You're right I should have clarified. If multiple stones could not occupy the same square, the odds would remain as I first explained them (3x, etc.). I think in my stones analogy and real life, stones should be able to occupy the same square. In fact, there should be a positive correlation (ie, given that there's a rock in this square, odds of a second rock being there go up).

> How is it appropriate to equate/compare "the number of squares you walk through in order to pick up all the stones" to "the number of times a digit should show up"?

The odds of coming across 3 units of a quantity are 3x as hard as coming across 1 unit. When we write numbers, we are either:

1) writing a truthful description of how many units we see/own/ate/taste/touch etc. (I ate 2 bagels, I earned $5, I ran 10 miles.)

2) lying.

By "lying", I'm including things like writing a novel. Maybe a better word is "imagining". With numbers, we are either writing down true observations or we are imagining them. It's just as easy to "imagine" $9 million in your bank account as it is to "imagine" $1 million, while truthfully finding $9 million in your bank account is a lot more difficult :). This is why Benford's law doesn't apply for "imagined" numbers. By using Benford's law, you can quickly classify a number set into either "real" or "imagined".