IPhone 4S with Flappy Birds?

Apparently iPhones with Flappy Birds are selling at nutty prices on EBay, so I've jumped on the bandwagon and listed mine (you never know, eh?)

Question is, if I sell it, how do I leave the game on it? I assume games are linked to my iTunes account. Would I just simply delete everything I didn't want on the phone, remove my payment details from iTunes and then just start a new iTunes account with my new phone?

Or am I missing something. I just want to sell the phone with the flappy app on it, nothing else.

Any ideas?

You could reset your phone, set it up with your iTunes account, go to updates, then purchased, from purchased select flappy bird. Download the app. Then go to settings>iTunes and App Store> log out of your account. Then the phone will have flappy bird and nothing else on it!

Yeah sure