A carnival offers a game, called Nerves of Steel. It is played with a standard die, except that the "six" has been replaced with a skull.
You start by paying $7, then rolling the die. Each time you roll a number, that value is added to your running total. After each roll, you can either stop, receiving your running total in dollars, or you can roll again. However, if you ever roll a skull, the game immediately ends while you walk away seven dollars lighter.
So, if you rolled a 5, then a 3, then stopped, you would win \$1 (5+3, minus the \$7 fee). If you rolled a 4, then a 4, then a 3, then a skull, you would lose \$7.
What strategy maximizes your expected winnings?
If you want, you can also try to find what your expected winnings will actually be when you play optimally, but I wouldn't recommend doing this without a computer.