The servers will not go down/be restarted when RoS goes live, a lot of people don't seem to know this so I'm just posting it so people understand you can be logged in and whenever the expac goes live in your region the features will just be automatically unlocked and you begin. I've read a lot of people worrying about error 37 and being able to login. Just make sure you're logged in 2 hours (or more) before launch.
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Diablo III will be available the night Reaper of Souls goes live and there will be no need to patch or exit the game once the clock strikes GO! We advise logging in ahead of time to reduce potential queue times. Once you're in-game and the Reaper of Souls has launched in your region, you'll see a server broadcast message letting you know that the expansion is now available to play. This means you can continuously play Diablo III all night long and jump straight into Act V the moment it’s available! Note: In order to access Act V once Reaper of Souls is live, you will need to exit your current game and select Act V from the Quest Select window. If you want to avoid having to recreate your game, we recommend that you set up your game so that you're killing Diablo after your gameplay region's launch time. This way, you can naturally transition into Act V without any additional effort.
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EDIT: Added RoS opening times:
For Asia, the expansion will be available to play at 11:00 a.m. PDT on March 24.
3:00 a.m. KST on March 25
2:00 a.m. CST on March 25
For Europe, the expansion will be available to play at 4:00 p.m. PDT on March 24.
23:00 GMT on March 24
00:00 CET on March 25
01:00 EET on March 25
03:00 MSK on March 25
For the Americas, the expansion will be available to play on 9:00 p.m. PDT on March 24.
10:00 p.m. MDT on March 24
11:00 p.m. CDT on March 24
12:00 a.m. EDT on March 25
1:00 a.m. ADT on March 25
1:30 a.m. NDT on March 25
12:00 p.m. SGT on March 25
3:00 p.m. AEDT on March 25
Remember to be logged in well before these times!