That formula assumes that you always have investment opportunities with multiplicative returns. This is not true in practice for many people.

To illustrate the difference, assume the following (simplistic) model: an agent has an income of $1000/period, minimum/subsistence spending of $998/period, and power-law "emergencies" that bankrupt you when you cannot afford to pay. Then the question is: what is more unlikely, a long-enough time without being bankrupted that you accumulate $10M (or even $100k), or winning a $10M jackpot?