You went to a Casino, and saw a quite interesting stall.
The cardboard besides the stall says:
You first pay \$$5$
You have to toss the fair coin. If it lands heads, you can throw again. If it lands tails, you have to stop. You throw the coin until it lands tail. The the money you get is the number of throws squared.
But is this worth it?
Bonus: What is the expected money gain or loss per round?
Ok, this puzzle is quite easy. This is because I want to celebrate that I hit the rep cap for three consecutive days.