I am not impressed by this paradox: https://manifold.markets/dreev/is-the-probability-of-dying-in-the

Is the probability of dying in the Snake Eyes Paradox 1/36?

93% chance. You’re offered a gamble where a pair of six-sided dice are rolled and unless they come up snake eyes you get a bajillion dollars. If they do come up snake eyes, you’re devoured by snakes. So far it sounds like you have a 1/36 chance of dying, right? Now the twist. First, I gather up an…

If you start with a finite number of people and explain carefully what you do if you take all of them, there does not seem to be any paradox. If you set up the parameters in such a way that the expected number of people you take is finite, there does not seem to be any paradox. In Saint Petersburg paradox, if you say you cannot win more than C dollars for some C, there does not seem to be any paradox. Or am I missing something?

I think that approximating finite problems with infinite models may be very useful, e.g. I find the central limit theorem and approximating the binomial distribution by Gaussian very impressive. But looking at the Snake Eyes Paradox or Saint Petersburg Paradox, I see a question that makes sense in the finite world being generalized to the infinite world in a very fishy manner (what does it mean you started with a literally infinite number of people? Is it supposed to be an approximation of a very large number of people? But then where is the paradox? ). Why should I care about these paradoxes?

I see an abstract reason: if I am impressed by at least some infinite math like Gaussian distribution, I should hope that mathematicians will make sense of the questions like "in which situations can you take limits of finite models?" or "When can you sum infinite series?" etc. Any other reason?

This question resolves YES if I will be substantially more impressed by the Snake eyes paradox or St. Petersburg paradox than I am now. I will be very happy to change my mind as I am a big fan of probability, I just don't see a reason why should I be impressed other than the abstract argument above. I will not bet on this question.