Comparison of Material Power in Variant-Chess Games



Comparison of Material Power in Variant-Chess Games

by vickalan


The leading image includes games at intermediate points of play:
Classical Chess - Magnus Carlsen vs. Anish Giri, Jan 21, 2017
Bulldog Chess -   foofooes vs. vickalan, Jan 21, 2017
Waterloo Chess -  LXIVC vs. IvanKosintsev, Dec 19, 2016
In one of my previous threads I made a very simple analysis comparing the power of material in Bulldog chess to Classical chess. I went back to that analysis and decided to extend it to some other games too. In this update, I included the following games (this list includes games I'm most familiar with. If you'd like to see other chess variants compared please see the comment at the end of this article):
1) Classical Chess: (the "baseline")
2) Classical Chess, Endgame only: Chess endgames can be challenging puzzles in their own right. They represent a condition where there is much less piece value on the board, but tactical strategy can still be complex and interesting. I included a chess ending with KQRR vs. KQR, which is the highest value of pieces from an endgame of seven pieces (assuming no promotions). This represents a "lower limit" game condition, where if there was any further reduction of power (simplification), the game could start to become less interesting.
3) Janus Chess: Invented about 40 years ago. Has two januses (= bishop + knight) for each player in addition to other normal chess pieces.
4) Capablanca Chess: Invented in the 1920s. Uses an archbishop (= bishop + knight), a chancellor (= rook + knight), and other normal chess pieces.
5) Seirawan Chess: Invented about 10 years ago. Uses two new pieces for each color (bishop + knight, and rook + knight), and other normal chess pieces.
6) Musketeer Chess: A more modern chess variant, which allows the players to choose from ten special pieces to be added with other pieces. The ten pieces include archbishop, chancellor, dragon (= queen + knight) and seven other powerful pieces. In this analysis I use only a sample game using archbishop and chancellor.
7) Bulldog Chess: This variant (introduced in 2016) includes two guards and two siege-towers with other normal chess pieces. The siege-towers are a pawn-type piece, and the guards move with king-like ability.
8) Bulldog Chess with Witch: A Bulldog variation where each player has one witch, one guard, and other normal chess pieces. The witch does not capture, but pieces adjacent to her become transparent to friendly pieces of her color. (The witch's rules were developed by evertVB).
9) Bulldog Legacy Chess: Another Bulldog variation where each side starts with 18 pieces rather than 20. The game uses a guard along with other normal chess pieces. The two outside files have only a single pawn for each player and no other pieces.
10) Waterloo Chess (5th Edition): This edition of Waterloo was released January 1 of this year, and features seven variant pieces in addition to other normal chess pieces, played on a 10x10 board.
11) Chess on an Infinite Plane: Play for this variant started January of this year. Each side has two chancellors, two hawks, two guards, and other normal chess pieces. The playing area does not have borders.
12) Amsterdam Medieval Chess: A chess-variant designed as an intermediate form between classical (FIDE) chess and the more complicated Waterloo chess. It was released recently and has not been played yet.
Material Power Density - Method of Calculation:
This analysis compares chess variants by their "material power density". This is the sum of the value of all pieces starting on the board divided by the size of the playing area (total squares on the board).
It is generally presumed that a higher power density leads to faster games, and the attacking patterns can be more complex and dynamic. Each side can quickly create threats, and the other side will need to react quickly to defend and create counter-attacks. On average, games will often progress into an endgame quicker, often without pawn advances playing a dominant role.
In games with a lower power density, the opening game will usually last longer, and both sides will have more moves to strategically create defensive formations, while also initiating threats to disturb the opponent. Accurate play and strategy is required in advancing pawns, as this is both necessary to create defensive formations, and to create opportunities to promote one or more pawns (or at least create the threat of doing so). It is much more likely the endgame will feature one or more queens earned by a pawn promotion.
The following table shows piece value assumptions used for this analysis (not exact, and can be affected by board size and other pieces on the board):
With piece values assumed, I summarize the result in the table below showing board size, number of pieces, piece density, and material power density. Rows are ordered with classical chess first, followed by games in increasing order of power density.
We see that "Chess on an Infinite Plane" has a power density about 58% lower than that of classical chess. This is based on an assumption that most play will take place in a range of 18 x 20 squares. This is the horizontal span and 2 ranks less than the vertical span of the outermost pieces (starting position). The board actually starts with a range of powerful pieces, including four chancellors and four hawks. The added power is necessary so that enough power exists in the endgame for one player to achieve a checkmate, considering that the board has no borders, and trapping the king in a corner is not possible. But due to the large assumed playing area this game has a very low estimated power density.
The next lowest power density is found in Bulldog Legacy, which is about 18% less than that of classical chess. Few players of classical chess believe the game is too simple, and no player or chess-engine has found a method to win every game. For this reason, I believe that variant chess players will continue to find spectacular play in variant chess games even when the power density is substantially lower than that of classical chess.
Continuing down the list, we see Seirawan Chess, Musketeer Chess, and Amsterdam Medival Chess (still never played) have power densities 40% or higher than that of  classical chess. Last on the list is Waterloo Chess, with a power density of 2.72, which is more than twice that of classical chess! This is due not just to the strong pieces, but because 60% of the board (6 of 10 ranks) is occupied by pieces at the start of the game.
I have checked the play of one complete game, and played one game myself. In neither case did the game enter into what I regard as an interesting or spectacular endgame. But I believe the game's powerful pieces and interplay between them can make a game extremely complex, and chess variants with very high power densities deserve to continue to be explored.
In conclusion, I believe there is no "wrong" or "right" chess-variant game of any type. We learn about the games by playing them. There is not a game I regret ever having played, and every one of them taught me at least one new lesson or strategy, that I believe will make future games more enriching. Is there a best chess variant? I have no idea. I just say play games!
In developing this article, I would like to thank the following chess-variant players, who have played against me, at home or on, and help me learn about new and spectacular play that comes with these games of all varieties:
evertVB           knig22       NoisyEcho
brainking2016     gyrados      Var
BattlechessGN18   foofooes     cobra91
musketeerchess    astuteoak    bowlinggreen
If you enjoyed this article or have any comments please leave a message. Also, if you have any particular game that you enjoy and would like it compared in the same way, and have played it in a public forum, please let me know the details. If it includes new pieces not in this article I'll need to have estimates of their value. At some point in the future I may update the tables to make them more comprehensive and accurate.
Links to game instructions and examples on this forum:
1) Musketeer chess: (example game)
2) Bulldog Chess: (rules and analysis)(example game)
3) Bulldog Chess with Witch: (example game)
4) Bulldog Legacy Chess: (example game)
5) Waterloo Chess: (example game)
6) Chess on an Infinite Plane: (rules and example game)
7) Amsterdam Medieval Chess: (rules)

