When to stop rolling a die in a game where 6 loses everything You play a game using a standard six-sided die. You start with 0 points. Before every roll, you decide whether you want to continue the game or end it and keep your points. After each roll, if you rolled 6, then you lose everything and the game ends. Otherwise, add the score from the die to your total points and continue/stop the game.
When should one stop playing this game? Obviously, one wants to maximize total score.
As I was asked to show my preliminary results on this one, here they are:
If we simplify the game to getting 0 on 6 and 3 otherwise, we get the following: 
$$\begin{align}
EV &= \frac{5}{6}3+\frac{25}{36}6+\frac{125}{216}9+\ldots\\[5pt]
&= \sum_{n=1}^{\infty}\left(\frac{5}{6}\right)^n3n
\end{align}$$ 
which is divergent, so it would make sense to play forever, which makes this similar to the St. Petersburg paradox. Yet I can sense that I'm wrong somewhere!

I interpreted this such that you're in competition against another player.
If playing second your strategy is simple - play until you've won.
If playing first, you must accumulate enough points such that the next player is statistically more likely to lose than win - that means making them roll more than 6 times (since they have a 1/6 chance of losing every roll).  To achieve this you must amass at least the value of the average scoring roll (3) multiplied by 6, which is 18.  Any score above this is statistically more likely to win than lose.
