I roll 6-sided dice until the sum exceeds 50. What is the expected value of the final roll?

Question

I roll 6-sided dice until the sum exceeds 50. What is the expected value of the final roll? I am not sure how to set this one up. This one is not homework, by the way, but a question I am making up that is inspired by one. I'm hoping this will help me understand what's going on better.

Answer 1

The expected value of the final roll is the same it would be if it was the only roll. It is independent of the previous rolls. Thus it's 1/6(1+2+3+4+5+6)