Given the following assumptions:
A. A priori, there is a probability greater than 0 for the multiverse option (infinite universes), but this probability is smaller than the probability of a single universe (for example: 20% for a multiverse and 80% for a single universe).
B. A person is asked: “Are you in a multiverse or in a single universe?”
C. That person’s goal is to give the correct answer.
C1. Suppose that if he gives the correct answer he gets a million shekels, and if he is wrong he dies (the questioner somehow knows with certainty what the correct answer is; it doesn’t matter how—for the sake of the discussion, it’s some kind of magic).
D. There is no way to perform an experiment or do anything else to check the nature of the universe or gather empirical results in any way. All this hypothetical person has available are the assumptions written here.

Is it preferable for the person to answer 1) multiverse or 2) single universe?
The claim made in the video is that from the person’s perspective there is a greater chance that he is in a multiverse. After all, if we “run” an experiment in which the person always gives the same answer and we check both answers, we will see that he will succeed in answering correctly an infinite times 20 out of every hundred trials on average, and be wrong only in 80 out of every hundred on average if he always answers multiverse, and he’ll get the opposite results if he always answers the opposite.
So from his perspective within the world, it is preferable for him always to answer multiverse, even though a priori there is a higher probability of a single universe.

A. If you’re talking about infinite universes, then you’re in completely undefined territory. So first you have to define what exactly you mean:
1. The number of universes is not infinite. Maybe you mean very many. How many?
2. What distinguishes different universes from one another? Different laws of nature?
B. What does it mean to be in a multiverse? I am in a certain universe. Do you mean to ask whether there are other universes that I am not in?

Why should I care what it is preferable for that person to answer? The question is what is true.
Who are the people you’re asking? Is each one in a different universe?

In short, either I didn’t understand the argument, or there is no argument here.

Just out of curiosity, what do you think the correct solution is to the Sleeping Beauty problem mentioned in the video:
https://he.wikipedia.org/wiki/%D7%91%D7%A2%D7%99%D7%99%D7%AA_%D7%94%D7%99%D7%A4%D7%94%D7%A4%D7%99%D7%99%D7%94_%D7%94%D7%A0%D7%A8%D7%93%D7%9E%D7%AA

Is it one-third or one-half? (Or one-quarter?)

If I have time later, I’ll think about it a bit more concretely. For now I’ll say that from my experience with these kinds of paradoxes, the answer depends on how you define the experiment. Try to think about an actual experiment, and how and when you ask Sleeping Beauty your question (mainly what changes between the experiments and how you randomize the different situations), and I assume you’ll get both answers in two different experiments. By the way, in principle I think it’s possible to carry out a similar experiment in practice as well (without beauties and date-rape drugs, of course) and test it.
This reminds me a bit of the Monty Hall door experiment (there too there are two possibilities, 1/2 or 1/3).

For the sake of the discussion, a very large number like a billion would certainly suffice.
For the sake of the discussion, let’s assume the laws of nature are identical (you could also just take only part of the set of universes and refer only to them). The state of the world is probably similar, though not necessarily identical (you can also go with a version in which the state of the world is identical).
B. Yes, “are there other universes that I am not in?”

Why should I care what it is preferable for that person to answer?
– What is meant by that is that we are measuring from that person’s perspective. As an outside observer, I might count the entire multiverse as one unit.
Who are the people you’re asking? Is each one in a different universe?
– I am asking one person. He does not know whether there are other universes or not. What I wrote is a thought experiment that that person can use in order to reach an answer.

Your attempt to answer illustrates very well just how poorly defined the question is.
If all the universes have the same laws, then why not say that all of those are one universe? For example, I am in the universe of Earth and you are in the universe of the moon.
Beyond that, if you assume that each person being asked is in a different universe, then you have already assumed that there are many universes. The experiment you proposed begs the question.
You still haven’t explained why I should care what it is worthwhile for him to answer.