Would that mean that GameCenter is going to report, in your case 6 different entities/accounts?
There should only be a 1:1 relationship, even if you have multiple devices. You would just sign in to the same account on each device. Unless GameCenter does it differently. Can you confirm kenlem that GameCenter tracks each device as a separate entity in terms of leaderboards etc? Thanks.
if you have multiple game center accounts it will report different ones yes.
GameCenter accounts are completely independent of AppStore accounts, there is no 1 : 1 relationship unless a single user with a single account is using them.
It has nothing to do with devices though
But as families with 3-5 devices and everyone having an own GC acc can be using your app, its reasonable to expect seeing a factor > 1 on the relationship there
I have an iPhone and my wife has an iPod. Both of our devices are registered to the same account on iTunes so I only buy apps once, but when it comes to game centre or other accounts They are different.
Another thing I have noticed is that most families who have 1 iPod or iPhone device usually ends up in other family members acquiring more devices due to them being exposed to their annoying awesomeness.