Thanks for taking the time to explain your "philosophy of moderation", Walter. I do admit to having the opinion that "3) All posts must be approved" meand "moderated" and that "1) Everyone can post" means "unmoderated". In my experience, "moderated" newsgroups do indeed have a smaller number of posts; however, the posts are all "on topic" and flame wars are (of course) nonexistent. On the other hand, you volunteered for the job of moderator and no one else has any business telling you how to do it (and I hope that my post did not sound like someone trying to tell you how to do it). Interestingly enough, I think if Ed had simply instituted "3) All posts must be approved" and not allowed any posts not directly related to Gothic Chess, he would still be moderator. Of course, that's just my opinion...

It is a shame that the Gothic Chess discussion board has been subjected to the "danoschek vs. Trice" war. Neither one of the participants seems to have the sense to realize how silly the flame war has made both of them look. In fact, too few people seem to realize that simply ignoring inflammatory posts is the best course of action: The poster will soon realize that his/her posts are having no effect and will give up. The really sad thing is that both danoschek and Trice are extremely intelligent and would have very interesting comments to make if they would only bother to leave their flame war alone. I will miss Ed's posts on Gothic Chess.

I found your comments (as well as Chessmaster1000's reply) regarding the originality of Gothic Chess (as compared to Capablanca Chess, Bird's Chess, etc.) interesting. My guess is that the patent has not actually been tested in court and that the patent holder hopes that it never is. Of course, I should add that I am not an expert on patent law and have no intention of challenging one. I am just glad that the initial piece setup that Ed discovered makes Gothic Chess a fair game and enjoy playing Gothic Chess for the fascinating game that it is.

As for actions for the moderator, I used to think that a moderated discussion board meant that prospective posts were first screened by the moderator before being posted; that is, only the moderator can actually post to a moderated discussion board. Apparently that is not the case here, but such a procedure would certainly have made it possible to avoid the silliness we've seen without having to resort to banning anyone. Is such a thing possible, or is it more work than a reasonable person is willing to take on? I appreciate the effort you've put into being moderator, Walter, and would support any of the actions you feel are appropriate (up to and including banning certain individuals).

<edited to correct silly grammatical errors>

And when were you planning on telling me, Caissus? :-)

Ed, I appreciate your compliment regarding my playing ability and am delighted that you have found any of my games worthy of archiving. I still have trouble with the suggestion that there might be cheating involved, though. I realize that I'm not the tournament director, but I would suggest simply awarding the prize to the winner as was promised at the outset. There's been no cheating. I fail even to see how a player could benefit by throwing a game in a winner-takes-all tournament.

Perhaps some background on my playing method would be illuminating. I almost never resort to analyzing over a board (electronic or physical); the most I allow myself is a sheet of paper to record moves to help me visualize the variations. This, of course, makes me more subject to the possibility of making an egregious blunder. My 11-move loss to Caissus was due to just such a blunder: Nothing more, nothing less.

Since my name was mentioned as someone who lost on time, I'll just mention that I simply got too busy and didn't manage to login within the time limit. $250 is not enough of an inducement for me drop the other irons I have in the fire, so to speak (and I suspect this to be the case for most members of this site). I apologize if my inaction aroused any suspicion, but it seems rather paranoid to attribute any of this to behind-the-scenes dealing. From a public relations point of view, threatening to withdraw the prize would seem to arouse more suspicion than short draw agreements and mass losses on time. Is $250 too much of a financial burden for the tournament organizer to bear? Perhaps this response is overboard as well; I apologize if anyone perceives it so. However, I honestly can't see why anyone would go to all the trouble to make deals with other players for a mere $250 ($25,000 would be a different story ...) and so I admit to being astounded that such suspicions would even be considered. Of course, it could just be that I'm naive...

