The proposal “what are the chances of…” rests on the fact, even promotes it, that there is a significance to one number coming “after” another number.

But there is no more or less significance to a number coming after a number than a number not coming after another number.

We see, then, that there are no grounds for any chance or probability that certain numbers can come up, or not, other than the grounds we arbitrarily impose on numbers, and these are not mathematical grounds.

The number system, and the grounds we impose on it, have unique sources and so are not essentially related.

Whatever the sequence, it is determined by what comes next. But there is no mathematical significance to the idea that one number comes “after” another number, any more than the mathematical system can detect - find a significance to - a “next to”.

Preamble:
There is no number that is “more valuable” than any other number. We do, however, use numbers to represent what is valuable. For instance, whether there are 3 digits or 4 on your bank account statement is significant to you. The function of numbers isn’t different than that of words; we use them to represent, organize, communicate, and understand the world.

To the point:
I. When you are calculating probability, you use numbers to represent things about the world. If you want to calculate the probability of a dice roll, you have to use a set of 6 numbers as the base set. This is not an “arbitrary imposition” —it’s because the actual physical dice has that many sides. None of this is arbitrary. And none of it implies that there is a significance to numbers beyond the significance of that which they can be used to represent.
II. Furthermore, it makes no difference to your calculation whether you write the numbers {1,2,3,4,5,6] or [6,5,4,3,2,1]—or any other way. What matters is that there are 6 numbers in the base set. That’s all.

Afterword:
I think this is fairly in line with what you’ve said—the only objection was the use of the word: “arbitrarily”. …No, on second thought, this is very different. For calculating probability, the order of the numbers in your base set does not matter, at all. —No “significance”.

Numbers are just symbols like words. Mathematics is just another language with its own “grammar” so to speak. I don’t know if this post is relevant to the topic, but I just felt that I needed to say that.

We calculate chances due to the number of times it has occured or not occured in the past. So the odds or the chances are not truly math but they have a basis in math in that we do have to add subtract and come up with the answer. there is a significant reasoning that uses mathematical calculations in the odds . Number is a category just as home is a category or family is, or work or anything else. All have significance. Without categories we would be far more screwed up than we already are. Imagine your brain unable to seperate data. If you can’t, try a good hit of acid you might get the idea then.

Considering that numbers and counting are constructs, then there seems little reason to think what you’ve noted is significant. It would be like saying “have you ever noticed that the order in which letters go is irrelevant, and it assumes some kind of significance of each letter?”

Yes I have, and no it doesn’t matter. That’s kind of the idea. It’s a construct of some kind. That’s what they are. If they were naturally occurring somehow then you wouldn’t have a point to make because there would be some natural significance.