The Ergodicity Problem: Why the "Average" Person is Dead 💀

The fatal difference between Ensemble Average and Time Average, and why it ruins your portfolio.

Six people sit at a table. They place a revolver with one bullet in the chamber to their heads and pull the trigger once.

• Result: 5 people are alive. 1 is dead.

• The Statistician’s View: The survival rate is 83.3%. If I am an observer maximizing for the group, this is a risky but survivable game.

Now, change the game. One person sits at the table. They pull the trigger. If they survive, they spin the cylinder and pull it again. They do this six times.

• Result: The survival rate is 0%.

• The Reality: The probability of surviving the sequence is (5/6)6≈33%, but as n→∞, the survival rate drops to zero.

This is the Ergodicity Problem.