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Description
Okay, so you probably all know what shiny Pokemon are, right?
Good, so you probably also know your chances of encountering them are only ~1/8192.
Sure, you can grab your Poke-Radar and head out there, raising the chances to ~1/200 after a chain of 40, but it's so damn difficult to keep that chain!
The Masuda method could work, but you'd have to breed so many eggs you'd be a Yamask by the time you finally got a shiny.
Well, here's a much easier method
As of Pokemon X & Y, there's a new method of getting shiny Pokemon: Consecutive Fishing!
This is a lot like chaining for shinies with the Poke-Radar, but much easier.
Here's what you do:
Get any of the three fishing rods(Old, Good, or Super), and register it in your bag for the Y Button.(Super rod found on route 16)
Go catch either an Inkay or an Octillery with "Suction Cups" Ability, or any Pokemon with either Suction Cups or Sticky Hold ability, this makes it almost impossible for you not to get a bite when you fish. Put in the front of your party.
Stock up on lots of quick balls, net balls, ultra balls, dusk balls, whatever you might need, you want to make sure you CATCH the shiny when you find one, right?(Tip: If you got an Inkay/Malamar, teach it Hypnosis via level up/move relearner).
Go find a good fishing spot and start fishing.
Your chances of finding a shiny will slowly increase the longer your chain gets, and you can usually find a shiny by about 30 to 40 encounters in one chain.

Things that break your chain:
Moving/Turning(Don't move AT ALL in between when you cast your rod).
Using another key item or roller skates(Seriously, just fish, don't do anything else).
Nothing biting(That's why you want Suction Cups/Sticky Hold).
Reeling in too fast/slow.
Saving your game and restarting.

Things that may(unconfirmed) break your chain(Through my experience, I don't think they do):
Saving.
Using any menus.
Using non-key items(e.g. Berries).
Catching a Pokemon.
Finally encountering your well-earned shiny.

Things that don't break your chian:
KO'ing the Poke.
Running from the wild animal(unlike when using Poke-Radar).
Encountering a different Poke then you did the last time(again, unlike the radar).

Sometimes your chain will break due to nothing biting even when you have suction cups/sticky hold, but usually not until your chain is already ~50 or so(I was at 58! ;( )

This is easier than using the Radar as you can much easier build up your chain(if you're careful), and you can find your shiny quicker(sometimes before you even hit 20!). It seems that your odds gradually increase with each encounter, as opposed to simply above or below a certain threshold, I may be wrong though. Also remember, unlike with the radar, nothing bad happens if you encounter a different Pokemon than before, NOTHING! Only if you DON'T encounter anything, does your chain break

I don't know exactly what the odds are of an encounter but in one day out of about 141 encounters I caught three shinies(Clawitzer, Seaking, and Poliwhirl). So 3/141 = 1/47 odds! This is probably nowhere near what the odds actually are, and they probably change as you chain, but damn!
1/8192 to 1/47!!!!!! THREE SHINIES IN ONE DAY!!!!!(I used quick balls and net balls, if you're wondering). As long as you're careful you can carry a chain almost infinitely, like I said, I got to 58 once.

Tips:
When you find your shiny, throw a quick ball the first turn, then if it escapes use Hypnosis(if you have Inkay) to lull him to sleep. Now throw dive balls/net balls like a mad man!
If you already got rid of hypnosis, get a Pokemon to learn thief(TM in Camphrier Town), fish in the route before Cyllage with the Old Rod, and use thief on the first turn if its Luvdisc. Once you have a heart scale, fly to Dendemille(I think) town to find the move relearner.
If it's night time/in a cave feel free to use Dusk Balls.
If it's a high level or you're paranoid you'll somehow fail, you can choose to use the master ball(I'd just buy lots of other balls, though, I still have mine and have caught three shinies, Xerneas, Mewtwo, and Zygarde).
Sometimes, you may just fail, don't give up, just try it again, it's much easier than any other method.
Pay close attention when fishing, reeling in too slow/fast breaks your chain.
Remember, a shiny isn't always that valuable on the GTS. Let's say you have a shiny Clawitzer, it could be worth and Yveltal.... maybe. If you put it on GTS asking for Yveltal, though, you probably wont' get one. No one(probably) will be on GTS searching for a Clawitzer with the intention of trading an Yveltal. There's no function to just seek out shinies, so don't overvalue your shiny Pokemon as trading chips. For trading, just catch a few version exclusives(I've gotten starters, stone-evolved Pokemon, pseudo-legendary, etc., just from a few Swirlix).
Shiny Clawitzers are red!
Shiny Seakings don't look very different, they're slightly more orange.
Shiny Poliwhirl are almost impossible to tell apart aside from the sparks, they're almost the exact same color.
Staryu/Starmie are exclusive to X.
The rod doesn't affect your odds of finding a shiny.

Happy Hunting! Leave feedback below.

