Probability can be confusing (maybe…)

I’ll skip the long story that leads to the following statement, but I currently have a 1-year subscription to Blinkist. I think it’s a pretty good service that provides some interesting (but sometimes a little biased) summaries for nonfiction books.

So I was reading one of them, on The Drunkard’s Walk by Leonard Mlodinow and it had the following statement:

Imagine you start rolling a dice and recording numbers. Would you expect the results to be perfectly random? If they were, each number would appear exactly once every six rolls.

I stopped and re-read this a couple of times to make sure that I had it right. Well, outside a pet peeve of mine of using “dice” as the singular, where it should be “die”, the problem is that this is not the definition of “perfectly random”. It’s a definition of “very biased, where the 6th roll is always deterministic”. They are treating rolling dice as if it’s sampling with no replacement, which that’s not how dice work. The side is always there even after you roll it once.

First, I don’t think this is a problem with the original book, but with the summary provided by Blinkist. So why did the summary author make this mistake? Well, I think that it’s because actually probability thinking is not something that is natural to people. The book even talks about it being reasonably recent when it was formalized on even simple things like “why is it more likely to roll a 10 when you roll 3 dice than a 9?” It’s fascinating to think about that from the other side of having studied statistics for a while.

But don’t give up on the summary just because of a mistake like this, even if it was a little bad. The rest is actually pretty good. It doesn’t fully convey what is in the book, but it has a good amount of interesting bits that makes it worth reading.