Turn off notifications on iOS devices

Select Settings >> Notifications and select game/app you need to turn off notifications in Include section.
You can select None to turn off all notifications from games or still get notifications but turn off "Show on Lock Screen" so you won't see them on the screen. 

Turn off notifications on Android devices

Select Settings >> Apps to show all installed apps.
To turn off notifications from 1 game/app, select that game/app. An information board about that app will be shown: memory storage, turn on/off app, delete cache... You remove the tick in"Show notifications" to turn off notifications.