Going from 30 to 100 in a coin flip game.
The game may last very long, but the probability that it does not end is zero.
Since the coin is assumed to be fair, the expectation value of the game is zero. Now the expectation value is given by $E = P*70 + (1-P)*-30$, where $P$ is the probability of winning the game. Setting $E$ equal to zero, we can solve for $P$ with the result: $P = 0.3$.