Comments by JorgKnappen
The Jelly is actually a nice suggestion for the Queen. I estimate it a little (about 0.5 to 1 pawns) weaker than a Queen. This weakness is overcompensated by the overall strength of the rest of the Bakery Bombers. Since the Jelly is an extended Bison (LJ or Camel-Zebra compound) it has the can-mate property. The Jelly is a tactically very dangerous piece because it has many immanent threats against the pieces on the opposite baseline. Against the FIDE army, it can enforce "Queen exchange" with the manoeuvre 1. Jelly b3 e6 2. Jelly e5 -- Black gets two moves for a nominally bad exchange, maybe not that bad. Black can save the castling rights at the expense of one move by answering 2. ... Nc6. I checked that there are no immediate other dangers, 1 ... e6 is an almost universal weapon against early Jelly attacks. I have not tried the other canonical armies of Chess with Different Armies yet, they may have weaknesses against a Jelly on d1. I also have not yet checked whether other piece may orchestrate an early Jelly attack.
Thanks for the clarification, probably I was too distracted by all the rules against indirect lion exchange to see the obvious. Also thanks for the additional details on X-Ray protection and modern Japanese practice.
Good to have your chess variants back online! I browsed though them again and found Matron Chess very interesting. Just a little rule change to make Queen exchange more difficult, but very different game dynamics. The rule change is in some sense the opposite of the rule on Chu Shogi lion exchange: With the Matron it is more difficult to initiate a Queen exchange while Chu Shogi makes it difficult to complete the Lion exchange by capturing the Lion back. The Matron variant leads to a more offensive play which seems to be a good thing.
I think a got a proof for the hex geometry. We orient the hexes such that there is a horizontal line of rook movement, and denote that direction by 1. The other directions of rook movement are denoted by \omega and (\omega-1) [the use of the letter \omega is inspired by Eisenstein numbers]. The centre of a hex is given by a+b\omega with a,b integer numbers. First step is a drawing: When we go horizontally firs and vertically as a hex bishop second, we can reach only one half of the hexes (a+2b\omega). We repeat this for the other rook directions and mark the hexes accordingly. They fall in two classes: (i) hexes which can be reached in one way only (ii) hexes that can be reached in all three way. The second class forms a grid described by 2a+2b\omega (both coordinates must be even. Finally we map these to rook and bishop moves. The path to a three-way reachable hex (2a+2b\omega) using horizontal and vertical moves (elementary vertical bishop step: (2\omega -1)) consists of b bishop steps and b+2a rook steps. Therefore the number of rook and bishop steps are both odd or both even, giving an even SOLL. The other direction: Take r rook steps and s bishop steps and demand that r+s is even. Then we go to r+s*(2\omega -1) = (r-s) +2s\omega. This is a three-way reachable square again, because (r+s) even implies (r-s) even.
I like the idea of circular riders moving on exact circles, and the generic name Orbiter is a good fit. In particular, I find those orbiters interesting that have more squares on their circle than just the minimal number (4 for straight or diagonal distance, or 8 for skew distance). Unfortunately most of them are much too large to play well on usual chessbords (eben 16x16 is small for them). And it needs some training to visualise their possible pathes. They have so many directions to go! P.S. A less symmetric version are orbiters orbiting around the center of an edge, the simplest variant has four squares marking a rectangle. P.P.S. One of the orbiters (the circular King) is alreay found in Betza's article here: http://www.chessvariants.org/d.betza/chessvar/16x16.html
I learned that there was a german edition of this game published in 1972 by Parker under the title "Schach dem Schlaukopf". The pieces are Dummkopf (Ninny), Schlitzohr (Numskull), and Schlaukopf (Brain). Source: http://de.wikipedia.org/wiki/Schach_dem_Schlaukopf
I'd suggest changing the "punchline" to something more descriptive than "http://www.spartanchessonline.com". Suggestion: "The spartan army with 2 Kings and novel pieces fights against the persians (standard chess army)" The punchline occurs in several listings on this site, including the favourite games listing.
"Unchained bishop" is a rather vague concept at the moment. It is my model to explain the excess value of Queen and Archbishop (Janus/Paladin) compared to their raw components. The bishop itself is hindered by board geometry and pawn structures (there is always a so-called bad bishop in the team) to move from one good position to another good position. Combining it with some other piece lifts this restriction and some of the value of a queen (specially the queen-chancellor difference, maybe more) comes from the "unchaining" of the bishop. Your measurement of the Archbishop's value suggests that adding a knight is sufficient to "unchain" the bishop. I don't think that colourboundness is a big issue for the bishop. It may be testable by comparing BDD (Duchess or Adjutant) to the Bishop-Panda compound; the latter is not colourbound, the former is, while the pieces are very similar to each other in other respects. At last, I am interested in the outcome of the R2 tests, since I made a prediction of its value. Depending on the knight's value (300 or 325 cP) it should be one or two quanta of advantage (30 to 60 cP) less than a knight.
Jeremy, I don't do a mobility calculation. I just steal Ralph Betza's idea for mobility calculation to do an interpolation of piece values. Both endpoints (the values of wazir and rook, e.g.) are empirical piece values coming from playtesting; therefore the interpolated values are also piece values including all the factors affecting the piece value. And yes, it is only an interpolation, not a calculation from first principles. I think there is still some point in it, seeing the different values of "magic" for Rook, Bishop, and Queen. And seeing that an "unchained" bishop is worth almost a rook maybe explains the surprising fact that the Janus/Paladin/Archbishop is worth almost a Chancellor/Marshall. At least, this is my current interpretation of the data. The next riddle to solve is What constitutes the pair bonus?
