Inhabited tenants - when is the time for eviction?

[Jo W.]

Hello everyone,

I recently (09.18.18) purchased a two family house in Buffalo NY and this is my first real land-lording experience (I don't count my house hack). 

The rent is way below market value (450$ instead of 700-800$). I sent the upper tenant a 30 days money for keys letter as he said that he cannot afford paying 750$. He did not pay rent for October (450$) and after a 3 days pay or quite letter he called and said that his niece will move in with him so he will be able to afford the rent and that he will pay me the rent by Monday 10.08.18 .

He didn't pay (Surprise) by that date so i sent him a text message and he reply with "no need to do eviction, i will be gone by the 25th"

My question is what do you guys think i should do? start an eviction process anyway? (It will cost at least 450$ and it will take almost a month anyway) or wait for the 25th and if he doesn't leave start the process?

P.S i don't have a security deposit.

Thanks in advanced for any help :)