18/38 - 47% chance of success
$1 to $100 - $10 to spend
With this given information, their is two routes to take, play it safe, or defy the odds. Though, a 47% chance isn’t far from 50/50, and at the end of the day, it is only $10 to lose. Therefore, in my opinion, even with the expected value, I would say to bet all the money at once, since the goal is to leave with $20.