I am posting this build for a friend. If you like it, feel free to vote it up, if you don't, I don't really care.
This build has netted me three penta-kills to date, and an average Takedown:Death Ratio of 7:1.
If you miss your skill shots, this build isn't for you. If you can't manage mana, this build isn't for you. If you don't know when it's safe to commit for a kill, this build isn't for you. That is all.
I will update this more in the future. Probably.
I hadn't planned to add an image, but a friend suggested I do so, so I just pulled my most recent games list.
And here's some solo ranked.
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I end up using Spell Pen marks, Health seals, AP/Lvl glyphs, and health quints.
You may benefit from mana regen seals instead of health, and either AP or mana regen quints. I usually don't have many mana problems, especially since I usually ***** blue a decent amount (deadly cadence means that blue is infinite spam past around level 8.) If you play a comp where someone else on your team frequently needs blue, or you find that you keep running out of mana, then the mp5 may be worth it. I use the health to dive a bit more for early kills.
21/0/9 Offensive caster. The all-out offense with the mana regen and movement outta utility helps her staying power, while damage is always Cassio's best defense.
I start with a Doran's Ring basically all the time. If you're good at aiming, you will win almost any harass war, and Twin Fangs effectively counters most mids who commit early. I rarely find that I have to run away to the point that a flash isn't enough.
For my second item, I usually get boots. Since I tend to feed early, I usually build towards a Mejai's before finishing my Sorcerer's Shoes. If you are having trouble getting early kills, or are getting ganked, feel free to get the shoes first. As always with Mejai's, if you don't think you can get the kills to justify it, don't bother getting it.
After my Mejai's and shoes are finished, I go after Rylai's next. Why? It gives you tremendous chase and escape ability. Between the noxious blast speed boost and a full slow off Twin Fangs, it becomes very hard to pin down Cassio. It also gives you the option to go after the belt first if you're feeling squishy, or the AP if you're feeling aggressive.
After the Rylai's is finished, I grab a deathcap to capitalize on the AP I should have from my Mejai's stacks by now. At this point I usually build towards an Abyssal Scepter to help soften enemy casters' blows while strengthening my teams. Again, depending on comp, you may want to go for a Zhonya's first, or even a Banshee's Veil. Replace your Doran's Ring with your last piece, and the build is done. You have overwhelming offensive strength, bonus health, MR, Armor, and of course Zhonya's to stop the inevitable focus fire you'll be taking if you actually finish this build in a game.
As noted above, Mejai's is risky since Cassio is squishy. If you can't maintain the stacks, I recommend getting a Will of the Ancients instead for the spell vamp. Simply skip Mejai's in the build and get WotA before Deathcap (but after Rylai's) if you're dying a lot, or after Deathcap if you're doing okay.
Noxious blast is an obscenely powerful poke, and you should always get it first. Due to it's low mana cost, it is quite doable to use this as your harass of choice, even at level 1, for the first half of the game, while strengthening your Twin Fangs for committed fights. Obviously, if given the chance, the Q-E harass is best, but even straight Q can work, and often (incorrectly) tricks the enemy into believing you won't be strong if they commit. Bring out the Twin Fangs and profit from their aggression. Also, bear in mind, the speed boost from hitting an enemy champion shows up as a buff on Cassio. You can use this to see if there's a champion hiding in the grass, or even detect stealthers if you have a strong enough sense of where they may be.
Miasma's level 1 slow SUCKS. It will not get people off of you, and really only functions to set up twin fangs, punish a melee on top of you (especially in combination with your ultimate), and to cut off routes of escape. It isn't until it's higher level that it becomes a decent slow, but its damage is still lackluster, since most non-morons will avoid it. I have seen Cassio builds which prioritize its leveling, but unless your team is very high on damage and low on CC/slows, I just don't like it.
