Suppose we have a classic Gambler's Ruin problem as follows:
Person A starts with $100$ dollars, and will keep betting $10$ dollars each round until he either reaches $180$ dollars or goes broke, where $p$ is the probability he wins each round.
Now suppose he makes $5$ dollar bets each time instead, but has the same initial fortune and the same goal.
How can I explain why the expected number of games has to be more than doubled?