Saint-Petersburg Paradox

This is a paradox where you get paid $2^n$ dollars for the number of heads you hit in a row before you hit a tails.

The Expected Value is $1+1+1\cdots =\infty$, since you have $2^1\frac{1}{2^1}+2^2\frac{1}{2^2}+\cdots$ where the denominator represents the probability of the action happening, and the numerator is the payout.