[plexiq]

Hm, the actual setup is:

You are offered a 120$:100$ coin-flip today.
You are offered a 200$:100$ coin-flip tomorrow.
But you only own 100$.

So, the thing you are missing here is that, if we loose the first coin-flip, we will pass out on the second one.

So, 50% of the time we will end up with nothing (-100$), because we loose our first bet. 25% of the time we win both coin-flips for winnings of +320$, and 25$ of the time we win the first, but not the second flip, resulting in +20$.

So, taking the first bet, we have an expectation:
0.5*(-100$)+0.25*320$+0.25*20$ = +35$

If we skip the first bet, and only take the second one, we have an expectation of +50$.