is the EV for this game really infinity?

[pococurante]

Actually I just used the graph at http://en.wikipedia.org/wiki/St._Petersburg_paradox for an estimate for 20k hands. I also found another graph on a second site with similar results, so I assumed it's fairly accurate. (And now I see that the game being used on there gives $1 for an immediate loss, while the game the OP used gives $2 for an immediate loss, so all my numbers are completely wrong. sorry.)

As for losing at first, but then going up later, that's because of the infrequency of the large wins.

If you pay $6 to play the version that starts at $1, chances are you will be losing for quite a while. Your first handful of games will probably be a bunch of 1s and 2s with an occasional 4 or 8. Only after a few thousand games, when you will have come across some large "jackpot" wins, will you become profitable in the long run.