Comments/Ratings for a Single Item
Yes Zillions overestimates hoppers and ranks the Cannon slightly below the Rook, and the Vao slightly below the Bishop, and the Leo slightly below the Queen, which is really excessive for the 3 of them.
I really love the work he's done making this list, but I have to ask: Why is the Cannon rated higher than the Leon? If I understand the Leon right then it's strictly better.
Also, from what I've heard, the Cannon belongs way lower down than just beneath Rook. Maybe Zillions has some glitch when it comes to screening pieces, or maybe it's all in the starting location implemented.
H. G. Muller wrote on Thu, Sep 6, 2018 02:26 PM UTC:Interesting for sure, but to be taken with a rather large grain of salt. As the author points out, this is just how Zillions of Games values the pieces. Zillions is not always right, and not very strong. E.g. it has been shown by extensive computer self-play with far stronger programs that BN and RN are worth 8.75 and 9 (on a scale where Q = 9.5) on 8x8, which deviates a lot from the ratio 109 / 134 that Zillions get through some (propriatry) point-counting algorithm.
That being said, the Lion is indeed very strong, because of its ability to make hit-and-run captures. In Chu Shogi (12 x 12 board) it is considered about 1.66 times as valuable as a Queen, in the middle game. (In the end-game, where the board empties, the Lion becomes less valuable because it cannot be shielded well from slider attacks.) On 8x8 this ratio should go up significantly, as in Chu the Queen benefits from the larger board, while the Lion hardly does. An Amazon (QN) appears to be worth exactly as much as a separate Queen and Knight on 8x8, i.e. about 1.33 Queens.
Also note that the value of pieces can be strongly affected by what the opponent has. E.g. three Queens lose to 7 Knights (and only Pawns and King in addition) on 8x8, which violates all our ideas about the relative value of Q and N.
I just stumbled on this page, and it's quite interesting. (Very old, but still good.) I am, however, very surprised to see the Lion listed as the most powerful piece. If I needed a snap decition between Amazon/Lion I would have said Amazon on reflex....very interesting.
Ivan Derzhanski has compiled an impressive list of chess variant pieces. I wish that he had included more detailed notes, for the benefit of newcomers to this site. Here are some brief comments.
Nightrider combination pieces are discussed in the 'Notes' section of my variant Unicorn Great Chess.
I believe the 'short queen' (moves one or two squares like a queen) has been around for decades, under a variety of names. Peter S. Hatch calls this piece a Seeress in the ELVES army of his Fantasy Grand Chess (1999 and 2000). Tony Mez calls it a Guard in his Combo Modern Day Chess (2006). Peter Aronson and Ben Good use an unusual piece with the same two-square move in their variant Golem Chess. (2002)
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Consensus values for pieces in Xiangqi are R=10, C=6-4 (opening-endgame), H=4-6, A=E=2, P=1-3 (unpassed/passed). So C and H only approximately half a Rook, and it depends on the game phase which of the two is somewhat stronger. And one should realize here that the Horse (Mao) is only worth half an orthodox Knight on a board as crowded as orthodox chess. (Which is quite a bit more crowded than Xiangqi, so that extrapolating the Xiangqi values to that higher density might give H=3 and C=7. That would then imply N=6, which indeed gives the correct relative value of R and N. So this suggests C could be worth slightly more than a Knight in a FIDE context.)
In games without drops the opening value of pieces is dominated by what they will be worth in the end-game. E.g. it is still much better to have a Rook in the opening than a Bishop or Knight, even though a Rook on a crowded board trapped behind his own Pawns is hardly of any use at all. But it is almost unavoidable that it will get to express its true power later in the game, so that hanging on to it is a good strategy. But for Cannons the end-game value is low, and rather than waiting for their potential to develop with time, one should try to trade them in the most-favorable way before that time.
To do a meaningful empirical test of the Cannon value you would need to do it with an engine that handles it well. Otherwise the value will be underestimated. ("A piece is as strong as the hand that wields it.") And handling hoppers well means you have to be very much aware when it becomes time to exchange them for other minors. If you do that too early you would not have exploited any superiority while it still existed; if you do it too late you will be stuck with them when they get nearly useless. To make the program seek trading at the right moment it is essential that it makes the hopper value dependent on the piece density, in the correct way. Which would have too be determined empirically too.