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

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?