The bad news, at least for those of us in North America, is that we're apparently not getting the deluxe, "Non-Stop Climax Edition" of Bayonetta and Bayonetta 2 that Japan (and Europe) are getting. Many missed out on the games for the Wii U, so this is a very pleasant surprise. The sequel, Bayonetta 2, was released in 2014 as a Wii U-exclusive.
Unfortunately, at less than a minute long, the Bayonetta 3 teaser trailer is incredibly brief. It shows that developer Platinum Games is creating the game and that it will once again star the game's namesake, Bayonetta.
Moreover, Bayonetta 2 will support amiibo (including the Bayonetta amiibo for Super Smash Bros.) and players will be able to record gameplay videos of up to thirty seconds as well.
Like Bayonetta 2, Bayonetta 3 will be published by Nintendo and more details about the game will be announced in the near future. The gaming company definitely seems to be listening to their fans on this console generation.
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In addition to an announcement of Bayonetta 3, Nintendo revealed an upcoming Switch port of Bayonetta 2, packaged with the original Bayonetta. There were also rumors that Platinum Games would be releasing a Bayonetta and Vanquish bundle for the PlayStation 4 and Xbox One, but that has not yet materialized.
In short, just get both of 'em on February 16.
Bayonetta 3 is still in development, but we will have more updates about the game as more information begins to surface and it comes closer to release.