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.
If it follows the median, the percentage of losers increases exponentially from 50%.