I seems to me that Slate's resignation was premature. Perhaps he felt his King was too far away. However, I can't see how Black can make progress: His Rook is tied to his c-Pawn and moving his King over to support it would allow White to get his King over to a2 with an almost certain draw (assuming best play, which might be a stretch for mere mortals playing a R+P endgame). By the way, the notoriety of the R+RP+BP vs R endgame goes back to Marshall-Rubinstein, San Sebastian, 1911 and it is just as drawn on a Gothic board as it is on a regular chess board since the dynamics of R+P endings are determined by how close the closer side of the board is to the Pawn(s); the extra width on the other side makes no difference (as long as the Pawns are all on one side of the board).

All right! I finally won something! :-)

Of more immediate interest to me would be an interface (like WinBoard, for example) that could seve as a digital Gothic chessboard and that could read and save moves in PGN format. However, I do think a strong chess engine would also be nice (to play against, practice with, and analyze with). I would be more interested in an extensive endgame tablebase than an extensive opening book, but I may be in the minority. A downside to having a strong Gothic Chess engine is that some would use it to play for them in online games (as happens with chess now).

Of course I can! What is this? Boot camp? ROFL!

It appears to me that after 39...Qxh7 40.Nxh7 Kxh7, White must play 41.h5 (41.Ah5 doesn't seem to go anywhere since it doesn't even set up a check next move). Then, after 41...Nxf4 42.Ai5+ Ki7 43.Bc1 e5 44.Ng6+ Kh6, it's not at all clear (at least to me) how White is supposed to force a perpetual check. It does appear that White can gobble up a couple of Pawns along the way and that his chances of holding the draw are excellent, though.

Interesting! I admit to not considering 39...Qxh7 seriously since it appeared to give up Black's advantage. OK, I've spent enough time on this and don't see how White can force a draw in this line, although it seems to me that Black's chances for winning have essentially evaporated. I guess I'll just have to use the stainless steel mug I already have! :-)

OK, I'll step up to the plate; after all, it's my game! In fact, I think perhaps I should get a GCA mug just for coming up with the idea of 35.Rxh6+ against Ed. :-)

After 38...Ng6, 39.h7+ Ki7 40.Ah5+ Kh6 41.Aj7+ Kg7 42.Ah5+ Kh6= (42...Kf8 Axg6+)

After 38...Qe8, 39.h5 (with the idea 40.h7+ Ki7 41.h6+ Kj6 42.Ai6 Ng6 43.Ah5+ Ki5 44.Aj4+ Kj6=). If 39...Qf8, then 40.Ai5 followed by 41.Ah7+ Kj6 42.Ai5+ Ki8=. Moving the Bishop doesn't help: For example 40...Bf6 41.Ah7+ Kh8 42.Ai6+ Ki8=.

After 38...Nc6, 41.Ai5 followed by 42.Ag6+ Kj7 43.Ai5+ Ki8=. If 41...Rg8, then 42.h7+ followed by 43.hxg8=Q (or, perhpaps, 43.hxg8=C). If 41...Qj7, then 42.Ag6+ Kj8 43.Nh7+ Ki8 44.Ni5+ wins Black's Queen for a Knight.

I'm "Juan Grande" on IYT. I'm working on all of my opponents (other than jestone, who's already here) to play Gothic Chess on BrainKing.com.

Hi, Felix! Yes, I got your question about Professor McFarland; unfortunately, I am not acquainted with him (even though the web page I referred you to regarding the opposition was part of his Finite Mathematics chess course - what a cool coincidence!) By the way, if you go to my profile and then to my list of finished games, you can play through the game via BrainKing's interface.

