In a Mojang blog post, Jakob Porser has declared that Scrolls is officially in alpha. Although they are only initially sending out a small amount of codes, more will be sent out in the future, as Porser declares, "So, if you do not get one, don't lose hope!" The first and second draft of alpha testers are selected randomly and those who aren't chosen initially will have to wait until the open beta.
The alpha includes deck building, single player, and multiplayer. The initial experience is limited to smaller AI battles, nothing too exploratory, but the ability to play against other alpha testers is quite interesting.
Admittedly still missing a large chunk of the intended features that they plan on implementing in the near future, this design is similar to Minecraft's trajectory and will hopefully be as successful in the end. Lightning rarely strikes twice, but Mojang is trying their best to make that happen with Scrolls.