This is a mini-game that can be played by Vivi at the beginning of the game in Alexandria. Talk to the girls (who are playing jump rope... hmm, go fig) west of the ticket booth.
Just as a side note, I just wanted to voice my opinion when I say that this is one of the most pointless and tedious mini-games since the 'Mog Mating Arcade Game' at the Gold Saucer in Final Fantasy VII. Take THAT Squaresoft. Thank you.
The purpose of the game- wait, why am I telling you the purpose? Haven't any of you ever jumped rope before? Sheesh. Anyway, you need to hit the confirm button each time you see the '!' bubble appear above Vivi's head.
Each time you reach a milestone in the number of jumps, the speed of the jumps will change, and you will receive a prize. Here are the milestones:
* 20 jumps; speed increase/10 gil
* 50 jumps; speed increase/Cactaur Card
* 100 jumps; speed increase/Genji Card
* 200 jumps; speed decrease/Alexandria Card
* 300 jumps; no speed change/Tiger Racket Card
*1000 jumps; end of game/Key Item: King of Jump Rope
How to get Excalibur:
If you go to the auction house in Treno (disc 4), you can bet on an item called the Magical Fingertip. Make sure you have extra cash on you before you attempt to participate, it can get up around 80,000 gil or so.
After you have that, go to Daguerreo and talk to an old man near the Inn. He'll ask you to look for the Magical Fingertip. Give it to him and he'll give you Excalibur.