OK, since we've started showcasing games (and mating patterns), here's my submission. The game is also accessible via my profile. (I would provide the link, but since Ed's link to Terry's game didn't work for me, my link probably wouldn't work, either.) I also won't claim that the game is "high-caliber", but the mating combination at the end is an interesting Knight-Chancellor mate.

good7972 vs. juangrande
1. d4 f6
2. e4 Ac4+
3. Ae2 Axe2+
4. Qxe2 Nc6
5. c3 d5
6. g3 Cd6
7. exd5 Na5
8. g4 Bd7
9. Bg2 Bb5
10. Cd3 Bxd3
11. Qxd3 Cf7
12. b4 g5
13. bxa5 Nh6
14. Qe2 Bg7
15. Nh3 Qd7
16. Bf3 O-O
17. O-O Nj5
18. Rg1 Nh4
19. Be4 Ch6
20. Nd2 Ci4
21. Bh1 Nj3+
22. Kj1 Cxh2#

Thanks, Felix, for interjecting some humor. I've apologized privately to Ed for the tone of my message since I think I crossed the line of friendly discussion. We are very fortunate that he takes the time to frequent this discussion board (and that he asked Fencer to implement Gothic Chess on this site). It is my hope that anytime I challenge anyone's statements on this board that they understand it is because I find the issue interesting and would like to generate further discussion in an attempt to reach a clearer understanding.

I freely admit that I misinterpreted Ed's statements; however, in my defense, the term "the square" in King and Pawn endings refers to "the square of the Pawn" and is always used in the context of a passed Pawn as a device to check whether the opposing King can catch it in time. Of course, if one wishes to generalize the term's meaning to include King position, there is nothing wrong with that; but it's not the generally accepted meaning (that is, until the majority is enlightened :-) ). Ed has indicated that his playing experience seems to show that misunderstanding of the subleties of chess on a 10x8 board is widespread (or, something like that, I think), so that games are lost more quickly on a 10x8 board (even after the Gothic pieces are exchanged) than most people expected. That's an interesting observation. However, it should be pointed out that King position and opposite-colored Bishop endings are often mis-evaluated in regular chess as well. That is, after a flurry of exchanges in regular chess, one could easily find oneself in a lost King and Pawn endgame because of inferior King position; and, opposite-color Bishop endings are not necessarily draws in regular chess either, particularly when there are Pawns on both sides of the board. Perhaps these considerations are magnified on a 10x8 board. It would certainly be interesting to test these theories.

:-) Well, Felix, I must say that now I feel a bit silly for taking such a mathematical/scientific approach to your question since it appears that what you really meant by "speed" refers to the "feel of the game", a feature which can't be quantified. It seemed like you were taking the scientific approach by asking about the effect of the 10x8 board after removing the Gothic pieces, so that's what my reply addressed. Oh well, we both appear to agree that Gothic Chess is a richer, more complex, and "faster" game than regular chess. :-) BTW, see
http://math.uww.edu/~mcfarlat/177endg2.htm
for a brief description of opposition. For a more complete discussion of the fundamentals of King and Pawn endgames, see
http://www.chesscafe.com/heisman/heisman.htm
Note that everything said about King and Pawn endgames carries over to Gothic Chess.

I think Felix's question is deeper than the two previous answers would indicate. First of all, the question of whether Gothic Chess "takes longer" should be interpreted as "takes longer on average". Ed has stated on his website http://www.geocities.com/bow_of_odysseus/why_change.html that the average length of a game of regular chess is 55 moves and that the average length of a game of Gothic Chess is 30 moves. If we agree that "length" means "number of moves required to decide a game", this would indicate that Gothic Chess is significantly "faster" ("shorter") than regular chess. However, this difference in the length of Gothic Chess games versus regular chess games appears to be a result of the "increased firepower" on the board (Chancellors and Archbishops) rather than from the geometry (size and shape) of the board, so this result does not address Felix's question. the65thsquare claims that is hard to define "faster" or "slower", but the above definition that "faster" means "fewer moves, on average, for a decision" seems easy enough; and while I agree that a shorter checkmate is not necessarily better than a longer checkmate, it would appear to be hard to argue that the shorter checkmate is not "faster".

