# Which version of the St Petersburg paradox is the original one?

There is are basically two versions of the St Petersburg paradox.

They differ only on a minor point, namely in the amount that is paid. In one version, $n$ heads and then tails gives a payout of $2^{n+1}$ (minus the price that was paid to play the game). In another version, $n$ heads and then tails gives a payout of $2^n$.

I'd like to know which version was originally used. I think the letters wherein the paradox was introduced are present in the second version of Ars conjectandi, 1713. However, I haven't been able to find the paradox or those letters in the versions of Ars conjectandi I found.

Cinquiéme Problème. On demande la meme chose si A promet à B de lui donner des écus en cette progression $1, 2, 4, 8, 16$ etc. [Fifth Problem. One asks the same thing [see: Fourth Problem] if A promises to B to give him some coins in this progression $1, 2, 4, 8, 16$ etc. ]