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Launch the Play Store application on your device.
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Tap the menu icon in the top-left corner → My apps and games.
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Find the game in the list and click on it.
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On the game page, click Update.
 
You can also set up automatic downloads of updates for applications installed on your device:
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Open the Play Store app.
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Click on the menu icon in the top-left corner.
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Go to the Settings section.
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Tap Auto-update apps.
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Select one of the update options:
 
— Always: Wi-Fi or a mobile network will be used to update applications.
— Only via Wi-Fi: Updates will only be installed when connected to a Wi-Fi network.