If you pay to remove ads as an in-app purchase in Solitaire, your scores will transfer over to other devices sharing the same Apple ID, and you will no longer receive ads. We recommend connecting to Game Center so that your scores and times will be stored for future backups in the case that you need to transfer devices.
Please keep in mind that your statistics do not transfer over if the app is deleted or reinstalled.
To learn more about Game Center, check out this support article, How do I transfer my Score and Best Time from an old device?
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