:) (Smile) — Description
Okay, so you probably all know what shiny Pokemon are, right?
Good, so you probably also know your chances of encountering them are only ~1/8192.
Sure, you can grab your Poke-Radar and head out there, raising the chances to ~1/200 after a chain of 40, but it's so damn difficult to keep that chain!
The Masuda method could work, but you'd have to breed so many eggs you'd be a Yamask by the time you finally got a shiny.
Well, here's a much easier method
As of Pokemon X & Y, there's a new method of getting shiny Pokemon: Consecutive Fishing!
This is a lot like chaining for shinies with the Poke-Radar, but much easier.
Here's what you do:
Get any of the three fishing rods(Old, Good, or Super), and register it in your bag for the Y Button.(Super rod found on route 16)
Go catch either an Inkay or an Octillery with "Suction Cups" Ability, or any Pokemon with either Suction Cups or Sticky Hold ability, this makes it almost impossible for you not to get a bite when you fish. Put in the front of your party.
Stock up on lots of quick balls, net balls, ultra balls, dusk balls, whatever you might need, you want to make sure you CATCH the shiny when you find one, right?(Tip: If you got an Inkay/Malamar, teach it Hypnosis via level up/move relearner).
Go find a good fishing spot and start fishing.
Your chances of finding a shiny will slowly increase the longer your chain gets, and you can usually find a shiny by about 30 to 40 encounters in one chain.

Things that break your chain:
Moving/Turning(Don't move AT ALL in between when you cast your rod).
Using another key item or roller skates(Seriously, just fish, don't do anything else).
Nothing biting(That's why you want Suction Cups/Sticky Hold).
Reeling in too fast/slow.
Saving your game and restarting.

Things that may(unconfirmed) break your chain(Through my experience, I don't think they do):
Saving.
Using any menus.
Using non-key items(e.g. Berries).
Catching a Pokemon.
Finally encountering your well-earned shiny.

Things that don't break your chian:
KO'ing the Poke.
Running from the wild animal(unlike when using Poke-Radar).
Encountering a different Poke then you did the last time(again, unlike the radar).

Sometimes your chain will break due to nothing biting even when you have suction cups/sticky hold, but usually not until your chain is already ~50 or so(I was at 58! ;( )

This is easier than using the Radar as you can much easier build up your chain(if you're careful), and you can find your shiny quicker(sometimes before you even hit 20!). It seems that your odds gradually increase with each encounter, as opposed to simply above or below a certain threshold, I may be wrong though. Also remember, unlike with the radar, nothing bad happens if you encounter a different Pokemon than before, NOTHING! Only if you DON'T encounter anything, does your chain break

I don't know exactly what the odds are of an encounter but in one day out of about 141 encounters I caught three shinies(Clawitzer, Seaking, and Poliwhirl). So 3/141 = 1/47 odds! This is probably nowhere near what the odds actually are, and they probably change as you chain, but damn!
1/8192 to 1/47!!!!!! THREE SHINIES IN ONE DAY!!!!!(I used quick balls and net balls, if you're wondering). As long as you're careful you can carry a chain almost infinitely, like I said, I got to 58 once.

Tips:
When you find your shiny, throw a quick ball the first turn, then if it escapes use Hypnosis(if you have Inkay) to lull him to sleep. Now throw dive balls/net balls like a mad man!
If you already got rid of hypnosis, get a Pokemon to learn thief(TM in Camphrier Town), fish in the route before Cyllage with the Old Rod, and use thief on the first turn if its Luvdisc. Once you have a heart scale, fly to Dendemille(I think) town to find the move relearner.
If it's night time/in a cave feel free to use Dusk Balls.
If it's a high level or you're paranoid you'll somehow fail, you can choose to use the master ball(I'd just buy lots of other balls, though, I still have mine and have caught three shinies, Xerneas, Mewtwo, and Zygarde).
Sometimes, you may just fail, don't give up, just try it again, it's much easier than any other method.
Pay close attention when fishing, reeling in too slow/fast breaks your chain.
Remember, a shiny isn't always that valuable on the GTS. Let's say you have a shiny Clawitzer, it could be worth and Yveltal.... maybe. If you put it on GTS asking for Yveltal, though, you probably wont' get one. No one(probably) will be on GTS searching for a Clawitzer with the intention of trading an Yveltal. There's no function to just seek out shinies, so don't overvalue your shiny Pokemon as trading chips. For trading, just catch a few version exclusives(I've gotten starters, stone-evolved Pokemon, pseudo-legendary, etc., just from a few Swirlix).
Shiny Clawitzers are red!
Shiny Seakings don't look very different, they're slightly more orange.
Shiny Poliwhirl are almost impossible to tell apart aside from the sparks, they're almost the exact same color.
Staryu/Starmie are exclusive to X.
The rod doesn't affect your odds of finding a shiny.

Happy Hunting! Leave feedback below.