The card game... completely baffling at first yet hugely addictive when you understand how the damn thing works. We at WA always like to heighten your experience in the Final Fantasies (Cause we're so kind-hearted) so for you my friends I present the fullest explanation possible of the best mini-game ever devised...

'The Triple Triad' card game:
Square have created some really brilliant mini-games in the past and they were at the height of this 'mini-game mania' with FFVII. The problem a lot of people had with the mini-games was that, while they were fun for a while and there were alot of them, they didn't have a huge amount of depth. This was unfortunate since it was clear that quite a lot of effort had gone into making them fun but ultimately they got reppetitive... QUICKLY. In Final Fantasy VIII Square took a different, and the majority would say, BETTER approach to mini-game creation. Thus we have the genius 'Triple Triad' mini-game.

You get to try out the card game right at the start of FFVIII. After the class with Quistis, make sure you talk to the man on the bridge leading to the elevator. He will give you some cards and a brief explanation (Little more than telling you how to ask people to play with you... er...). Now go up to someone, yes, anyone, and press the Square button. If they feel like a card game then they will reply 'Do you want to play cards?' Or words to that effect. Of course you then reply 'YES PLEASE!' Or words to that effect... Ahem. So you start up with the cool, jazzy music and you are prompted whether you are 'sure' you want to play cards. Again the usual 'YES PLEASE!'. Then you are asked to select five, thats F-I-V-E cards from your menu. It is advised you pick the cards with the highest ratings (Obviously), however if you have discovered some 'rare' cards and don't like the thought of losing them then either don't use them or be prepared to load back your last save-game. Also another thing to remember is that from around Disc 2 onwards (I think) you can no longer pick the cards yourself. They are picked at random... which can be a bit of a pain in the @$$ at times but thats Square for you.

Cards:
Here is a (VERY basic) diagram of what a card looks like:

There are many ways you can obtain new cards - here are a list of those:

1) Beating someone at a card game - this is usually your best chance of getting 'rare' cards for example - play Edea to get her card.
2) Turn a monster into a card - This is one of 'Quetzecoatl' GF's abilities and is also useful if you do not want to gain experience - simply turn a monster into a card (Doesn't always work - keep trying).
3) Kill a monster - Sometimes when you kill a monster you will get a card - this is rare and it will be displayed on the screens after a battle where it says what items you got from a battle.
4) Talking to people - As in EVERY RPG you should always talk to everyone - they sometimes give you things... and it's good when they give you a rare card.
5) Defeating a GF - Most of the time you get a card when you defeat a GF - Ifrit, Odin, etc. Also When you defeat the 'Brothers' you get two cards (One for each 'brother').

The numbers represent FOUR numbers that is 'up', 'down', 'left' and 'right'. Now some people seem to get confused and don't realise that there are actually FOUR numbers on each card. This is because the left and right numbers are not very far seperated - This can give the illusion of ONE number therefore you think that each card has THREE numbers. The 'element' represents a cards 'element'. Only certain cards have this. For example have a look at your Ifrit GF card (You WILL have this card as you get it when you beat Ifrit). If you look in the top right corner you wil see a little fire symbol. Certain cards have these 'elements' because sometimes you will play a game and there will be elements ON the grid. This means that if you place Ifrit over a 'fire' element then a little sign comes up saying '+1'. Staying with the same example, if you place Ifrit on a 'water' or 'ice' element then '-1' appears. These plus and minus numbers mean that you have +/- whatever number from the vlaues on your card. You don't see elements on the board untill around the start of Disc 2.

Cards are placed on a 3x3 grid similar to that of a normal game of "Noughts 'n' Crosses" Or "Tic-Tac-Toe". When two cards placed together have differing numbers, for example 1==>3 then the person that placed the '3' card down gets a point. This works for all of the up, down, left, right values. Here is a diagram of the grid to where the cards are placed (Again, VERY basic):