Oh, right. This then:

Quote Originally Posted by gamefaqs
-Side Quest 1: The Queen of Cards-
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In order to gain some of the Rare Cards, you must lose some of the Rare
Cards that you have to the Card Queen. Once she has the Card that she
requests, she will give you a clue to her whereabouts and move to another
city and her father will create a new Rare Card based on the one that you
gave up in a Card Game to her. Once you have the new Rare Cards, you can win
back the Cards that you lost to her in normal fashion. Here is the listing of
what Cards come with the forfeit of the Cards the Card Queen requests.

Forfeit - New Card - Location
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Mini Mog - Kiros (Can be gained in Deling City from the man in black)
Sacred - Irvine (Can be gained in Fisherman's Horizon from the mayors wife)
Doomtrain - Phoenix (Can be gained in Esthar at the Presidential Palace from
the Aide)
Chicobo - Chubby Chocobo (Can be gained in Balamb Garden from the student
outside the library)
Alexander - Doomtrain (Can be gained in Timber from the Pub's owner behind
the bar)
I didn't even know this quest existed. :o