Felix's question (paraphrased) is this: Would regular chess be faster or slower on a Gothic Chess board (10x8)? Ed (GothicChessPro) claims that it would be faster because more games would be decided by an outside passed Pawn due to the increased width of the board. I find that hard to believe. Of course, if one could create an outside passed Pawn and exchange pieces down to a King and Pawn endgame with the opposing King outside the square of the passed Pawn, the win would indeed be simple (and fast). However, King and Pawn endgames are far from being the most common type of endgame and it is not at all clear that just because the board is wider that the proportion of games decided solely by an outside passed Pawn would be significantly higher. Here is another factor to consider: All of the elementary mates (K+Q vs K, K+R vs K, K+B+B vs K, K+B+N vs K) take longer (on average) on a 10x8 board because it takes longer to corral a King on a larger board. In fact, this is one of the points being discussed in the K+B+N vs K discussion thread. One should also take into consideration that, even though the Chancellors and Archbishops are off the board, the game may still be decided before an endgame is reached.

My personal opinion is that the "length" of a game with regular chess pieces on a 10x8 Gothic board would, on average, be very close to being the same as or only slightly longer than on an 8x8 regular board. Of course, this opinion is based on my interpretation of the theoretical considerations mentioned above, and not on any actual data, which reminds me of a well-known quote of Donald Knuth: "Be careful with the following code. I have only proved it to be correct, I haven't actually tested it." :-)

This is a re-post of my original, just to be sure I'm included in the competition! :-)

I'll make an educated guess for the setup, since I don't have the resources to conduct a detailed search. :-)

White: Ka8, Be8, Nj2
Black: Kc8

Of course, the mirror image positions should be considered equivalent:

White: Ka1, Be1, Nj7
Black: Kc1

White: Kj1, Bf1, Na7
Black: Kh1

White: Kj8, Bf8, Na2
Black: Kh8

And thank _you_, Fencer, for implementing Gothic Chess on your site and providing us with such a nice interface for playing and discussing it!!

I'll make an educated guess for the setup, since I don't have the resources to conduct a detailed search. :-)

White: Ka8, Be8, Nj2
Black: Kc8

Of course, the mirror image positions should be considered equivalent:

White: Ka1, Be1, Nj7
Black: Kc1

White: Kj1, Bf1, Na7
Black: Kh1

White: Kj8, Bf8, Na2
Black: Kh8

That sounds like a very interesting exercise and I would certainly be interested in playing a two-game match of it. Would you like to ask Fencer if he can set it up?

:-) It would certainly be interesting to see the results of such a database! The K+A+P vs K+R and K+R+P vs K+R certainly would be a very interesting test of the Archbishop versus Rook. I hadn't really intended for you to go to _that_ much work, though! I will go out on a limb and re-state my hypothesis that the Archbishop and Rook would be approximately equal in an endgame. So, if you do create such a database, I want to be one of the first to be told of the results! :-) :-)

By the way, thank you so very much for taking the time to contribute your pioneering knowledge of Gothic Chess. I, for one, appreciate it very much!

Of course everything you said was true, Ed; I would expect that from you. :-) My point was simply that the endgame theory of regular 8x8 chess carries over essentially unaltered to the 10x8 Gothic Chess board (with K+B+N vs K a notable exception). In the particular example we were discussing, White wins against "passive defense" if there are at least two squares on the "short side" of the Pawn, and this is true on both the 8x8 and 10x8 board.

Have you ever looked at the question of K+R+P vs K+A or K+A+P vs K+R? That appears to be an interesting question and a true test of the relative strangth of the Archbishop and Rook.

