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My only solution would be to re-install but seeing as you have already done that. When at 100%, Steam is still in the process of updating the game.
Just keep waiting, don't close the window, and eventually it will be done, and you can play. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).
Players will still be able to join servers that have not updated, but I strongly suggest server owners install the update anyway.
570 is the steamid number for Dota 2 (as seen on the dota 2 store page).
These folders need to be writable by all users in order to update properly.
Sometimes these user permissions break and need to be refreshed.
Would you like to answer one of these unanswered questions instead?
Here's a list and a guide with step by steps on how to possibly fix the stalling update/download for Dota 2 client. • Clearing out the Dota 2 files from your depotcache folder.