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If I get a rental from Red Box for my Xbox One and then buy the game somewhere else do I keep my save data.
Yes your data is saved, the console does not know how you are playing the game. Your save data is located on the hard drive so you are able to play it no matter what disk you use.
If you have Xbox Live Gold all of your save data is also backed up onto the cloud if you ever have the need to move or access your data somewhere else. This is in addition to @Ramirez 's answer.
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