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If you're logged into the Facebook app on your Android device, syncing your game will usually be a lot simpler. You can install the Facebook app by opening the Play Store or the Amazon App Store and searching for Facebook. You'll find this in your Apps list after installing it. Open your Apps list by tapping the ⋮⋮⋮ button on your Home screen.  Your Facebook feed will load and your account will be logged into the Facebook app.  It may be on your Home screen, or you can tap the Apps button (⋮⋮⋮) and find it in the list. This button will look different and be in a different location in every game, but can typically be found on the game's main menu or title screen. Look for the Facebook logo, or a button that says "Connect." You may need to open the game's Options or Settings menu.  For example, in Subway Surfers you'll need to tap the Gear button in the upper-right corner of the main menu, then tap "Log in to Facebook." As another example, King games like Candy Crush Saga and Bubble Witch require you to tap the ☰ button in the lower-left corner of the main menu, then tap the Facebook icon. If you're already logged into the Facebook app, you'll likely not be prompted to enter your login details again. Some apps may still ask, and you'll be asked if you don't have the Facebook app. Once you're successfully connected, you should be able to start the game and resume from where you left off on the Facebook website.
Install the Facebook app. Tap the Facebook app. Type in your Facebook login information. Tap Sign In. Press the Home button to return to the Home screen. Tap the game you installed. Find the Connect to Facebook or Log in to Facebook button. Type in your Facebook login information (if prompted). Start playing the game.