Get ready for some math geekiness:

There is a HUGE misconception that because there are 5 cards, there is a 1 in 5 chance of getting the card you want. However, this is not the case. There are 4 tiers of heroes: gray, blue, purple, and gold. Each one has it's own chance of being drawn. For simplicity, we'll say gold is 1%, purple is 5%, blue is 10%, and gray is the default. Once you hit shuffle, the game calculates your odds of winning the gold, purple, and blue. No matter how many of those cards are in the pile, they have the same chance. So if you bring up 3 blue and 2 gray, your chance of winning the blue is still 10%, not 30%. So the game picks a number at random between 1 and 100 three times. 1 for each pick you can possible make (2 and 3 picks are for the VIPs). If you have a gold card, and the game rolled a 100, you'll win the gold card. If there are 2 purple cards and the game rolled a 98, you'll win one of the purples, and so on. If you don't get a "hit" on the roll, then whatever card you flip will be the gray.

So, in reference to mattp169's post above (is it rigged or predetermined), it is plainly obvious that it is predetermined. Here is the proof: During Ragnarok, try pulling a few YouTube videos at once during an intermission. Anything internet intensive that will bog down your connection will work. Now, watch your scores on the bottom. Before you go in to combat, you'll notice that either your kills or your losses tick up. This means the game calculates the outcome prior to the combat cutscene. There are other examples of this too. Tynon does all the math first, then plays a scene to correspond to it's answers.

So there you have it. It is not rigged, it is simply not the 20% chance it seems to be. To be clear, however, the game NEVER states that your chances of "winning" are 1 out of 5.