A fair coin is flipped 100 times in a row. For each flip, if it comes up heads you win \$2, if it comes up tails you lose \$1. You start with \$50, if you run out of money you must stop prematurely. If you don't run out of money you stop after 100 flips.
What is the expected value of this game?
So for the case where you have no stopping condition before 100 flips you get that $E(100)=50$, and I assume the possibility of stopping will reduce this expectation somewhat. But how exactly is it changed?