So, with the help of the Java applets at the Chess Variant Pages, I've learned the basics of how to play shogi, the Japanese game most closely related to chess.
(Never mind the fact that the English-speaking users of the site call shogi and the other games I'm talking about "chess variants" like a bunch of ethnocentric butts; when they say "chess," they mean "game played on a board with pieces that move geometrically," not "the western game descended from a game from India which was originally just another variant itself." Chess players take themselves awfully darned seriously for people obsessed with a game that can be played more effectively by a mathematical pattern than a human brain.)
I've had a fair bit of fun playing shogi this way.
I've also learned the basics of playing xiangqi, the Chinese game most closely related to chess.
I've also had fun playing xiangqi this way.
I've learned the basics of playing janggi, the Korean game which is mostly a lot like xiangqi.
I... haven't had much fun playing janggi, because I hate the elephants. But I won't go into that too much, because I don't feel like dwelling on my incoherent rage. (The cannons also aren't nearly as fun as in xiangqi. Yes, xiangqi has cannons. It's kind of awesome, and they're the whole reason I play it.)
I've also, thanks to similarity between the games, played some yitong, which doesn't have a Wikipedia article, presumably because it's not actually much of a game.
Whether this game is an accurate recreation of a particularly popular game or not is irrelevant; what's relevant is that the red army, which you might notice is down quite a few pieces, probably will always win when a player is of reasonable skill. Why?
Chess has several kinds of pieces; the most powerful piece in modern international chess, the queen, is the combination of the two next-strongest pieces. An even stronger piece adds the knight's movement to become a piece so dangerous that it could take on most of a chess army by itself.
The rook (actually a chariot) that the red army retains from its original lineup is three combined pieces, the chariot/rook, the horse (a knight that doesn't jump), and a cannon. The thing about adding a cannon to a rook/chariot is that the only thing that holds back a rook from being unstoppable is that pieces block it; a cannon can and must jump a piece to attack, and so this is a nearly unblockable rook that also attacks a wide area. This piece would arguably be stronger than the aforementioned queen/knight hybrid piece, and as long as you don't do anything stupid, you can checkmate quickly and easily with that piece.
While it's not much of a game, though, it's still fun. Stupid fun, but fun regardless.
*I can't, as I noted in the title text, tell pieces in shogi, xiangqi, or janggi apart well. Unfortunately, whoever edited the shogi article there thinks that pictorial representations on shogi tiles are stupid and irrelevant, and so I couldn't form associations with pieces until I played with the Java applet, whose programmer had no such snobby ideas. It's awfully hard to get interested in something where someone marginalizes you for not being able to read the language they're using. The article says that the pieces can be told apart by size, but that's not helpful either. Fortunately, the Chess Variant Pages are friendlier about pictorial representations in general.