can i really play all the games in CL

this corresponds to Chocobo's Lagoon. i've played most of the games, but i don't remember. all i know is that Mog can tell me how many games i've played and how many there are left. i have discovered that the numbers of games i can play increases a little if i get a 4-treasure success in the previous game. but what if i played 300/300 games? Chocobo Lagoon disappears?

As long as you have enough Gil you can play whenever you want, forever.

"#/300" is the number of times you've played Chocobo H & C in the Lagoon compared to the number of games you've played in total. Looking at mine right now, it says "# of games played (Forest) / Total: 52/82, so that means I've played 52 in the forest and 30 elsewhere.