The object of the game was simple. A rider sits on the outer row and when the carousel spins around, the rider reaches out and grabs one of the metal rings from the dispenser. Since not all the rings were brass - typically one brass ring per ride among many non-brass rings - getting the brass ring was a special treat. The brass ring usually entitled the holder to a free ride when they returned the brass ring to the attendant. Or could be kept as a good luck charm, memento, etc.
It's important to note that in their heyday, most carousels were pay-to-ride amusements. Back when a couple pennies, a nickel or a dime was still significant change, a free ride on the carousel would seem much more relevant. Therefore, to get the elusive brass ring was to win a notable prize equated with fun, gratification, fulfillment, etc.
Amy grew up to be a pleasant, pretty, hard-working young woman. She got married, started a family, and lived in a nice modest home with her husband. Together they worked towards prosperity and raised a good, healthy family. Amy was very happy. Again, Amy got the brass ring.