Traditional Chess variants, as rated by Grandmaster Larry Kaufman
Benedikt Rosenau
Germany Göttingen
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Larry Kaufman is a mathematics professor and an avid player of many games. In Chess, he made it to grandmaster by becoming the world champion of the seniors. He plays Shogi at a level close to that of a professional, and he has considerable strength in Xiangqi, too. He is involved in the programming of the world's strongest Chess engine Rybka. Some of his articles on this matter, like Evaluation of Material Imbalances, are groundbreaking.
Kaufman has written a short methodical treatment about the pros and contras of traditional Chess variants. In this, he compares traditional Western Chess, Western Grand Chess, Chinese Xiangqi, Korean Janggi, Japanese Shogi, and Japanese Chu Shogi.
His criteria are: 1. Frequency of draws 2. Equal chances for either player 3. Importance of memorizing openings 4. Variety of play 5. History and tradition 6. Game length 7. Count of strategical principles 8. Early interaction in the game
Normally, the more the better, but not for frequency of draws and memorizing openings. Game length and variety of play may become too much, too.
Kaufman assigns one point maximally to each of the criteria, and he breaks it down to quarter points. So, overall, a game might reach 8 points. The result is (game, Kaufman's result, and the result adapted to a 1-10 scale that need not be that of BGG):
Game, Points (of 8), Points (of 10) Shogi 7 9 Grand Chess 6,25 8 Chu Shogi 5 6-7 Chess 4,5 6 Xiangqi 4,5 6 Janggi 4.5 6
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1.
Board Game: Shogi
[Average Rating:7.40 Overall Rank:486]

Benedikt Rosenau
Germany Göttingen
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Draws 1, equal chances 1, memorizing 0.25, variety 1, history 1, game length 1, principles 1, early interaction 0.75.
Quote: [T]he evidence is strong that shogi is the best game in the entire chess family, and with the risk of offending Go players (a game which I also play and respect greatly), perhaps the best game of all.
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Benedikt Rosenau
Germany Göttingen
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Draws 1, equal chances 1, memorizing 0.5, variety 0.75, history 0, game length 1, principles 1, early interaction 1.
Quote: It really is an excellent game and deserves a bigger following.
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3.
Board Game: Chu Shogi
[Average Rating:8.75 Unranked]

Benedikt Rosenau
Germany Göttingen
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Draws 1, equal chances 1, memorizing 1, variety 0.5 (too much), history 0.5, game length 0 (too long), principles 0.5, early interaction 0.5.
Quote: I do enjoy playing the game on occasion, but since I have not played enough to know the moves of the promoted pieces without reference to the manual, both my skill and my enjoyment go way down late in the game.
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4.
Board Game: Chess
[Average Rating:7.09 Overall Rank:244]

Benedikt Rosenau
Germany Göttingen
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Draws 0, equal chances 0, memorizing 0, variety 0.5, history 1, game length 1, principles 1, early interaction 1.
Quote: Shuffle chess would score the same, gaining a point on memorized theory but losing it back on history and tradition, of which it has none.
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5.
Board Game: XiangQi
[Average Rating:7.27 Overall Rank:411]

Benedikt Rosenau
Germany Göttingen
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Draws 0, equal chances 0, memorizing 0, variety 0.5, history 1, game length 1, principles 1, early interaction 1.
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Benedikt Rosenau
Germany Göttingen
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Draws 0, equal chances 0, memorizing 0.25, variety 0.5, history 0.75, game length 1, principles 1, early interaction 1.
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Göttingen
SA
Yes, I was about to no the omission of Capablanca Chess as well. Personally, I think it deserves a seperate listing.
Salinas
California
Mr. Kaufman did not use the word "traditional" at all in his article. Blame the OP of this list.
I would agree some of his criteria are odd and interlocking: He apparently like balanced games (in the sense that the (dis)advantage of going first is minimized), but non-drawish ones. He wants "long history & tradition" (guess he's never heard of the "Cult of the New"), but openings that are not memorized (though to a certain extent, opening books are a result of exceptional popularity of a game. Why bother developing & memorizing opening if few people play?)
The real odd thing is that giving equal weight to all criteria. Some elements, like strategical principles should outweigh history.
Shoots his academic credentials in the foot right there. Does constructing an elaborate oversize gameboard sound like medieval Japanese humour to you? Aren't practical joke objects kind of a Twentieth century innovation? Unless there exists some sort of tradition of novelty gameboards that I haven't encountered, he is dismissing this game as being an example of something that hasn't been demonstrated to exist.
The article is also full of "I feel" and "I think" statements, indicating that this is really just an analysis intended to find the best game for him, rather than the best or most interesting or even most demonstrably complex game.
Göttingen