Internet nonsense and the St. Petersburg paradox

On various social media sites I’ve seen the following hypothetical scenario bandied about: You are given the option to get $50,000 automatically or flip a coin for a 50% chance to win $50 million. Which option would you take? Most people, it turns out, will opt for the $50k, which caused a lot of internet randos to say that people clearly aren’t very numerate, because the best return on investment is Option 2, which will on average give you $25 million. A lot of you can probably already see the flaw with this basic argument about which choice is best, but it reminded me of a classic “paradox” in probability theory known as the St. Petersburg paradox. This felt like a good excuse to talk about that paradox and connect it back in a roundabout way to the scenario described above! The St. Petersburg paradox doesn’t directly have to do with St. Petersburg; it just so happens that it was invented by Nicolas Bernoulli and analyzed by his brother Daniel Bernoulli in Commentaries of the…