This is actually an awesome illustration of why a lot of famous results in academic finance were wrong in the 70s and 80s. Returns don't average, they multiply. If you get HHTT or TTHH you're in terrible shape:

2.25 * .36 = .36 * 2.25 = .81

You started with $1 and now have 81 cents. I recently learned that a lot of early computer-era academic finance actually made the same error of averaging returns, as described in Finding Alpha:

http://falkenblog.blogspot.com/2016/08/finding-alpha-pdf.htm...

After many rounds, you expect to see half heads and half tails. In that case your outcome at n rounds would be around 1.5^n/2 * 0.6^n/2 = 0.9^n/2 which trends towards zero.

You would need around 26% more heads than tails just break even (0.6*(1.5^1.26)=1). But even if you were lucky at first, you will always "regress toward the means" in terms of head to tails ratio if you kept playing.