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Almost every person who plays the game will see their money decay towards zero as time goes to infinity.

but, since it is somewhat like a random walk, isn't it guaranteed that if you go on for infinitely many tosses, at some point you will be very rich?

[1] https://math.stackexchange.com/a/493446

if true, an interesting question is - on average - how many tosses are needed for you to reach some arbitrary value (e.g. $1M)?

It's exactly like a random walk... with downward drift. If you take the log of the wealth, the steps are: log(1.5) = 0.18, log(0.6) = -0.22. So at each step, there's a 50% chance you go up 0.18, and a 50% chance you go down 0.22.

Random walks with downward drift don't inevitably go up arbitrarily high like ones without drift.

Knowing the time scale is very important.

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