You’re right. I made a mistake - I thought you were trying to contradict the theorem I stated. I’ve just realized you were saying something orthogonal.

As for the proof of my theorem, By taking logarithms, the process becomes an additive random walk with negative drift (log 1.6 + log 0.5 < 0). This is well known to converge to negative infinity almost surely. After exponentiating to undo the logarithm, this is exactly the statement I made.

It does not matter how many test subjects there are ( as long as there’s finitely many) because, informally speaking , you can just wait for each of them to become irrevocably bankrupt in turn.