Someone proposes the following bet to you. A symmetrical dice will be rolled only once. If is rolled, the challenger gets euros, otherwise, you get euros. The probability of rolling is and the probability of not rolling is , times bigger. Would you accept a bet? What would you do if the stake was euros? Understanding of the concept of probability will certainly help you in making a decision. What do these probabilities tell us about the actual roll of the dice? These probabilities give us a very good estimate of what will happen in a larger number of dice rolls. E.g. if we roll the dice times, the probability of to roll  predicts that in rolls will be rolled about of the time – somewhere around times, maybe a few times more or less. In any case, you can be quite certain that will not be rolled more than, say, times. So the challenger would win at most times and you at least times. You would earn at least euros (expected earnings are approximately euros). I would certainly accept a bet on dice rolls. But the challenger offers a bet for just one roll! Probabilities give us a very good estimate of what happens over multiple rolls, but they can’t tell us what will happen in a single roll. Then, they can only tell us which choice is more reasonable. Becasue it is times more likely that will not be rolled that that it will be rolled, we can say that it is times more reasonable to bet that will not be rolled than it will. However, if you accept the bet, regardless of the fact that your decision is times more reasonable than the challenger’s decision, the dice will be rolled and will appear or it will not — you will win euros or you will lose euros. For a euro bet I would accept that uncertainty, for a euro bet maybe (I would have to talk to my wife) and for a euro bet I certainly wouldn’t.

Here is a much more dramatic game: you can’t avoid the bet, the challenger is Death and the stake is very high – your life. However, within the game itself, Death gives you a choice. You can choose one of the two boxes. The first box contains numbers from to . If you choose that box, Death will randomly choose one number. If she chooses , she will take your life, otherwise she will spare you. The second box contains numbers from to . If you choose that box, Death will randomly choose one number here as well. If she chooses , she will take your life, otherwise she will spare you. The probability that a person will die if they choose the first box is one thousandth and if they choose the second box, it is one millionth. Which box to choose? As with a dice bet, in a larger population, such as a population of million people (for example, my country is that big), if everyone chooses the first box, about people will die, and if everyone chooses the second box, about will die. Therefore, at the level of the whole society, it is correct to make a recommendation or order that everyone must choose the second box. But what about an individual? Sometimes the choice that is good for a society in general does not have to be good for an individual (let’s just remember war times). Is the second box also a good choice for the individual? As with the dice bet, at individual level the probabilities cannot save us from uncertainty. They cannot predict what will happen to the individual, whether they will die or not, no matter which box they choose. But probabilities tell which choice is more reasonable, even how many times more reasonable. The probability that you will die if you choose the second box is a thousand times smaller than if you choose the first box. That’s why, despite the inevitable uncertainty, it’s a thousand times more reasonable to choose the second box. And that’s why in this game I would choose the second box.

Life and death in the age of the COVID-19 pandemic are far more complex than the previous game, but that game is a basic simple model that roughly determines what will happen to society and an individual. By choosing not to get vaccinated against COVID-19, the individual choses the first box where the probability of dying of COVID-19 is of the order of a thousandth. By choosing vaccination against COVID-19, the individual choses the second box where the probability of dying of the vaccination is of the order of a millionth. The construction of more complex models, which are more appropriate to the real situation and which are more precise, does not significantly change the inexorable mechanism of this basic model.

More complex models associate individuals with probabilities that are more suited to their specificities, e.g., age, specific health problems, or the social circumstances in which they live. For example, the probability of death from COVID-19 (which includes the probability to get COVID-19) is strongly influenced by adherence to epidemiological measures, not only by the individual but by the entire society, as well as the vaccination rate in the society. It is also important to know that probability itself is not associated with an individual but with a group to which they belong. For example, the probability that a resident of my country will die in a car accident within a year is of the order of ten thousandths (one hundred times greater than from the vaccination against COVID-19). This probability estimates what percentage of people in my country will die in car accidents within a year. However, for a resident that likes fast driving, the probability of dying in a car accident is higher. Now, this probability estimates what percentage of people in the group of fast-drivers will die in a car accident within one year. This probability better describes the chances of a fast driver to die, compared to the probability within the overall population. The probability of the narrower group to which an individual belongs better describes her chances. It is the same with a person’s chances in this pandemic. The more specific the group to which the person belongs, the probability of death from COVID-19 or from vaccination for that group is a more suitable measure of risk for the person. Ideally, the group should be so specific that, for example, the probability of death from vaccination is 1 (everyone in that group will die if they receive the vaccine) or 0 (no one in that group will die if they receive the vaccine). If science could find such a group for every human being then we would know exactly who is allowed to receive the vaccine and who is not. However, there are too many parameters involved and the processes are too complex for us to have a full understanding and the compete control over the outcomes. One could say that the probabilistic models we currently have about COVID-19 also measure our knowledge. If the model manages to describe a more specific group, then our knowledge is greater. In the time available and with the knowledge gained, the best that science can do at this point is to determine the probabilities of death from vaccination and death from COVID-19 for not very specific groups (as in the simple model described above), and to give general guidelines on behaviour, as well as  identify specific groups that could be highly vulnerable to vaccination or COVID-19 disease.

Science is not omnipotent but in situations like the current pandemic it is the best that our society can offer. We need to consult science when we make decisions, no matter of whether science gives us quite definite predictions or just probabilities. It is true that there is corruption in the scientific community. Huge amounts of money are being turned around in the pharmaceutical industry. But there is a far greater corruption in other communities, especially in those that are trying to convince us without any evidence that we should not get vaccinated. Unlike such communities where corruption, in addition to manipulation, has fertile ground, the nature of the scientific community is such that it suppresses and detects corruption. And science says that by vaccinating and adhering to appropriate epidemiological measures, we are protecting ourselves and those we love, as well as society as a whole.

To be vaccinated, or not to be vaccinated? It is wrong to think that if we are going to be vaccinated against COVID – 19 that we are unnecessarily exposing ourselves to the risk. The risk is already there, and vaccination is significantly reducing it. We cannot escape the uncertainty, but we can act reasonably. And probabilities help us do do so. If you have not been vaccinated and if there is not knowledge on whether you belong to the group that is vulnerable to vaccination, your by far the most reasonable decision is to get vaccinated.