Now distribute 10,000 sided dice to 6 people, which will be an example just as relevant.

It sure makes sense to assume we're neither alone nor first, as until we actually prove it either way that's just what the odds are - but I'm tired of people acting like this means we're definitely not the first. If you gave 10,000 people a number between 1 and 10,000 in random order, the probability that any given person got number 1 is 1/10,000, and yet the probability that someone got 1 is 1.

(though there's another problem at play: "first" may not necessarily be a well-defined term at these scales)

In this analogy the unknown is the number of sides on the dice (probability of life), we know there are an astonishingly large number of stars and planets that life could evolve on, so a very large number of throws, we just don’t know how hard it is for life to emerge.

I agree with you the odds are strongly in favour of us not being first or unique. I didn’t say we must be first but find it very unlikely given the numbers.

Yes, and if the probability of life turns out to be even more astonishingly small number, you may very well end up with six 10,000-sided dice :)

My intuition tells me it's not like that, but it's nothing but intuition.

10,000 sided dice over 10^25 throws has a high probability of success for any given no.

But you've got six throws there.

It's the proportion that matters, not absolute numbers.

The dice weren't supposed to be a parallel to the odds of other life in the universe, but just about finding if you had any limits to your agnosticism.

The dice example is one where we can readily compute the probabilities.

The problem with origin of life is we can't do that with the information we have. It's not that the probability is high or low, it's that it's unknown.