About Ahri
Ahri is popular champ in tournaments and Solo/Q.She is a very flexible champ that can be used successfully with many playstyles.You can play Ahri like high-burst Assassin or heavy utility DPS mage. Ahri got strong early game,but she lose some power in late game.

About me

I use standard ap mage masteries for ahri

Pros
+Have sustain
+Hight mobility
+Good harass
+All spells deal dmg
+More dmg while charmed
+Easy escape
+Nice tail

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Cons
-Geting stunned in teamfight mean DEAD
-Rich history of getting nerfed
-Does not exactly hard couter a lot of champions

Essence Theft: is Ahri passive, its ready when your orb glowing green, your next spell will give you HP depending on how many enemies it hits.You have to wait for new minion wave, toss an Orb of Deception down a minion wave for get maximum hp from it.Try not to waste this on a Charm or Fox-Fire because that can only hit 1 target or 3 targets.

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Orb of Deception:is useful throughout the game.It deal magic damage and on way back it deal true damage. Orb of Deception works well with Essence Theft.Max it first for a more penetrating DAMAGE.Range isnt biggest, but you can understud it and learn to smartcast it.It realy helps you to deal faster damage.

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Fox-fire:use it after Charm following by Orb of Deception for big burst. It has a 5 second cooldown max level, so spam it during team fights.Max it like second not like first (i saw people maxing it like first with idea: more burst damage alright ?).All 3 little flames aply the 35% slow on Rylai's Crystal Scepter.

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Charm:this is what makes Ahri Ahri and Amumu need it.enemy is forced to walk towards you, so you can give Fox-Fire and Orb of Deception only for 210 mana, isnt that worthy price Horst ? If someone is so foolish to dive you, you alredy know what to do ... Charm him,write /l and watch how is turret killing him.Charm also increases Ahri's damage on a charmed target by 20%, so it's best to start off your combo with charm.If you miss, Charm your assassination potential drops. Ahri can easy rage lots of people and she is useful at every time of game, in late game Charm on adc for easy VICTORY.Is'nt that so easy ?

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Spirit Rust::Must i explain Ahri's ultymate ? No way you have to know it.In Early/Mid game, use Spirit Rush for getting closer to your target and set up your charm combo or escaping from ganks. Spirit Rush---> Charm---> Fox-Fire---> Orb of Deception i mostly cast the last two spells at same time thanks to smartcast.Use it to the end of your burst combo, chase low-hp enemies, or escape from a team-fight.Not entering them like me when i were in bronze got it ?

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.........................................................................HOMBO COMBO..........................................................................
If you are maxing like this: Use this combo:
---> ---> --->

Is needed to speak here about Flash und Ignite?Okey,dont shout at me.
You can think: why take Flash when Ahri can same think with Spirit Rush?
Answer is easy, Flash helps you escape from gangs when you dont have Spirit Rush,
trolling enemies,you can also flash behind minion and Charm him (good agains enemy with low hp).The possibilities are endless.

Use Ignite for complete combo or burst.

Alternative summoner spells:
Barrier
Take Barrier if your enemy is hight burster what can kill you instantly like Veigar.

Teleport
Great for getting back to lane, ganging top and bot, but it makes you weaker in lane.