St. Petersburg paradox

(post from old site)

Coin toss game. Pay u 2^n if you get head on the nth toss. How much would u pay to play this game?

U'd probably would like to calculate the expected value of this game...
basically, for each possible outcome, u calculate the outcome multiplied by the associated probability. Then u sum it all up.
50% chance to get head in the first game to give u $2, which gives u an expected value of $1.
within the remaining 50% chance, u have half chance to make $4 in the 2nd game, which gives 0.5/2 *2^2 = 1.
as we continue , nth game would give an expected value of (1/2^n)*2^n =1.
if we sum all possible outcomes, we'll be adding 1 for each possible outcome, which will be infinity.

would u even pay $1k for this game for an expected value of infinity ?

That's quite counter intuitive.

supposedly, the paradox is solved with the introduction of utility function, ie point of diminishing return.

I guess 1 thing to learn is that We should be happy to pay 1k for one game of this rather than playing lottery over and over again...