Connecting your account to Facebook allows you to continue from where you left off on other devices that you've logged into.
Also, since your game progress is automatically saved, even if you lose your phone or tablet or can't use it anymore, just log into Facebook; your progress will be just as you left it.
Here's an example scenario:
Zero loses his iPhone, but had already played PotK for ten hours by that point. Fortunately, he connected his Facebook account to his PotK game account.
Zero gets a new iPhone and re-downloads PotK. He connects his game account to Facebook once more, eager to continue the game progress he accumulated on his old device, this time on his new one.
...two months later...
Zero gets an iPad. He downloads PotK onto his iPad then connects his game account to Facebook to continue from where he left off on his iPhone. But he doesn't always want to play on his iPad.
Zero commutes to work, with no iPad in sight. He starts up PotK on his iPhone, continuing from his latest iPad play session. Zero swaps back and forth between his iPhone and iPad for months, never worrying about losing his progress.
We store your game save data on our servers, and use your Facebook ID to identify that you're the same person with a user access token.
Other than the information we receive based on the access rights you permit to us through this token, we receive no personal information from Facebook, and Facebook receives no personal information from us.
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