It would be interesting to see where Chu Shogi would rank on this scale. You could value the generals at 2.5, the Lion at 15, Dragon Horse and Dragon King as 5 and 7. Not sure how the Lance and Reverse Chariot should be valued, though. These are confined to the edge files, so perhaps they (and the edge files) should be igored altogether.

BTW, you seem to over-estimate the 'Guard'/King. If you are not yet in a late end-game it is worth less than a Knight. And the ratio between slider and leaper values might increase when the board gets larger.

I quickly checked some of the details about Chu Shogi. Wikipedia has some piece exchange values for the pieces (from German Chu Shogi Association). It shows a rook is 6, so I normalized the data by 5/6 (there's no pawns in Chu Shogi):
qty pc.          (v) (v, R=5) (total)
1 King            4     3.33   3.33
1 Queen          12    10.00  10.00
1 Lion           20    16.67  16.67
2 Dragon king     8     6.67  13.33
2 Dragon horse    7     5.83  11.67
2 Rook            6     5.00  10.00
2 Bishop          5     4.17   8.33
1 Kirin           3     2.50   2.50
1 Phoenix         3     2.50   2.50
1 Drunk elephant  3     2.50   2.50
2 Blind tiger     3     2.50   5.00
2 Fer. leopard    3     2.50   5.00
2 Gold general    3     2.50   5.00
2 Silver general  2     1.67   3.33
2 Copper general  2     1.67   3.33
2 Vertical mover  4     3.33   6.67
2 Side mover      4     3.33   6.67
2 Reverse chariot 3     2.50   5.00
2 Lance           3     2.50   5.00
2 Go-between      1     0.83   1.67
12 Pawn           1     0.83  10.00
Total (46 pcs)               137.51
x2 sides                     275.02
Based on the board size (12 x 12) this gives a piece density of 64% and a power density of 1.91. This puts it right around the power level of musketeer chess and the Amsterdam medieval chess (you helped with):happy.png
I think it's pretty interesting. Chu Shogi is evidently a sound game that people really enjoy, and it fits right in with the higher density variants of chess.
About the guard, I agree its probably not worth 4 (but Wikipedia has some convincing info that it's very close to that). On larger boards I think you're definitely right. Probably somewhere an average of around 3.5 throughout a game?
Thanks for reading the article!happy.png

