Lots of people go straight to the guard at the front gate or the Trepie in the cafeteria, but these two are so easy to beat when you only have the starting cards. If you need Elnoyle, Abyss Worm, Tonberry King, Adamantoise, etc. just head to the library as soon as you get your first cards. These two are seriously bad at Triple Triad and drop everything you need in the early game.
CRTs do wonders to creating fidelity where there actually isn't any.