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I agree with the reasoning for why Chess has a greater state-space complexity and a greater game-tree complexity than Chinese Chess. Having programmed the rules of both games, I will add some thoughts on computational complexity. This is primarily a factor of the number of possible moves available to a player each turn. Since Chess pieces all have greater powers of movement than their Chinese counterparts, a computer playing Chess may have to make more calculations to evaluate a move to the same depth. The main factors in favor of greater computational complexity for Chinese Chess are the larger board, the presence of Cannons, and the rule against opposing Generals. The larger board affects mainly Cannon and Chariot moves, since other pieces have limited ranges, and the opposing Generals rules. A Cannon is less computationally complex than a Rook, because it normally has fewer spaces it can move to. A Bishop is also less computationally complex than a Rook. Although the code for a Bishop move will be nearly identical to the code for a Rook move, it has as many possible moves as a Rook only from some positions. A centered Bishop has 14 possible moves on an empty board, the same as a Rook, but as a Bishop moves toward the edge, it has fewer possible moves on an empty board. I haven't done the math to tell which is more complex, but I suspect the Cannon is. Although a Horse sometimes has fewer moves than a Knight, it adds the computational complexity that comes from being able to pin pieces. A horse move can affect the possible moves of the opponent in ways that a Knight move cannot. The main source of greater complexity for Chess comes from the greater powers of the King and Queen, the ability of Pawns to promote, and the rules concerning castling and en passant. A Queen may have as much complexity as two Cannons, maybe more. A King normally has more moves than a General, and the opposing Generals rule only adds one more move to consider. Based on these considerations, I suspect that Chess is more computationally complex, but I have not done the math that a proof would require.