Decision to play on in perfect square die game Question:You have a six-sided dice, and you will   receive money that equals to sum of all the numbers you roll. After each roll, if the sum is a perfect square, the game ends and you lose all the money. If not, you can decide to keep rolling or stop the game. If your sum is $35$ now, should you keep play? 
Attempt: Should we be incorporating the $35$ already accumulated, in which case we have:
\begin{equation*}
E(\text{Winnings after 1 throw}) = \frac{1}{6}(-35)+\frac{5}{6}(35+4+3.5).
\end{equation*}
The $4$ comes from the fact that if we don't throw a one in the next toss, the average is $20/5 = 4$. And if we do not throw a one on the next toss, we are guaranteed not to hit a perfect square on the second toss after that, so we expect to make an extra $3.5.$
My approach: you lose your 35 dollars with 16.67% chance, or with 5/6 chance you keep your 35, plus gain the average of the next roll (2+3+4+5+6)/5, and also after the first roll, you are guaranteed to be too far away from the next perfect square (49) so you have an added 3.5 to look forward to with certainty

If you count rolling a $1$ as $-35$, then your reference point is your current $35$, and you shouldn't include $35$ in the chance of further winnings.
On the other hand, you can certainly keep rolling while your score is below $43$.
So I would take the value of the next roll to be at least $(1/6)(-35)+(5/6)8$ which is positive.
