Towards the very beginning of the game, Vivi can choose to participate in a Rope Jumping game in the Alexandria town square. It’s definitely worth doing, as it’s really enjoyable! Depending on the number of jumps you manage to complete, you’ll get a progressively better item. Here are the rewards:

20 Jumps: 10 gil
50 Jumps: Cactrot Card
100 Jumps: Genji Card
200 Jumps: Alexander Card
300 Jumps: Cat Paw Racket
1000 Jumps: King of Skipping Title (and a sore thumb!)