Hello and welcome to my guide.
Many LoL players are thinking that Karthus is troll pick in 3v3.
I want to prove that they're wrong.I hope that the guide will provide you with the minimum information about Karthus in 3v3 , and I would appreciate any and all feedback that you may provide.


Without further talk, I present to you, my Karthus guide. I've put quite some effort into this guide, so I beg you to give it a shot before any downvotes.
And above all, thank you for taking your time to read this Karthus Guide.

Pros + Heavy damage early/late game + Requiem is very useful against lucky heroes like: Tryndamere, Twitch, Shaco and so on.... + Very good farmer mid-late game + Has a build in Exhaust(almost) + Lucker buster + Underestimated

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Cons - Low AP ratio - Item dependent - Hard to master - Easy to counterattack

Why did I chose speed?
I like speed it's the best escaping and chasing "passive" it works very nice with Wall of Pain and Rylai's Crystal Scepter.

But instead of speed you could have chosen to enhance your armor/hp/ap!
Yes I could, but think about it logically we take for example....ummm Greater Quintessence of Movement Speed if i'd have taken Greater Quintessence of Health instead i'd gain 78 HP.
If we could amplify that with 50%(which is unlikely to happen but still!) we'd have 117 extra HP! Is that such a lifesaver?
Also while speed is a stat that can be used both in chasing, escaping AND blocking lots of abilities HP can be only used in defense. But this is also relying on your style of play, I like to go berserk, spam like hell and then retreat or just harassing.

Damage amplifier
Executioner is just awesome and works really nice together with Havoc

AP
For AP I chose Mental Force , Blast and amplified it with Archmage which give a nicely 5% extra. Arcane Knowledge for 10% magic penetration.
Mana
I chose Expanded Mind and Meditation for a little mana regeneration

Other
Summoner's Insight 'cause of Flash and Clarity
Swiftness because I love 2% more speed

• Greater Quintessence of Movement Speed: Speed, I love speed :)
  
• Greater Mark of Magic Penetration: Magic penetration, I gain at least 3 more Damage Points with this.
  
• Greater Glyph of Ability Power: For the AP.
  
• Greater Seal of Cooldown Reduction: CD, I hate it, these little things reduce my ulti's CD by a few seconds.

Flash: Great escape Alternative: Ghost

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Clarity: Because I decided to focus my build on HP early game, you WILL have problems with mana, this is a workaround. Alternative: Cleanse, Ignite

• Death defied: Ahhh, may become the best passive in LoL, but that's depending on your teammates. If you're the Kamikaze type then you will love this!
  
• Lay waste (Q): This is your harass attack, very useful early game and vs squishy champs.
  
• Wall of Pain (W): Sion is after you, the only escape is this beauty which, if you're smart enough may become your best escape ability and engage as well!
  
• Defile (E): Very awesome AoE, very good for faming mid-late game and alongside with Rylai's Crystal Scepter will keep melee enemies away from you.
• Requiem (R): Very useful against lucky heroes like: Tryndamere, Twitch, Shaco but casting time is 3 seconds and that's enough to be countered.

• : I love speed, great for chasing great for escaping. Alternative: Sorcerer's Shoes
• : A fix for the ultra squishyness early game, also the mana will be sufficient and the passive is awesome!
  
• : This will fix your mana problems once and for all and it will boost your AP quite nice, the passives will boost your AP and your mana.
  
• : Ahhhh, this is my personal favorite, this will stack very nice with your movement speed and your abilities as well(except for Wall of Pain).
  This is used mostly for chasing but can be used for escaping as well.(Works awesome vs Teemo)
  
• : A must-have for every Mage.
  
• Extra : Usually in 3v3 you never make it to the last item so this one is kinda useless, choose whatever you need, I'd go with Morello's Evil Tome 'cause of its Ap, CD and the active which is simmilar to burn(especially useful as counter for the most counters of your ulti!
  Alternatives: Pretty much everything else under the Magic or HP topic.

Solo fights
I initiate with Wall of Pain toggle on my Defile and spamming with Lay Waste (bear in mind that the cast time is 2 seconds).

Team fights
I usually go first, the enemies are focusing me and I die while activating my passive(I usually cast my ulti then since it can't be stopped) but it's very important that your teammates don't spread as soon as you die since you can't move while you're in your passive.

Escaping
From AP casters/support: Wall of Pain should be enough since their movement speed is 380.
From melee: Wall of Pain + Lay Waste(if you have Rylai's Crystal Scepter) should be enough (as long as they won't jump, flash and especially stun)
From tanks: Wall of Pain and Lay Waste if it's a tank that has an ability that boosts their speed.
*Keep in mind that Defile is slowing the enemies that are near you. It's very effective against right click melee champs and those who have short range abilities.
* Your ulti slows too!

Chase
Wall of Pain + Lay Waste usually does the trick
Flash + Defile is acceptable too if you haven't mastered Lay Waste and Wall of Pain is on cd(keep in mind that Defile has little range)

So, 3v3 gameplay is a little different than 5v5, the 1st thing you'll have to know is that AS(attack speed) champions are op in 3v3, riot focuses the balance in 5v5 only but if you're smart enough you can still own (I usually own Tryndamere even if hes so op in 3v3 because he doesn't usually buys hp ;))
Since you're playing in 3v3 you must move much more than in 5v5, now here's some tips when playing in 3v3:

Warding :Well personally I don't need any wards since I can escape so easy but you will until you master Karthus.
I recommend only warding those spots with the Vision Ward, the others are overkill but if you want to gank somebody while jungling I guess they're helpful then.
*If you use Vision Ward you are able to see the enemy ward and destroy it.

Ganking :
be sure to gank often, since you will have some extra levels than the enemies in bot so it should be no problem when it comes to gank then. I recommend early gank since they don't have so much HP but make sure you're around 2 levels higher than them
(at that stage you should at least have Boots and Sapphire Crystal buyed).

Early game :
You should get some HP ,Mana items and Boots, and gank since all you abilities can hit multiple target. This is your key to a good beginning, usually the top enemy will be more powerful than you so it won't be easy to harass him (unless hes an useless tank or a hero with low hp). I recommend bot ganking.

Mid game :
After you're level 12 you should not have any Mana problems at all (given that you already have at least Tear of the Goddess). I recommend jungle for more money and items, but don't forget to gank from time to time, also check the dragon since it's around then they begin to take it.

Late game :
Time for ulti spamming, you only have 120 seconds CD, that's not much! After getting Rabadon's Deathcap your ulti should do around 1000 damage(-28% which is the usual magic resistance after the magic penetration). Don't avoid teamfights since all your abilities can be targeted on more than one champion!. In late game I use to get at least double kills!

Kamikaze! :
You should decide when its good to activate you passive, the outcome can be at the best triple kill and at the worst food! The passive is much better in 3v3 since the map is smaller. I go kamikaze when there are at least 2 enemies that have less than 1/3 of HP (watch out for Heal!)

If you still think that I'm trolling then let me give you some proof that I don't!
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Well that's all I've got to say so far, I hope you liked the build, and I can't wait for your answers, please let me remind you once more to actually test the build before you downvote it.

Many thanks to jhoijhoi who posted the tutorial about making a build which can be found below:
http://www.mobafire.com/league-of-legends/build/making-a-guide-101506

Also thanks to SpartaDeathAngel for the gameplay in 3v3 tip.