Do android apps work on a smart tv? I just got an lg smart tv and I'm wondering if I load apps that i have on my phone would it work on a smart tv?

ex. I have the game cut the rope on my phone can i just move that to the smart tv and start playing it?
First off, currently only Hisense TVs have the rights to be powered by Android.  Other TV manufacturers will start using Android in the coming years.  At least thats what the sales assistant at JB Hi-Fi told me.

Secondly, I just searched the google play store on my TV and it doesn't have Cut the Rope.

Alternatives may be screen mirroring.  Eg, some Android phones can cast the screen to the Chromecast.

It all depends on the capabilities of the devices you have.