Author of the article here-- right! This was the key "real world" motivation for this experiment as an attempt at a pedagogical tool; from the article:

> As an aside, I think the fact that this particular concrete application happens to be recreational, or even downright frivolous, is beside the point. For one thing, recreational mathematics is fun. But perhaps more importantly, there are useful, non-recreational, “real-world” applications of the same underlying mathematics. Cryptography is one such example application; this experiment is really just a birthday attack in slightly more complicated form.

Sometimes I find these concrete investigations necessary for our brains to make peace with the unreasonable effectiveness of mathematics, as it's been called.

I would say one of the first great discoveries for a person is the exponential series (a real world examples: population growth). Another is the divergence of the harmonic series 1/n and convergence of 1/n^2 (my preferred real world example: pizza slices that converge to 1 pizza or diverge to infinitely many). E.g. give me 1/n slices for the rest of my life and I'll pay you $100 (-:

When travelling, I also have go-to experiments that I like doing (e.g., elementary proofs that the earth is round/spherical such as: great circles; N-E-S-W always at 90 degrees; shadow angles [Erastothenes]; seasons; etc.)

There are other things to investigate that are not really "proofs" or "combinatorial evidence", but equally interesting. One example is using music (esp. the piano) as a physical logarithm device. The music "sounds" additive but the frequencies are multiplicative.

Author of the article here; this is a great point. This experiment initially stemmed from a nice analytical solution to the problem of computing the expected value (via generating functions as described in the post). Computing other moments, let alone the entire distribution, required some Monte Carlo simulation, as shown at the end of the first article (https://possiblywrong.wordpress.com/2019/01/09/identical-pac...) before I started the experiment.

And even this histogram assumes a distribution of total number of Skittles per pack (that varies) that I had to guess at beforehand. In hindsight, the final sample distribution suggests that I probably initially overestimated the true variance, and thus also overestimated the expected number of packs I would need to inspect. In other words, this experiment arguably took longer than "average."

So you're right-- this experiment could have extended into 700 packs, 800 packs... and still have been consistent with the assumed model, but I would have simply been in an unfortunate 90-th percentile possible universe where it took much longer than "average."

> "For these reasons, I'm actually a bit surprised that the author's data matches the theory so closely... The fit is so perfect I actually suspect he... ah... played with his data slightly after the fact. A "fortuitous" choice for alpha is obviously helpful too."

Author of the linked blog post here. I made the comment that "if I had instead chosen 12, or 13 (for alpha), the resulting predictions would not agree nearly as well." This is perhaps overstating the "luck" of my initial midpoint choice. Here is a quick plot showing the same data with predictions using 12, 12.5, and 13: http://imgur.com/lP5sjwB

(Note also that a better least-squares estimate of alpha is actually about 12.7.) Even these "endpoints" still look to be in reasonable agreement with measurements. That is, if 12 to 13 calories per pound really represents most of the range of variability among the (male) population, then one can likely make useful predictions without needing to be spot-on with their choice of alpha.

Of course, it's a valid question whether 12 to 13 really covers a large chunk of the distribution. Are there men out there with alpha<10, or >15, for example?