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I added two games to the summary, Chu Shogi (I don't know much about it), and Grasshopper Chess.
Grasshopper chess is on a little board (8 x 8), but I've found it quite fun due to many grasshoppers (value = 1.8?) in a little space. The only thing not fun is that it seems like I'm losing my first game. sad.png

Whoa, one could do so many useless things if he's jobless.

nimzomalaysian wrote:

Whoa, one could do so many useless things if he's jobless.

I guess I could have been working on something like 7-tips-to-be-cool by nimzomalaysian instead.wink.png

Just for fun, I checked out what are the largest chess-like games (largest playing area). Here are some images of them (12 x 12 and larger).
Chu Shogi (12 x 12):
Clash of Mythic Titans (16 x 12):
The Six Clans (16 x 16):
Maka Dai Dai Shogi (19 x 19):
Tai Shogi (25 x 25):
Chess on an Infinite Plane (28 x 22, span of pieces in one game):
(game is a hybrid of "Chess on an Infinite Plane" and "Formation Chess")
Taikyoku Shōgi (36 x 36):
Background on some of the games: 
Chu Shogi: Probably developed in the 14th century, and is still played today in Japan and many western countries.
Clash of Mythic Titans: Not sure if this game has ever been played.
The Six Clans: Not sure if this game has ever been played.
Maka Dai Dai Shogi: May have been played in the 15th century. Each player starts with 96 pieces of 50 different types.
Tai Shogi: May have been played in the 15th century. This game may take more than an hour to setup, and finishing a game may require thousands of moves. Each player starts with 177 pieces.
Chess on an Infinite Plane: Developed recently. Each player starts with 38 pieces. Only the guard, hawk, and chancellor are uncommon with pieces in FIDE chess.
Taikyoku Shōgi: May have been played in the 16th century. Each player starts with 402 pieces of 209 different types, but the exact rules of the game are unknown. If played with physical pieces, it would probably take more than an hour to setup, and require several days of continuous play to complete a game.

(images from):

Tenjiku Shogi (16x16) would also deserve to be in this list. It could also score very high in power density. Each side has 78 pieces, and two of those are the incredibly strong Fire Demons, which capture not only the square they land on, but also all adjacent pieces (some what like in Atomic Chess, but only enemy pieces, and they do not self-destruct). Apart from sliding in 6 directions it can also make 3 King steps in independent directions (but not capture in passing). Trading the Fire Demon for merely three Queen-class pieces plus some Pawns is considered a bad trade. There are also several other pieces significantly stronger than a Queen (like a Queen that can jump over arbitrary many pieces for capturing, or a Queen that is capable of double capture at close range). Waterloo should be considered a very 'tame' game compared to Tenjiku Shogi. Hundreds of Tenjiku games can be found on the PBeM server (although I have no idea if any are recent), so I suppose it is significantly played even in the west, although the game ismore than 300 years old.




I have designed three 13x13 variants with about 50 pieces per side myself, which are demagnified versions of Tenjiku, Dai Dai and Maka Dai Dai Shogi. (I called them Nutty, Cashew and Macadamia Shogi.) The idea was that reducing the size by roughly a factor 2, and eliminating the boring bits, (the very weak pieces), these games (which often have very original rules) would become more accessible for playing. So far I suppose they count as games that are not played, however.

That's really cool and I'm glad you pointed it out to me. It looks like a great variation of the Shogi-type games because it probably has a faster exchange of pieces, which is needed when you start with so many pieces. (I have nothing against long games, but if it would take more than a year to finish by correspondence then that is probably becoming a bit too much).
If you want to try your Macadamia Shogi let me know. I probably cannot start right away, but maybe in a week or so (and after I have time to read about the pieces) I might be able to play a game.