Twin Fangs is your bread and butter. If they're not poisoned, 9 times out of 10, you had better not hit this button, even if it is your only guaranteed shot. Make sure you smart cast it on poisoned targets, and you can even stand toe-to-toe with most melee early game, which will surprise them immensely. Obviously make sure you don't set yourself up for a gank doing so.
Petrifying Gaze is simultaneously one of the most obscenely overpowered ultimates in the game, and one of the most frustrating for the user. When it works right, it is amazing. Wide cone 2 second stun with high damage? Great! But, even after the fix, it still has a tendency to not stun people that are facing you and it tends to bug out when used too quickly after flash (a new bug). Thankfully, I have not seen any incidents of it not even hitting the target since the patch, but that used to happen as well. Your primary use for this is, obviously, for its stun. You can punish people coming at you, either for a gank, or to escape from someone else. During the laning phase, you can also use it, especially while hiding in the grass, to ambush enemies attempting to come for a gank, or jungle, through a surprise stun and quick kill. During team fights, attempt to use it on as many enemies as possible, for obvious reasons. Having a teammate bait towards you in wait is immensely effective, and can result in stunning and dealing heavy damage to the entire enemy team.
The 60% slow it gives even if you dont attack from the front is decently effective, and can be used to prevent enemies from escaping. I generally wouldn't use it for this purpose unless you're taking down more than 1, or the enemy is an extremely fed carry. If possible, flash in front of them for the stun rather than use the slow. If you use the ult for a slow, and fail to follow up for the kill, prepare to be laughed at.
I use Ignite and Flash. The ignite adds yet another DoT for early kills and healer suppression. Combined with Cassio's already high dps, this gives her the ability to focus and kill almost anything in the game, regardless of heals, MR, or attempts to get away.
I personally think Flash is a no brainer for Cassio. Jungles are one of your best fighting grounds due to enemies' reduced ability to dodge your skill shots. Flash is almost always superior for escaping in a jungle. In addition, Flashing in for a kill, or to get in front of someone for a stun, can deny enemies the safety of turning their backs to you.
You can substitute Ghost for better mobility, clarity to combat Cassio's mana problems, or teleport for faster response to turrets under attack. I would usually substitute out ignite over flash, as Cassio really needs at least one escape to be effective.
In a team fight, Cassio's strength comes from her high AOE dps and pivotal use of her ultimate for a stun. Noxious Blast, Miasma, and Petrifying Gaze can all devastate closely grouped enemy teams. Twin Fangs, obviously, gives you enormous ability to focus a target.
Try to use your ultimate in a way that complements your teams abilities. Petrifying Gaze is excellent for punishing enemies after a lure, ambushing them from behind as they try to escape, or simply locking down the enemy team at a pivotal moment of the fight. Try to wait to use it when it will damage and stun as many of the enemies as possible, or interrupt crucial enemy abilities, such as ultimates. While using it early may guarantee your team a kill or two, using it to stun the entire enemy team may singlehandedly win the battle.
Cassio is frequently a focus target. Whenever possible, stay back from the fight, attacking with Noxious Blast and Miasma, to force the enemy to come to you. When they do so, stun them all and clean up the mess with your team mates. If the enemy has excellent focus capabilities, you may benefit from entering a battle after it has started. Give the enemy a few seconds to start blowing abilities on the rest of your team, before running in and unloading. More often than not, they will finish their current focus targets, leaving you free to obliterate them at your leisure.
Cassiopeia is often listed on "Top X Most Difficult Champion" lists. She is squishy, uses mostly skill shots, suffers from mana problems in extended matchups, and has limited escape once an enemy has closed on her. She also gets focused a LOT.
That being said, she has quite possibly THE best sustained DPS of any caster, and is an insanely strong duelist, with or without her ultimate. She can also double as an assassin in special situations, and, provided you keep out of harm's way, can contribute overwhelming AOE damage and slow in team fights.
While difficult to master, once you have done so, Cassiopeia is capable of being a very powerful offensive caster which the enemy team ignores at their own peril.