Consider this bet: we flip a coin. If it lands heads, your money increases by 50%. If it lands tails, your money decreases by 40%. Should you play?
If we look at a large group of people, the average result is a 5% increase in money after each flip. So, it seems like a good bet.
But if one person plays the game repeatedly, the result can be very different. If the person loses enough times, they can eventually lose all their money and cannot continue playing.
This idea is central to ergodicity economics, developed by physicist Ole Peters. The main question is whether we are looking at the average result for many people at one point in time or the result experienced by one person over time. These are not necessarily the same.
For example, imagine 100 people each visit a casino for one night. Some may lose all their money, while others may win. We can calculate an average result for the group.
Now imagine one person visiting the casino 100 nights in a row. If there is a possibility of losing everything on any night, that person may eventually go broke. Once they have no money left, they cannot keep playing.
The average result for the group may remain positive, while the result for one person over time can be very different.
Nassim Taleb expresses this idea with a simple example: you should not cross a river that is, on average, 4 feet deep. The average depth does not tell you whether you can safely cross it.
The important point is that the average result for many people is not always the same as the result one person will experience over time. Confusing these two can lead to serious mistakes in decision-making.