Pankratos: I know a bit about its history and how it got its name. I have proposed naming the two halves of the board, the Royalside (A-E) and the Courtside (F-J).

The castling on this site isn't quite right, but it works. The King when castled should either move next to the Rook, or be one space from the Rook. Notated on the Royalside as O-B, or O-C, and O-H, or O-I on the Courtside. As compared to how it is done on this site of just moving the King three squares toward the Rook and its adoption of the regular Chess notation, O-O ans O-O-O. It's a minor thing, as castling isn't as good of a plan for some reason, but this would fix the play and give the King a bit of space and some options. As you can imagine, adding two powerful pieces to the board really causes the King trouble.

The name comes from Modern Bird's Chess. MBC abbreviated instead of EC, and from there it is easy to say Em-ba-ssy. Henry Bird invented his version of the game in 1874. I do not know if he knew of Carrera Chess from 1617, yes Sixteen-seventeen, or not. About 50 or 60 years later Capablanca experimented with these pieces on 10 × 10 and 10 × 8 sized boards. Embassy Chess is from 2005. Its initial position is an attempt to find the best placement of the pieces at the start of the game, which a few players through the times found flaws in Bird's and Capablanca's set ups. The pieces are similarly lined up as in Grand Chess from I believe 1974, but played on a 10 × 8 with castling and regular Pawn promotion rules.

There is a symmetry to the pieces, and it balances all of the moving ways equally. Four pieces move as Rooks, four as Bishops, and four as Knights. The initial set up has all Pawns guarded at least once by a piece not counting the King. The Rook moving pieces guard the corners and the King. The Bishop moving pieces cover the squares diagonally equally from each side of the board.

As for opening theory, I have played a few games with White using the Queen's Pawn opening. Unfortunately I am not a strong enough player to see the depth on the many variations. Embassy Chess is a lot deeper than meets the eye, especially when compared to regular Chess. Many of the ideas of regular Chess carry over to Embassy Chess. The wider board can make the end game a bit different in many situations. Atrotos Atrotos made some videos notating a few games. I believe he posted the links if you scroll down a bit. 8 posts from here.

Knights can be very weak in the end game, especially if near the edge of the board. There's a few charts and studies of the relative strengths of the pieces on various sized boards. For the 10 × 8 sized board, Reinhard Scharnagl and Ed Trice calculated differing values for them. I use a modified chart that's easy to remember, but for the most part you can use the regular Chess chart keeping the Marshall and Cardinal at values just less than the Queen. The Marshall is a very strong piece, almost the strength of the Queen. The Cardinal is almost as strong as the Marshall. Very mobile from the start, unlike the Marshall which can have trouble with a closed position.

Here's the simplified chart.

9 = Queen
8 = Marshall
7 = Cardinal
5 = Rook
3¼ = Bishop
3 = Knight
1 = Pawn

Experience will show you when to think differently about trades based on these numbers. The Bishops and Knights can vary a lot and some players devalue the Knight to 2½ or 2¾. The Cardinal losses a lot of its strength when in the corner. As for the other charts, I think they can be found somewhere in the depths of this discussion board, or maybe you can try Reinhard Scharnagl who is SMIRF Engine on this site. SMIRF Engine He wrote a program to play many of the 10 × 8 Chess variants and also created Capablanca Random Chess.