Can I use my Game Center account on another device?

So, I have a iPhone 4s and have games like Temple Run 2, etc. I'm getting an iPhone 5 next week and was wondering if the points that I got on Temple Run 2 could be transferred because of Game Center.

Well that depends dose this perticuler game run through game center, if so yes… And in answer to your ''MAIN'' Qustion. ( Can I use my Game Center account on another device? ) YES

If you have iCloud it should transfer every thing over

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