**St. Petersburg Paradox**

I offer you a game in which you sequentially roll a die until you *lose* by rolling either a 1, 2, 3, or 4. If you've rolled the die N times before you lose, I will then pay you 2^{N-1} dollars. If you play this game many times, it turns out that your *Average Winnings* will be 2 dollars.
**I now alter the game a bit, stating that you lose only if you roll a 1, 2, or 3. You no longer a lose by rolling a 4. What do you think your ***Average Winnings* will now be?

**Solution**