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Most of the popular Facebook games are available for free on the Google Play Store. You'll be able to connect to your Facebook account and sync your progress.  It will be difficult or impossible to play games on the Facebook website using your Android's browser. Installing the game from the Play Store is the best way to play your Facebook games on the go. If you're using an Amazon device, open the Amazon App Store instead. You should still be able to find most games, but if the game you want is only available on Google Play, you can try putting the Play Store on your Kindle. You'll see this at the top of the Play Store screen. Search for the name of the game that you play on Facebook. You should be able to find the Android version of the same game if you type the name in exactly. Compare the name and the icon to the game on the Facebook website. You can also look at the developer name to ensure that you're downloading the same game. Pretty much any game that you played on Facebook will be available for free on Android.
Open the Play Store. Tap the Google Play search bar. Type the name of the game you want to play. Tap the app in the list of search results. Tap the Install button.