If your intent is to go, enter the Hamilton lotto and, if you lose, turn around and go home, it is a waste of time. If you want to do that in person and, if you lose, you will rush or get a discounted ticket to another show, then sure why not. But I wouldn't make the Hamilton lottery the centerpiece of the trip, since you are then adding disappointment as a factor. But if you hoped to see Hamilton, and had to settle for Fun Home, Disaster, American Psycho, or whatever tickles your fancy? Sounds like a nice day!