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The idea behind the game may be a good one, but I now think the game is flawed. It does address the problem with Chessgi of the pieces being a bit too powerful for a drop game, but it has problems of its own. The main problem is that the King is now surrounded by pieces that can't defend it well against attacks from dropped pieces. In a game I just played, I checked the King with a dropped Pawn, and even though the King, the General, and the Elephants were all in their original position, only the King could have potentially captured the Pawn. The General and Elephants were worse than useless, for besides being unable to do anything, they impeded the King's escape. My Pawn was protected, the King had to flee, and it was checkmate on the next move in a very short game. I now understand why Shogi replaces the General and Elephants with Gold and Silver Generals. These pieces are much more useful for defending the King from dropped pieces. Chessgi could be improved by using weaker pieces, but I no longer think that using Shatranj pieces is the way to go. Shogi pieces are better, but if that is the direction Chessgi must go to get better then I may as well stick with Shogi and not bother trying to fix Chessgi. Perhaps Halfgi, which has already been done, is a better way to go.
As to Mr. Gilman's question, doesn't a popular 4-player shogi variant with a reduced array of pieces on a standard shogi board (Yonin Shogi) already exist?
A house-rules version of 4-handed chaturanga and Chess of the Four Seasons that I know replaces the move of the ship/alfil with the move of the shogi elephant, a move that al-Beruni described as the movement of the piece in 10th-century chaturanga. Both games play much better that way.
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Shatranj is a cool variant mainly for its historic value, IMO. It's awkward, weak ferz and (especially) alfil (or elephant) pieces make it somewhat frustrating to play for many a modern player, again IMO. The present variant, Shatranji, removes some of this frustration, as dropping either of these weak pieces after they are captured allows the (now not necessarily permanent) binding of them to become less of an issue. However I find the elephant piece still awkward to use, while it is still on the board, in Shatranji, owing to its double binding. I'm wondering if a 'Modern Shatranji' version of Joe Joyce's Modern Shatranj variant (i.e. crossing it with Chessgi-like drops), with Joe's use of guards and modern elephants, rather than ferz' and alfils, might prove at least as good in practice as Shatranji.
[edit: Here's my tentative estimates of the piece values for this variant: E=2.06; P=2; F=2.25; N=3.5; R=4.]