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The formula for the Kelly criterion is f = p - q/b. If you plug in the odds of the recent record-setting mega millions draw, which was EV positive, f is 2E-9, which means it's Kelly-optimal to buy 1 ticket for every billion dollars of your net worth.

I don't think it's valid then to say it's rational for anyone with a net worth of $<1B.

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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?

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