For the uninitiated, the link system doesn't make any sense at all. It doesn't even begin to make sense until one actually participates in it, and not a moment before (at least, that was the experience with me). Here's a general sense of how it works: let's say that you are playing one of the Oracle games (it doesn't matter which one). The Oracle game is self-contained in itself; you could play just that one game and be satisfied. But the game makes it clear that the story doesn't end there. The real story, that of Ganon's revival, is only hinted at in the first Oracle game you play. The real story continues on in the other Oracle game in this way: once you beat the first Oracle game, you are given a password. When you start the other Oracle game, before you begin you enter the password given when you beat the first Oracle game. When you play the second Oracle game, events are slightly different from the norm. This is because in this Oracle game, it is known that you have already beaten the other game. Therefore, a normal Oracle game happens first, and the other, linked, Oracle game happens second.
For example, let's say you played Oracle of Ages first. You've beaten Veran, and you are given a password. The game then asks you if you want to save, and you agree to it. From then on, when you play that saved OoA game, it has the events from AFTER you beat Veran, not right before as is the norm. In most Zelda games, you can save up until the last boss, but in Oracle games you save AFTER you beat the last boss. In this completed Oracle of Ages game, you can walk around and talk to characters, and they all thank you for beating Veran and so forth. Several characters (like the farmers Bipin and Blossom, and Impa), have left notices saying that they have left to go to Holodrum (the land in Oracle of Seasons). Oracle of Ages is basically over at this point. All you can do now is plug Oracle of Seasons into your Game Boy, start a new game, and enter the password given to you when you beat Oracle of Ages. When you start the game, you immediately notice that things are different. First of all, the intro shows Twinrova cackling in front of the lit Flame of Sorrow (it was lit in Oracle of Ages by Veran's actions). Then, when you meet Impa and the traveling troupe, Impa recognizes you as the "hero of Labrynna." (Labrynna is the land in Oracle of Ages). As you can see, Oracle of Seasons has become an extension of Oracle of Ages. This is the concept behind a linked game.
The same thing goes if you play Oracle of Seasons first. After you beat Onox, you are given a password and you can save your game. Then you can walk around, and all the characters thank you for beating Onox, etc. Impa, Bipin and Blossom, and co. have all left for Holodrum. When you start a new Oracle of Ages game and enter the password, you see Twinrova cackling in front of the lit Flame of Despair. When you meet Impa, she recognizes you as the "hero of Holodrum."
No matter which game you play first, the ending is the same. After you beat the second final boss, all three Flames are lit, and Twinrova attempts to sacrifice Zelda in order to revive Ganon. Link stops Twinrova, but she sacrifices herself to revive Ganon. Then Link defeats Ganon, and the ending shows Link leaving on a ship. Zelda is waiting in Hyrule Castle, the Triforce is watching over Hyrule, the Triforce embodied as three birds is watching over Link's departure, and Link is waving goodbye to all his friends from both Oracle games.
At this point you might be wondering, very rightly, "if there are two ways to play through the Oracle games, which way is the 'right' one? But if there are two ways to do it, how can there be a logical and consistent Hyrulian history?" The answer lies in the structure of games themselves. All the Zelda games follow a fairly linear pattern. You visit the dungeons in a certain order, and events happen according to the clock. But, of course, you are given a little freedom as to how you, the player, make Link carry things out. For example, depending on what items you choose to get, you could beat one dungeon before another. You choose whether or not to explore around looking for heart pieces.
The Oracle games take this freedom one step further. If you consider the two Oracle games (one normal, one linked), as a single game, the storyline is fairly linear. Link goes to Hyrule Castle. The Triforce sends him on one quest. During that quest, Twinrova warns Link that she will revive Ganon. After Link finishes that quest, Twinrova lights one Flame. Link travels back to Hyrule Castle. The Triforce sends him on another quest. During this quest, Zelda comes to visit and is kidnapped, and Link rescues her. Halfway through this quest, Twinrova lights the Flame of Destruction. After Link has finished this quest, all three Flames are lit, and Twinrova kidnaps Zelda in order to sacrifice her and revive Ganon. Link defeats Twinrova and Ganon, saving Zelda. Zelda returns to Hyrule, and Link sails away on a quest for enlightenment.
As you can see, this linear storyline remains unchanged no matter which quest you decide to take first. The player, as Link, is given more freedom than is usual in one game, because the adventure is divided between two games. Regardless of which path the "real" Link took in Hyrulian history, the basic history is unchanged. In effect, Capcom has provided us with two different ways to play through history, since both ways are equally likely to have occurred. Of course, if you want to provide a conventional account of Hyrulian history, you will have to choose one order or the other. You might prefer to have OoA happen first, or you might think that OoS happened first.
Another difficulty in understanding the link system is the interaction between the first and second (linked) game via "secrets." It works like this: while you are playing a linked game, characters that have some relation to some character in the other game (like an explorer in Holodrum hoping to get a message to Dr. Troy in Labrynna) will appear, and they will tell you a secret. The secret really is a secret. You as the player don't get to hear what the person said; all you are given is a string of random characters. What you then do is play the first game (the normal game which you have already beaten), find the appropriate character, and tell him/her the secret. This character will usually give you an item, and then tell you a secret that will get you that item in the other game. You then play the other game (the linked game), and you visit Farore, Oracle of Secrets, inside the Maku Tree and tell her your secret. She uses your secret to magically produce the item. The Ring Secret works a little differently. When you beat the first Oracle game, you can talk to the red snake in Vasu's Shop, and the snake will tell you a ring secret. When you play your linked Oracle game, you can tell the red snake the ring secret you got. This will get you all the rings you collected in your first game.
It's difficult to see how the secrets system connects the two Oracle games together logically. If one game happens chronologically after the other, how does the exchange of secrets make any sense at all? I believe that, in practical terms, the system works in the following fashion. We must assume that travel between Holodrum and Labrynna is possible, because several characters do it once you beat the first Oracle game. So when a character in the linked Oracle game tells Link a secret, Link travels all the way back to the other land (the first Oracle game that you have beaten already). He tells the right person his secret, and then travels all the way back to the other land. Power given by the secret fades once Link is out of the first land, so in the second land Link must talk to Farore to restore the power of the secret. A similar system works with the rings. Link can only carry rings in a Ring Box; otherwise they will quickly lose their power. So carrying all his rings from one land to another is pretty much out of the question, since ring boxes don't hold that many rings. All Link can do is have Vasu's red snake (Vasu's Shop, like Farore, is mysteriously in two places at once) magically transfer Link's rings from one land to the other.
These theories aren't perfect of course, but after all, the Oracle games are games, and for games to be fun they can't always work in logical ways. The best we can do is try to imagine how things really happened in Hyrule's history, since the Oracle games can't give us a perfect picture of how things happened.
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