A logical fallacy in the argument arising from “God plays dice”

But can you give an example of an event that is so unlikely to happen that it is correct to assume that a supreme being was involved in it? Because so far the only thing I have found as an example of this is abiogenesis, which can also be applied to the theory of infinite universes, so that the probability does eventually become possible.

The multiple (not infinite) universes are irrelevant to the discussion. The question is who created them? And have you ever seen a random universe generator? This is a “turtles all the way down” type of explanation. And if you do think there is such a generator, then it is called God. Nice to meet you.
I also brought the example of the cube, and more on that path. For example, if you yourself roll a fair dice and suddenly get such a result. For example, if you hear a voice from above that teaches you the theory of quantum gravity and it turns out that you did indeed solve this complicated problem without any education in physics. In these cases, I would definitely consider the possibility that this is a supernatural event.

I think there is a difference between the lack of programming of abiogenesis and the lack of programming of a person to win the lottery 10 times in a row, as well as in the example of rolling the dice, since in rolling the dice and winning the lottery we know that there is still someone behind the draw or the roll, so we can point an accusing finger at him and say that he caused it to be so, while in the case of abiogenesis we have no prior proof that any entity exists.
Also, to the best of my knowledge, it is not enough to know about someone who won the lottery 10 times in a row to put him in prison without further evidence, but it simply raises suspicion a lot.
Am I right?

In my opinion, they are not correct.
You can refer and you can not. There are those who rolled the dice, but who said that there is someone responsible for the results? It goes without saying, so why blame anyone? Therefore, there is no fundamental difference between the cases. From the peculiarities, it can be deduced that there is an entity behind this phenomenon that is responsible for it.

So in a sense the physico-theological argument is a different formulation of the watchmaker's argument that we are familiar with, isn't it?
Or does the watchmaker's argument rely more on subjective feeling, compared to your argument which relies on more objective probabilities?

Indeed. I have written this many times. The arguments against Paley's watchmaker argument are incorrect.

I will quote here from Prof. Nathan Aviezer's book that shows the refutation of Paley's watchmaker's argument:
“Snowflakes are extremely beautiful crystals, with a complex and delicate structure. Each of them has a precise hexagonal symmetry, and each one is different from the next. However, we all know that there is no need for a snowflake designer. The delicate beauty of snowflakes is *not* created intentionally, but rather they are created naturally when suitable weather conditions prevail.”
He then also gives as an example a person who sees letters of the alphabet carved on trees in the forest, and from this concludes that some person wrote them. But in fact this inference is incorrect, since the reason he attributes a special status to these letters is his familiarity with the Hebrew language and his past experience with these signs. From the point of view of nature, nothing extraordinary happened here, and from this we understand that the inference is incorrect, since it is based on a subjective feeling.

He does say there that the refutation does not apply to the origin of the laws of nature themselves, but Paley's watchmaker argument does not talk about them, as far as I understand, but about the products themselves.

What do you think of these claims?

Sorry for posting in two posts, I just have a computer bug that prevents me from writing too much in one post.

I wrote this too. The evidence is from the laws and not from the phenomena.