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Game updates are instantaneous after the servers come back up. Which they are. Normally this isn’t. A thing. Like yesterday’s or the day before. You could login instantly no game download.
Some updates don't require an update to the game client, but some do - And in those cases, it can take a short while for Google Play to start serving the new version across the globe. We're working on a solution to this longer-term, but for now you might have to wait a few minutes whenever we push one of these updates.