Yes, your analysis is accurate. I'm also impressed with the historical background. However, I don't believe this example illustrates the difference between an 8x8 and a 10x8 board for Rook endgames (if, in fact, there is any difference). A Lucena position, according to my sources, is a position where the White King is on the last rank, directly in front of his Pawn, and the Black King is off to one side of the Pawn. As you pointed out, the standard winning procedure is to "build a bridge" as in the line you gave. This is the same on either type of board, as long as the Pawn is not on a Rook file. The other position (White: Kh6, Ra7, Pg6; Black: Kg8, Rb8) is called a "passive defense" rather than a Lucena position and is a draw if White's Pawn is on a Rook or Knight file, and a win for White if the Pawn is on a Bishop or central file, with the winning procedure exactly as your "Gothic" line. However, "passive defense" is still a draw on a 10x8 board if White's Pawn is on a Knight or Rook file (a, b, i, or j) and this is no different than on an 8x8 board. My point is that it appears (to me, at least :-) ) that the Rook endgame theory of the 8x8 board carries over "mutatis mutandi" to the 10x8 board. In fact, I can't think of any other endings that depend on the geometry of the board (10x8 vs 8x8) the way a K+B+N vs K ending does.

An interesting question in this topic is whether either a K+A+P vs K+R or K+R+P vs K+A is a win (or, under what conditions either one would be a win).

According to Reuben Fine in "Basic Chess Endings," the "longest mates" (on an 8x8 board) are as follows:

Pieces.................Longest Mate
----------.................--------------------
K+Q vs K.................10 moves
K+R vs K.................17 moves
K+B+B vs K.............18 moves
K+B+N vs K.............34 moves

All but the K+B+N vs K should be essentially the same on a 10x8 board, where any extra number of required moves would be small and due only to the extra space on a 10x8 board. The K+B+N vs K on a 10x8 board is more interesting, as Ed has pointed out. Once the lone King has been forced to a corner opposite in color from the Bishop, the lone King must be forced to the closer corner of the same color as the Bishop, otherwise the corralling procedure will fail. I haven't studied this enough to know for sure if it can be forced at all (although I suspect Ed has worked it out). The K+C vs K is easy since a Chancellor can be used as a "supercharged Rook." The K+A vs K is not really hard, but the procedure certainly has no counterpart in regular 8x8 chess, so seems strange when an 8x8 chessplayer first tries it.

I'm not sure I understand why Ed thinks the Lucena position needs a complete rewriting on a 10x8 board. The winning procedure is independent of the "width" of the board and would be the same on a 20x8 board. I suspect that many, if not most, endings do not really depend a great deal on the "width" of the board (the K+B+N vs K ending being a notable exception); the "height" of the board is the determining factor. I freely admit that I don't have a proof of this assertion, but it would surprise me if 8x8 endgame theory changed significantly on a 10x8 board. For those who are interested, a more dramatic geometric effect is produced by using an Omega Chess board (10x10 with 4 corner squares). On this board, several strange things happen:
1. K+R can no longer force mate on a lone K.
2. K+B+N can no longer force mate on a lone K.
3. An _unassisted_ Queen can force mate on a lone King.
4. K+N+N _can_ force mate on a lone K.
Omega Chess turns out to be a much slower game than Gothic Chess, and I'll leave it at that, since this is a Gothic Chess discussion board (and Gothic Chess is more exciting anyway).

Yes, that is usually true. If the position is "open" so that the Bishops have the run of the board, it is certainly true that the Bishop pair is worth more than the two individual Bishops. However, there are some positions (usually "closed", with blocked Pawn chains) which favor two Knights. In fact, the synergistic effect of the Bishop pair is one of the reasons I would question valuing an Archbishop more than two Bishops. (Of course, if you take this into account, you might still augment the value of the Archbishop... :-) )

