For Piet's Sake
Assuming you're following this guide, you should have won the Alexander Card from Piet while on the Lunar Base. If you didn't, you'll need to go track down Piet and win it.
Fly to Esthar, more specifically, Tear's Point, but don't get too close, as the monolithic Lunatic Pandora now hovers over the site. From here, fly south over Esthar's fence to find an isolated peninsula. Land and proceed on foot to the south, then to the west to reach the end of the peninsula, where you can find the landing site of Piet's escape pod. It's not marked on the map, so you'll just have to wander around blindly until you run into it (see image provided). Here you should find Piet sitting on the ground, and he'll still play cards with you - with the Lunar Base's rules - if you challenge him.
The Queen of Cards - Alexander
Once you possess the Alexander Card, it's time to track down the Queen of Cards again. If you're following this guide she should be in Dollet, so head over to the pub there, challenge her to a game of cards, make a junk hand including the Alexander Card, then lose Alexander to the Queen of Cards. Make sure she goes to Balamb after the game, as usual. You'll need to play her again soon enough.
After losing Alexander and ensuring the Queen of Cards goes to Balamb, find her son in the painter's shop and win back your Alexander Card from him, then leave Dollet and fly to Timber, of all places. The new card that the Queen of Card's father was inspired to make after you lost Alexander can be found here.
Enter Timber and head to the pub, where you'll want to challenge the man in the upper right corner of the pub. Play him and win his Doomtrain Card, although be wary, as he won't play this card often - it may easily take over a dozen games before you even see it. Winning Doomtrain is worth the effort, however, as it's a top-tier playing card, as it has strong left (A) and bottom (A) sides. You can refine it into three Status Guard items via Card Mod, but there really shouldn't be any need to do so, considering you should have obtained one during the Shumi Village sculptor side quest, and both Cerberus and Doomtrain can learn ST-Def-Jx4 natively.
The Queen of Cards - Doomtrain
As soon as you win Doomtrain, it's time to lose it again. Return to Balamb city and find the Queen of Cards near the train station. Make another dummy hand including four junk cards and Doomtrain and lose your precious new card to the Queen of Cards. Make sure she goes back to Dollet, then follow her there and talk to her in the pub to find out that her father created the Phoenix Card after being inspired by Doomtrain, which now is held by an official in Esthar.
First things first, let's win back Doomtrain from the Queen of Card's brat, and rejoice! You don't have to waste time playing him ever again!
Leave Dollet and fly to Esthar, enter the city and make your way to the Presidential Palace. Once inside, enter the first doorway you come across to return to the room where you were first brought after entering Esthar. Here you'll find a Presidential Aide, whom you can play cards with. Win the Phoenix Card from the aide which isn't really a great playing card. It can be refined into three Phoenix Spirit items, which will teach a GF the Revive ability. It's not a bad ability to spread around, but you can also learn it by buying sixty Mega Phoenix items (they can be purchased from the Esthar Shop!!! for 7,500G each, 450,000G total) and turned into twenty Phoenix Pinions (Tool-RF), which in turn can be refined into a Phoenix Spirit (GFAbl Med-RF). Do what you will, but there's little need to keep the Phoenix Card.
With that, you're done with the Queen of Cards quest, but if you want to potentially win back cards in disc 4 at a faster pace, you can facilitate that by moving the Queen of Cards to a specific location. It's not necessary, but it may prove helpful. If you can't be bothered skip ahead to the Max Stat Boosting section, where all the various ways of increasing your power will be discussed. If you can't be bothered, skip ahead to Lunatic Pandora - Part 2.
Note: If you're following this guide chronologically, you should now have every Triple Triad card in the game, save perhaps Odin, if you avoided him in order to also avoid acquiring Giglamesh, which will facilitate Angelo Search. If you don't have Odin yet (he's a Level 9 GF Card) don't worry - you can safely win him in disc 4.
Moving the Queen of Cards to Shumi Village
If you've completed the CC Group questline by the end of disc three (you have done that by now, right?) you'll be able to play them again in disc 4, and potentially win back lost rare cards. Whether you've refined these cards into other items or simply lost them in games, it doesn't matter, the CC Group will end up with them, and you'll be able to win them back. One player stands out in particular, and to influence her trade rules you'll need to move the Queen of Cards to the Shumi Village before the start of disc 4.
That being the case, you'll have to lose and win back several rare cards to move her round, and of course, some save/loading might be involved. Assuming the Queen of Cards is in either Balamb or Dollet, play her and lose the MiniMog Card (any rare card will do, but MiniMog is our favored sacrifice) and ensure she goes to Deling City. Follow her there (she's in the hotel) and win back MiniMog and send her to Fisherman's Horizon. In Fisherman's Horizon (you can land the Ragnarok right on Fisherman's Horizon!) you'll find her near the Save Point on the train tracks; lose MiniMog to her again, and make sure she goes to Esthar. Finally return to the Presidential Palace in Esthar (where else?) and you'll find her waiting just of the lift. Win back MiniMog one more time and make sure she goes to Shumi Village (Trabia).
When the Queen of Cards is in the Shumi Village, you should be ready to set aside cards for a good while now. Continue one with the Max Stat Boosting section if you want to see the various means of boosting your stats, or move on to Lunatic Pandora - Part 2 if you want to continue the story.