[FrojoS]

quote: "Obviously, they assumed that variability decreased proportionally to the number of coins and not to its square root."

Why is this so important? The fact, that the variability increases with smaller sample size was ignored completely by the protagonists in the provided examples. Realizing weather this inverse effect is linear or not doesn't seem to be the main problem in peoples intuition.

disclaimer: I have poor understanding of statistics.

[sesqu]

In the first example, which you quoted, they ended up allowing for greatly more variability than intended, leaving the regulator vulnerable for exploitation. The author speculated as to what sort of exploitation might have occurred, but did not state that it did.

The rest of the examples had nothing to do with the specific relationship between standard deviation and sample size, but with the more basic fact that a relationship exists. This observation is arguably the more important one, and is poorly argued in the chapter. It's also why some people always demand error bars, though I personally prefer plotting individual data points where possible.

The last example, while interesting, had very little to do with the equation (despite a claim to the contrary), which makes me believe the topic was an afterthought.