How To Define Coolness?

Greetings all. After watching from afar for months, finially decided to weigh in on some of the common topics if I may!

I've seen a number of postings related to coolness and how a cool index is calculated So if I may humbly offer my opinion. to me there are two elements to coolness: the math and the eye appeal. I'll mostly focus on the math.

What's missing IMO is the concept of relativity. I just plucked 14509630 out of my wallet, and I can proudly announce that it's 1/96,000,000 and thus super duper cool. But relative to what? EVERY bill has 1/96,000,00, thus while my math is right, me and my bill (me especially) are not cool at all. There needs to be a norm or a standard to compare to.

If we treat serial numbers like poker hands, and assume for now that the order of the cards (or bills) is not relevant, there are only 22 possible hands, ranging from eight digits all the same (AAAAAAAA) to eight digits all different (ABCDEFGH).

The most "average" serial number hand is AAABBCCD. Three of a kind, a different pair, another different pair, and a single number. An example would be 39923382. Three 3's, two 9's, two 2's and one 8. AAABBCCD. Why do I say that's average?

If each of the 22 possible hands occurred an equal number of times, frequency of each would be 1/22 = 4.55%. The composition of AAABBCCD occurs 1/24 = 4.23% of the time...about the same, so I'm calling that average.

Let's assume that as currency geeks we agree that radars and 4-digit repeaters are cool (1/10,000) and 6 of a kind in any order is cool (1/4409)....~200 to 500 times less frequent than average.

Applying to some serials in other postings, namely 11134343, 41177171 and 08990989:
--They are trinary (exactly three different digits in any configuration and in any order). Frequency of trinaries is 1/144 (.70%), about the same as a star note. That's [only] 6x less frequent than average but 30x more frequent than our hypothetical cool threshold of 6ok.
--There's no obvious explainable sequencing to add to the coolness IMO. If it were 11133344, the eye appeal would be greater and the math would be different but that's not the case.

My point is not to critique anyone's qualitative or visual concept of cool (I collect all trinaries!) but to explain the math objectively versus a 'average'. What does anyone think?