Interesting. So, the Archbishop is the only piece whose value you feel needs tweaking from its computed "safe check" value. I'd like to challenge that position, in the hope that the ensuing discussion will lead to greater understanding. First, two Bishops often work well together and I am not sure that it is obvious that an Archbishop should be worth more than a Bishop pair. I would be willing to grant that an Archbishop should be worth more than a Knight and Bishop for the same reasons that a Queen should be worth more than a Rook and Bishop, one of which would be that an Archbishop and Queen can "change the color of the Bishop." When discussing this, we should not forget that the actual value of a particular piece is dynamic and depends strongly on the position. Since the Archbishop is a jumping piece, one finds that it often joins the battle earlier than the Rooks and Bishops, so in the initial phases of the game, the Archbishop should be considered more valuable than a Rook or Bishop pair. In the endgame, however, the jumping capability is less important and it would not be surprising to find that a Bishop pair or even a Rook could be equal to an Archbishop. Of course, I still would not exchange an Archbishop for a Rook in the opening or middlegame, since my opponent's Arcbishop might checkmate me before I made it to the endgame :-). The issue of "dynamic value" also applies to the situation of a Rook versus two minor pieces. Certainly very few good chessplayers would play Bxf7+ Rxf7 Nxf7 Kxf7 as White for the reasons given. However, notice that this assumes that the exchange took place in the early to middle phase of the game, before the Rooks would be free to roam on open files and ranks; a Rook is very nearly the equal of two minor pieces in the endgame (and a Rook and Pawn is considered fully equal to two minor pieces in the endgame). I believe the reason a Rook is downgraded from 6 to 5 in 8x8 chess has more to do with the fact that two minor pieces can attack a square twice (unless, of course, the two minor pieces are a Bishop pair :-) ) rather than the actual strength of the Rook compared to two minor pieces, and that this is why a Rook is considered to be worth less than two minor pieces. In fact, one could argue that the Rook is the only 8x8 piece whose value was tweaked from the "safe check" value, since the "safe check" value of the other pieces are essentially the accepted values.

OK, I've computed the safe check probabilities for the chess and Gothic Chess pieces on both an 8x8 and a 10x8 board. As Ed mentioned, finding a nice formula for the safe check probability of a Bishop is hard, but since we are really only interested in the values on an 8x8 and on a 10x8 board, it suffices to compute them without bothering to find a nice formula. Of course, a Chancellor and Archbishop will never set foot on an 8x8 board, but their safe check probabilities on such a board are still of interest for the purpose of comparison. Normalizing the piece values so that a Knight on an 8x8 board has a value of 3.00, we obtain the following (SCP = "safe check probability", PV = "piece value").

(8x8 Board)
Piece.................SCP.................PV
-----................-------..............-----
Knight.............12/144..............3.00
Bishop.............13/144..............3.25
Rook...............24/144..............6.00
Archbishop......25/144..............6.25
Chancellor.......36/144..............9.00
Queen.............37/144..............9.25

(10x8 Board)
Piece................SCP.................PV
------...............------...............-----
Knight..............110/1580.........2.51
Bishop..............133/1580.........3.03
Archbishop.......243/1580.........5.54
Rook................249/1580.........5.67
Chancellor........359/1580.........8.18
Queen..............382/1580.........8.70

As Ed points out, the piece values go down (according to this theory) on a 10x8 board. The other interesting point is that this theory asserts that a Rook and an Archbishop have essentially the same value. In fact, because of the Knight's loss of range on a 10x8 board, the Archbishop appears to have slightly less value than a Rook on a 10x8 board. Of course, it would be naive to assume that this the whole story. It would seem that an Archbishop would be worth considerably more during the early part of the game when there are few open files and the Rooks haven't had a chance to enter the fray, however, it could be that a Rook and Archbishop have about the same relative value in the endgame (just as a Rook can often hold its own against two pieces in the endgame). I'd be interested to hear Ed's opinion on this. I suspect he added the mysterious "extra parameter" to the expression for the safe check probability for an Archbishop because, based on his playing experience, he didn't believe that a Rook was equal (or even slightly superior) to an Archbishop. In the end, playing experience is worth more than point values assigned on a purely combinatorial basis.