Looking differently on Ralph Betza's old idea expressed here, I take it for granted that a ranging piece may move with some probability one step further.
This gives the following formula for the value of a full rook:
R = R1 * (1 + p + p2+ p3+ p3+ p4+ p5+ p6)
Inserting R=5 and R1=1.5 gives us p=0.73. This averages over everything relevant, no model for crowded board mobility is needed.
The main point is: The magic number p is different for the ranging pieces; for a bishop it is only 0.5 and for the queen it is ≈0.715.
The low number for the bishop comes from the board geometry: The diagonals are on average shorter than the orthogonals. In addition, the bishop has only one way from a1 to g1, and this way goes through the well-guarded centre of the board.
The queens magic number is almost (but not fully) the same as the rook's number. This is very interesting and I interpret it this way: The queen almost lifts all the geometric restrictions of the bishop.
Below are tabulated results for n-step rooks, bishops, and queens. A Q2 is a nice rook-strength piece. All values are in centipawns.
X1 | X2 | X3 | X4 | X5 | X6 | X7 | magic number | |
Rook | 150 | 260 | 339 | 398 | 440 | 471 | 494 | 0.73 |
Bishop | 150 | 225 | 262 | 282 | 291 | 296 | 298 | 0.5 |
Queen | 300 | 515 | 668 | 777 | 855 | 910 | 950 | 0.715 |
It's a pity. Michael's creations were interesting and of good game design quality. I like his names for some pieces (e.g., Jerboa instead of Tripper), too.
Where has Michael Howe's Universal Chess gone? I still have a printout, but now Universal Chess is something different here. It was another system to create lots of chess pieces and assigning buy-point values to them; including names for ready-made pieces.
Nice and original board design: it looks like a world map. Unfortunately I cannot understand the text ...
Hmm... it your decision, at last. Possibilities include: (1) If you cannot gate in a piece in the last possible move because you are in check, this counts as checkmate and you lose the game. If you cannot gate in a piece in the last possible move and you are not in check (may happen on a very crowded board), this counts as stalemate and the game ends in a draw. (2) Game goes on and you just have forfeited the right to bring that particular piece in play (put it to the place where the captured pieces are). For most pieces this is a huge penalty, but you may even want to trigger this situation in order to avoid a Wuss on your side. Maybe additional rules become necessary: What happens if you can gate in either a pawn or a major piece, but not both (e.g., because you can block a check with a pawn move or a piece move)?
In Derzhanski's list ( http://www.chessvariants.org/piececlopedia.dir/whos-who-on-8x8.html ) tentative values for the Ultima pieces are given. They are calculated by Zillions of Games and may be grossly inaccurate, but I have not seen other estimates for them. Maybe experienced player of Ultima can say something about the practical values? In addition, I recommend reading the series Ideal Values and Practical Values ( http://www.chessvariants.org/piececlopedia.dir/ideal-and-practical-values.htm ) by Ralph Betza. It contains lots of insights in piece values. But the gold standard for piece values still is playtesting (between humans or in computer play).
Thanks for that links, it is a very enjoyable slide show.
Here's the position for mutual perpetual check with bishops and nightriders. You need two bishops on the same field colour (or a queen and a bishop); a position with bishops on different colour does not exist because the kings come too close to each other. Bishop's team: Ba2, Bb1; K b3/c2 Nightrider's team: NN f8, NN h6; K e6/f5 ... it just fits on an 8x8 board.
The square root of 2323 is 48, but the difference is just 11. Nothing of statistical significance. To get at some conclusions one has to sum up the results of many years or to extend the base of recorded games.
Thanks, Matteo, for digging out the reference. It says "Of the 2,323 public matches in fiscal 2008, white players won 1,167 and lost 1,156, a win rate of 50.2 percent, it was discovered on Tuesday. The previous highest win rate was 49.5 percent in fiscal 1968, and the lowest 46.4 percent in fiscal 2004." So, there was a constant black (who moves first in Shogi) advantage for 4 decades, but in 2008 the situation was reversed. Given the relative small number of recorded Shogi games, the 2008 result may be just a statiscal fluctuation. Are there more recent numbers published somewhere?
Can-mate Knight: Moves and captures as a normal FIDE Knight; but when the endgame KN vs. lone K is reached, it gives immediate check (and checkmate, if the lone King cannot capture it).
Switching off the can-mate property is not so easy. Just defining a Cannot-mate Rook as normal Rook, but when the endgame KR vs. lone K is reached, it it automatically a draw, unless the last capture gives checkmate -- seems to work, but in practice the stronger side will be keen to keep a pawn or two on the board and perform the mate with the full Rook before it is too late.
The compound of Quintessence and Rook is namend Leeloo in Quintessential Chess after the Fifth Element in Luc Bresson's film.
The compound of Quintessence and Queen is namen Pentere (with synonym Quinquereme) in Quinqereme Chess
The missing compound of Quintessence and Bishop I name Sai after Fujiwara no Sai, the ghost in the Go board in the manga Hikaru no go. Go is in japanese homophonous to the number 5. The ghosty connection is suggested by the analogous pieces Banshee (Nightrider-Bishop compound) and Dullahan (Knight-Ferz compound). Speckmann also reports that the Janus/Paladin (Knight-Bishop compound) was called "die reinste Geisterwaffe" (a pure ghost-weapon) by a problem solver.
The Sai is even stronger than the Banshee (having more directions and attacking more fields on the same board), but seems to be less tactical on 8 times 8. Because of its strength I wasn't yet able to design a CwDA army for the Sai. A simple modification of the Fearful Fairies is not possible.
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