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If you browse to http://salemthegame.com/ you will find the following message:
A while back we took in your applications for the closed beta, and right now we're processing those applications to sign everyone in gradually. Literally right now.
Missed the beta application? No problem! We're aiming for an open beta at the end of July, so your dream settlement or grumpy witch hunter won't have to wait long. More information will come through Twitter and Facebook, so be sure to keep an eye on those.
So should be this week or next week, but they haven't put up an announcement yet on their FB