Unintuitive Economics

Came across an interesting video on YouTube talking about the book “An Introduction to Ergodicity Economics”. The book is a bit pricey for me to grab on a lark for casual reading (it is listed for $200 on Amazon Canada), but the video is compelling.

One aspect that the video covers is Ergodicity, and how some economic processes are non-ergodic.

The example is simple to understand: Imagine that you have $100, and a magic coin flipping machine offers that on each flip of heads you gain 50%, and on each flip of tails you lose 40%. This game seemingly gives you a 5% edge1, and seems like free money, and to a ensemble group it is indeed easy money…to a point2.

Only the majority to vast-majority of players will end up losing most of their money as the flips progress. A group of players playing the game, each with their own machine, will, as an ensemble mean, come out ahead, but the median player will be bankrupted. After 100 flips, the median player will have seen their original $100 stake drop to about $0.50.

In any case, a simple, AI-slop example can be found here.

This seems pertinent to day traders, crypto traders, and options traders. Yes, a tiny number come out with a windfall, but the vast majority end up quietly walking away with nothing. It also seems relevant for the endless American right-wingers who love to cite how super rich you all are, at least if you pretend that your plutocrat’s massive wealth horde is partly yours, as more and more wealth is centralized to the few and the rest are conceptually in the soylent green waiting room, doomed to be the raw material.

Footnotes

  1. I’ve intentionally miscategorized this. In reality the game punishes the individual player by -5.14% per flip because of the brutal math of compounding. The edge only holds for a large enough ensemble, and as mentioned only a relationally calculated number of flips. ↩

  2. The ensemble group can push their luck with too many flips, as you can see in the simulator, where luck runs out and vastly reduces the probability of the big win outliers that carry the group. Over all worlds and unlimited simulations, big streaks will lift the expected ensemble mean, but it becomes more and more unlikely for a given ensemble with more flips, again demonstrating non-ergodicity. As you add flips, you need to add your players to achieve those increasingly uncommon runs of luck that lift the ensemble wealth, even if the overwhelming majority are left with pennies. ↩