The Queen is still the most "powerful" piece, so unless there is a positional consideration that favors a Chancellor or Archbishop, one should still promote to a Queen. Of course, if you can promote without your opponent being able to promote, any one of the three would grant you a winning advantage.

P.S. Pawn "promotion" is the standard term. Even in 8x8 chess, there are situations where promoting to a piece other than a Queen is the only way to win.

Hi, Ed! I couldn't help it: When I saw that Fencer had implemented Gothic Chess while I was logged on to BrainKing.com, I just couldn't resist rushing over to be the first to post. :-)

I would like to see how you came up with the formulas for the piece values (i.e. the "safe check probability"). I was able to derive the formulas for the Rook and Knight that you published in your article (Gothic Chess Review, July 2000), but those were the only two formulas you listed. (OK, I'll admit it. I'm a math professor, so I find that sort of thing interesting. :-) )

I just wanted to be the first one to post to the Gothic Chess discussion board! :-) Hopefully, Ed Trice will be along shortly and we can continue the discussion of the value of the Gothic Chess pieces that was started in the Janus Chess discussion board...

Thanks, I'll have to take a closer look at the value of the Archbishop (Janus). In the article, the author makes a cryptic comment about "adding an extra parameter" to account for the fact that the Archbishop can perform an unassisted mate of a lone King. I have to agree with you that my playing experience is that the Archbishop is definitely weaker than the Queen, although I think the Archbishop may be stronger in closed positions (just like the Knight is stronger in closed positions than the Bishop and sometimes even a Rook).

I've already asked for Omega Chess and Gothic Chess and provided Fencer with the URLs explaining the rules, setup, etc. It might still be worth anyone else mentioning it again to him in order to show that there is more than just one interested person. It appears lots of people are playing Janus Chess and I think lots would play Omega and Gothic Chess as well. So, show your support for Omega and Gothic Chess by sending Fencer another note! :-)

I have posted to the 'Features requests' board my request that Fencer implement Gothic Chess (and Omega Chess, another interesting variant). He said something like "Why not?", but it would probably be helpful if you posted a request for Gothic Chess as well.

By the way, when you say the value of the Archbishop was "clear deeper", do you mean that it is "clearly less"?

OK, the values of the pieces in Gothic Chess (a 10x8 board) are (according to the "safe check" theory) as follows:

Piece....... Value
------....... -----
Knight........2.50
Bishop........3.03
Rook..........5.67
Chancellor...8.17
Archbishop..8.41 (Note: Arcbishop = Janus)
Queen.........8.70

Note: According to this theory, the value of all the pieces goes down from that on an 8x8 chessboard. For example, the value of a Knight, Bishop, Rook, and Queen on an 8x8 board are 3.00, 3.25, 6.00, and 9.25, respectively.

One should, of course, realize that these "values" are, at best, guidelines. The actual values vary according to the position. Just like there are positions where a Knight is better than a Bishop (or even a Rook), there a positions where an Archbishop (Janus) is better than a Queen.

OK, I looked up the article on the relative value of the Gothic Chess pieces. Based on a computation of the "probablility of delivering a safe check," the values (on a 10x8 board) of the Queen, Archbishop (Janus), and Chancellor are 8.70, 8.41, and 8.17, respectively. It is interesting to note that this scheme rates the Chancellor the least of the three; however, my experience playing Gothic Chess is that the Chancellor "feels" more powerful than the Archbishop. The most surprising thing is how close the Archbishop and Chancellor are to the Queen in strength.

Interesting. Is this value of the Janus published anywhere or is it based on your experience? In Gothic Chess, giving up a Queen for an Archbishop (the same as a Janus) is called the "Gothic Exchange" and is considered less of a sacrifice than the standard Exchange (giving up a Rook for a Bishop).

The Janus is worth almost a Queen, according to an analysis by Ed Trice, the developer of Gothic Chess (which has a piece that moves the same as a Janus but is called an Archbishop). I think a good estimate is about 8.5 for a Janus.