when u build an annie build u have to build her as a nuker cuz when u go 1v1 u have to be able to nuke them down before they kill u .u can say that u should build her as leblanc she is also a nuker the tactic is to three hit the enemy so u have to get alot of ap.

doran´s ring is always a good starting item but u need alot of ap with annie so if u can handle it buy mejai´s soulstealer or else u can go for zhonya´s hourglass. then u go for the simple boots of speed then catalyst then sorcerers then u finish the rod of ages.and then rylais cuz u need hp so its good with rod and rylais. and then to max out your ap rabadon. and to get the last touch on the build void staff then u have 60 magic penetration so i dont think u need magic penetration runes.

i think ignite and flash are the maine summoner spells for annie but u can also use ghost to chase or escape and exhaust to chase and is good if you go 1v1 and u can use teleport to get fast to lane for gank push or def.

this build is my second build i didnt put in alot of effort in it but i think it works good anyway. but ill maybe update it when i have time