diaconis, noted that previous studies had not considered the face turned upwards at the time of launch. Being a former illusionist, he knew perfectly that there are techniques used by the magicians to control the outcome of the coin launch. These techniques consist in simply swing during the flight phase, without ever making it rotate. In this way, the coin will always land with the same face upwards with which it was launched, but to those who observe the launch it will appear completely “regular”.
He therefore decided to take into account this oscillation, which takes place in a lesser also in “regular” launches, in the creation of the physical model of the launch of the coin. According to the model of Diaconis and its research group theoscillation of the coin (in technical terms “precession”) it causes the initial face remain revolt upward For more timeincreasing the chances that the coin falls with that face facing upwards. According to its model, the advantage given to the “starting” face would be of the1%. So, if at the time of launch the coin has “cross” upwards, there is 51% probability that Croce exits and the 49% that will exit head. The Diaconis study, however, explained this phenomenon only at the theoretical level.
The study that demonstrates the advantage of the upper face
In 2023, a Team of European researchers he decided to test Diaconis’ hypothesis with a experiment on a large scale. The goal was simple: check if, in practice, the coins Really “they prefer” The starting side.
The experiment was one of the most accurate ever made on the subject: he involved 48 people who, in total, carried out 350,757 launches use coins belonging to 44 currencies different. All by following an extremely rigid protocol: each participant performed 100 launches sequences starting on the one side known (head or cross), recording the outcome and using as the starting point for the next launch the side just released. To collect enough data, real “head marathon or cross“Long up to 12 hours. All the sessions were films And, to avoid errors or influences due to individual characteristics, the participants also exchanged the coins with each other, so as to distinguish the effects related to the person from those related to the type of money.
https://www.youtube.com/watch?v=3xng51mv-fk
The result confirmed the forecast of Diaconis: there is a light advantage for the face Of departure. They found that the coin “preferred” the starting face in the 50.8% cases. They also discovered that this percentage varies from person to person, because everyone launches with a slightly different strength and style, influencing the oscillation of the coin during the flight. This advantage is small but real, and on large numbers it can become relevant. If, for example, a coin was launched 1000 times, betting 1 euro per launch, knowing the starting side would allow you to get an average win of 16 euros.
After reading this study, it is spontaneous to ask if someone really was so crazy to finance this research. The answer is clearly not! The authors themselves want to underline that have not received funds For this research and which has been carried out in their free time.
