Why Corki Jungle?

Why the hell would you play Corki Jungle? I mean there are a lot of more viable Junglers like Jarvan or LeeSin or whatever. The Answer is simple. First, your ennemies will feel trolled and not take you serious because they think that you're obviously a troll. An then Corki is at the moment a broken Champ with Trinity, who can carry hard a Mid Game. So i think it's better to play him Jungle since you can roam more during Mid Game and help your Team instead of Bot as ADC. It is especially important to know that the most of the Games nowadays finish at the Mid-Game. After this, you are not relied on a Support on the Botlane and is perfect for SoloQueing where you can meet some Plastic7 Supports. And another great aspect is that the ennemy will think that you're going ADC, so you can manipulate their Championpicks.

And finally, it is a lot of fun playing some NewMeta Gaming and win ;)
That's my reason to play Corki Jungle.

Pros and Cons
Pros
-Nice Ganks
-Clears Jungle Camps very Fast
-Strong Midgame
-NewMeta Troll gives you a lot of Fun

Cons
-Weak Early in Jungle
-Falls quickly behind if counterjungled
-Blue dependent if you spam your R

Runes & Masteries

I go for Flat AD Quints/Marks ; Armor Seals and Scaling MR Glyphs. The Flad AD allows you to Jungle as Corki, Armor Seals gives you some Tankiness you need early in the Jungle, and Scaling MR to not die insta if you gank Mid like LeBlanc or smth like this. Especially if you don't buy any MR/AR Items in MidGame. How ever, Flat MR might be even better against heavy AP Assasins like LeBlanc, and Armor Penetration should be viable too, giving you extra Damage for the Ganks, but i personally think that it'll make your Jungle life much harder.

For the Masteries I think that 9/21/0 is the best choice, since you need some Tankyness as Jungler to not die during a Gank and to survive early Jungle as ADC. I'll try 21/9/0 too and give you feedback if that works well.

Item Build

I start with Hunter's Machete and 5 Pots to give you some ability to jungle as an ADC. After that i go for Spirit Stone and Boots, for some mobility and Sustain, and finish my boots into Sorcerer's Shoes to get some early DMG (Your Q and R will deal an nice amount of extra DMG, which is way better than the extra AS you get from Berserkers Greaves). Then I usually pick up Spirit of the Ancient Golem to get some Tankyness and not to die during Ganks or if i get counterjungled. (Many ppl do because they think Corki Jungle is weak, what is acutally true compaired to J4 or Lee) After some sucessfull Ganks i head for a Trinity Force, which is the core Item for Corki's DMG output during Mid Game.

After This you are free to build any Item you think is good on Corki. I would Recommend Infinity Edge, Bloodthirster, LastWhisper for some Extra DMG, or a Locket of the Iron Solari, Spirit Visage, Randuins Omen, for some Tankyness if your Team needs badly a Frontline.

As Corki Jungle, it's quite simple. Start with a smiteless Blue, do you Red with Smite, and then gank a Lane if possible. And Always try to pick up Wraiths and Wolves since you can clear them very fast. I would only take Golems if I want to gank Top/Bot. And to get some extra Income you can clear very fast incoming pushing minions on a lane, if your mate has backed. Just use Q+R for the caster minions and some R for the melee miniosn, and the lanes is pushed back again.

How do I gank? - As Corki it is better when you Team Mates baits, so that you don't get focused when you gank. Just Use you W to get in, Q+E your Ennemy and spam some R(after 6), and usually you opponent will back off giving you free DMG due to RedBuff. Just keep chasing with R until he reaches the turret or dies. Remember that every 3rd R will deal 50% extra DMG which is a relevant Amount especially with Sorcerer's Shoes. So make sure that you got this 3rd Missile when you Gank if possible. It makes your chance to get a kill higher ;)

Counterpicks
Generally Jungler who are focused on counterjungling you early Levels, because they are simply op early. And with a Gap closer ability ,which can catch you if you fly away or heavy Burst.

Examples: -Lee Sin -Jarvan IV -Vi -Kha'Zix -Rengar

Synergies
If your Team has a Tanky Top as Frontline(e.g. Renekton, Nasus, Shen,...) And if you lack an ADC an your Botlane (e.g. you got a Urgot Bot, or if your bot is playing really bad)