So ive played about 10 or so games wit Kai'sa so far and the best build ive come up with thats given me the best results is as follows. BloodRazor > Zerker Greaves > Phantom Dancer > Black Cleaver or Maw depending on if they have a strong AP or not then grab the other > GA

This build gives her some good durability in GA and Maw with tankiness from Cleavers hp and this build absolutely shreds. Im a solo player so all of my games are with randoms so i dont always have good teammates to coordinate with and it just feels so strong for carrying and especially in 1v1s.

Some examples of some of my games https://gyazo.com/1fc5efbfd6cf48f06293a26ebb1eec6b https://gyazo.com/bee99c064dfbddb5f4e6651cc9bb0231 https://gyazo.com/b81caca3a34c65663dfbeb371f1cd31d
https://gyazo.com/7234fe0e3f3d29ed912f66196311368f

When i say this build shreds i mean it ABSOLUTELY shreds people. If you catch someone solo with this build with E up you can legit 100-0 them in about 2-2.5 seconds if they arent a tank. Some examples https://streamable.com/3m3o6, https://streamable.com/meqc9. Wish i could provide better ones as these were from PBE but i dont want to post some crazy one shot of me blasts someone 3-4 levels down or something. My scores however were from live servers. Still i think these show that her damage output is pretty crazy even without much crit outside of PD.

Rune-wise i go a pretty standard Press the Attack Sorc tree page splashing Celerity and Gathering Storm. Imo its a very very good build and urge you guys to give it a try when you get the chance and let me know what you think.