My first lesson when i begun to learn chess was: How pieces move.
My second lesson was, piece value. I was told that, a pawn is worth one “point”, knight and Bishop worth 3 Pawns, Rook worth 5 Pawns, Queen worth 10 Pawns. This was the first and only lesson related to piece evaluation. I then begun to play, learn books and improve my play. The more i learnt, the more i understood the beauty and complexity of chess, of chess positions, strategic and tactical finesses. And i begun to appreciate positional sacrifices etc.
This section, gives a first relative evaluation of the pieces used in Musketeer Chess. Although these values are definitely perfectible, they have the merit of giving a starting point.
In our research, we first developed a simple evaluation function as a starting point, then we developed an engine for this purpose. The computer was very useful to have thousands of games available rapidly, and helped in testing various ideas and “settings”. The result of these tests are shown here. We are actually writing an article explaining the simple method we first used to approximate the pieces relative values.
Pawn : 100
Knight : 315
Bishop : 315
Bishop Pair Bonus : 50
Rook : 500
Queen : 975
These are the values given by GM Larry Kaufmann, in his Evaluation of Material imbalance, work based on analysing Grand Masters Millions of games and used to improve his engine Komodo.
For the Musketeer Chess Fairy Pieces, we think that their relative values are as follows:
Leopard : 670, slightly stronger than Knight and Bishop combined. Even though the Bishop moves are restricted to 2 squares.
Archbishop : 770, globally worth a Pawn more than the Leopard due to extended Bishop abilities. My personal opinion is that the Archbishop is underestimated and is probably worth more especially in the opening and middle game. In my games i love to trade my Queen for an Archbishop. In the endgame compared to the Chancellor it’s probably 50-100 centipawns less valuable especially when the position is opened. My opinion Archbishop is worth as much as the Chancellor especially early in the game. In the endgame, the Archbishop is probably more useful, especially when the position is opened.
Cannon : 750, slightly less strong than the Archbishop. The Cannon is an excellent piece when playing the endings, especially when it is near the opponent’s king. This is one of the “surprises”: the Cannon is stronger than the Elephant. This was almost the only big difference between my “intuition” based on my personal games and play test, and probably more accurate calculations based on thousands of computer games.
Chancellor : 800-850. Probably worth slightly more than half a pawn compared to the Archbishop in the endgame. In the opening and early middle game, the Archbishop is a more useful piece to build attacks. The more open files in the position, the stronger the Chancellor becomes. The Chancellor is an equal match for the Queen. Probably worth 925-950 in the endings. When promoting i prefer promoting a Chancellor over a Queen because it can mate a Bare King alone.
Dragon or Amazone : 1250 – 1400. Worth slightly less than the value of the Queen + Knight in the opening as it can easily be attacked by much less powerful pieces. In the ending it is by far the strongest piece and is worth easily the value of Queen + Knight + one or two Pawns. It’s a historic piece, that’s why we felt it has its place here. It’s very strong for the small Classic Chess Board and there are definitely other pieces that are more fun to play with.
Unicorn : 560, worth less than two Knights. Stronger in the opening and middle game. The forking capabilities of the Unicorn make it a piece of choice for those who like to play attacking and tactical games. Even with less pieces on the Board, it’s still a very dangerous piece and can hold many positions against a Queen. In the endgame, among the heavy pieces, it’s probably more interesting to have a Chancellor or other Knighted pieces to gain the advantage more easily, as this restricts the forking capabilities of the Unicorn, compared to the Queen.
Hawk : 550, my favorite piece. It’s probably slightly less valuable than the Unicorn, and this especially true in the endgame where the position is opened, restricting its forking capabilities.
A Rook is probably slightly stronger in the endgame. Rook vs Hawk endings are tricky, probably one of the most tactical endings in Musketeer Chess for relatively equal strength pieces. A Hawk + King vs King can mate in around 22 moves whereas a Rook + King vs King is a mate in less than 14 moves.
Elephant : 630. Worth a Pawn less than the Cannon. This result was a surprise for me as in my tests i assumed they were of relatively same strength. This is probably explained by the relatively slow development of the Cannon compared the Elephant. As the Cannon is a very valuable piece in the endgame, capable of mating a Bare King alone, this is probably an explaination. This leaves room for more improvement once some finesses of positions will be better understood.
Fortress : 760. Slightly inferior to the Archbishop.
Spider : 815. It is the second strongest piece after the Dragon. Slightly stronger than the Archbishop. It’s main weakness is that it can be attacked easily by long range pieces.
Musketeer Chess begun to attract a wider audience. Some funs wrote blogs or articles. One of them is an interesting introduction to the game and to the relative piece value from the personal point of view of the author. He is Granola Ebinola, who was once involved in the invention of another Chess Variant (Chess2: The Sequel). You can read the above mentioned article here.
Another interesting work on the relative piece evaluation, is the result of Sbiis Sabian work, a.k.a @finitus on chess.com. He described an interesting methodology based on piece mobility. The article is available here: A mathematical approach to assess Musketeer Chess Piece Value .
I also welcome you to visit our youtube channel, with plenty of exciting games of Musketeer Chess.
We are currently conducting more tests, using Machine Learning techniques. A new and interesting approach to Chess and Chess Variants.
Our coming article describes our use of Optuna, a framework to tune Engines Evaluation Functions.
Pawn : 100,
Knight : 315,
Bishop : 315,
Bishop Pair Bonus : 50,
Rook : 500,
Queen : 975
Leopard : 670,
Cannon : 750,
Archbishop : 770-800,
Chancellor : 800-850,
Dragon or Amazone : 1250 – 1400,
Spider : 815.
Unicorn : 560,
Fortress : 760,
Elephant : 630,
Hawk : 550,