Just as ridiculous as the Stephen Colbert book, this build can take a lot of people by surprise. You generally play Corki the way you normally would, so if you know Corki there's not a lot to say. If you don't know Corki, learn him. The basics are this:

-W in like you're a Bronze/Iron scrub
-Haha, they've got you!
-Oh wait, you pressed E right away
-And follow up with Q... and they're dead

Yup, it's that easy. Most people expect you to have made a mistake when you Valkyrie forward, but you're pulling a fast one on them - as long as you know where the jungler is are safe from a gank. NEVER go all-in like this if there's a potential gank/TP from top to spank your little Corgi behind.

Your W and E are monstrous abilities with the capability to output enormous amounts of damage. Both of them:

-Proc Muramana's ability damage for each tick
-Proc Comet and Luden's to reduce their cooldowns
-Proc Ravenous Hydra's ability cleave

for each tick


That's right - your AOE damage with this build is insane. This synergy also works with your Package, which like the rest of your kit, has good scaling off of AD. Even better, your Package can damage epic monsters, allowing you to help surprise "burst" them down with your jungler. As said previously, you do primarily magic damage, so Luden's with its magic pen mythic passive and Void Staff/Sorc Shoes allows you to output a lot of damage even to high MR targets, on top of applying after your E reduces their MR. This does mean that Void Staff is less effective since it has %penetration, but it's the only other magic penetration option you can take.

The biggest divergence from "normal" Corki builds are Luden's and Ravenous Hydra. On top of synergizing with your AoE DoT abilities, Luden's provides you with movespeed to get in and out of trades more favorably, and provides magic penetration as its mythic passive, which is highly valued on Corki. Ravenous Hydra also has the AoE DoT synergies, and it provides you with omnivamp. This means that you're healing off of the massive amounts of magic damage you're outputting, in addition to the damage from your autos and Gatling Gun physical damage that lifesteal would provide. This massively increases your survivability as you're trying to dive in and all-in opponents, often letting you survive trades that should be suicidal.

DO NOT BUILD SERYLDA'S GRUDGE. Seriously, don't do it. The AD, slow, and ability haste are tempting, but the armor penetration is completely wasted on you. You are always better off getting Rylai's, despite the lack of ability haste. If Serylda's and Rylai's ever have a love child that gives ability haste and magic pen it's your new best friend, but until the day Riot makes that mistake just stay away from Serylda's.

Another way to lose the game is to not take advantage of your Package timer. This is your actual Ult: you're basically a Jayce/Nidalee/Udyr with less build flexibility. You want to either have your wave pushed out so you can use it to leverage a dragon/herald/etc with your jungler, or you want your wave pushed way in so that you can kamikaze dive on your lane opponent with it and pick up a kill. If that means waiting to pick it up until your next back, DO IT. It's better to delay your Package and get something out of it, than it is to get every Package the second you can pick it up. No one else feels pressured to Ult the second theirs comes up, so why should you? Your waveclear is already amazing, so if you use it for waveclear, your opponent should count that as a win.

Short answer: Lich Bane sucks.

If Lich Bane was good/useable, it might be worth getting, but until that changes you're better off getting something else.

Yes, Essence Reaver is an outside option, but if you need it for mana on top of Luden's and Muramana you're doing something wrong. Does it synergize well with Ravenous Hydra and Muramana? Sure. But is it worth getting over Rylai's/Void Staff? Not really, unless your opponents have no mobility and build no MR, in which case they're trolling so I guess it's fine if you do too.

"Why not build Sheen and sit on it?"
Because Corki's base AD isn't good. The amount of damage you add by weaving in Sheen procs between your abilities (which you should be doing with normal autos anyways) is comparable to the amount you gain by building AD due to the ratios on your abilities. In addition, the 1.5s recharge timer might not seem like much, but having to wait that full time to press another ability actually delays your burst.

Again, if you absolutely don't need the slow from Rylai's or the extra penetration from Void Staff, it's not the worst fourth item to build. But you do end up mostly wasting the crit chance, and your burst with Ravenous Hydra/Muramana/Luden's/Sorc Shoes is already astronomical.