Does anyone know what the acceped relative value of the Janus piece is (given that pawn=1 / knight=3 / bishop=3 / rook=5 / queen=9 or 10)?

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.

I think the Janus has a little less worth as a queen, I would say the value is 7,5-8,0. But the Janus has one special advantage: He can alone checkmate the king in the corner and in the middle of the game you have very interesting tactical possibilities

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).

No that is my own opinion which is based on the worth of knight and bishop (Janus,archbishop) on the one side and the worth of rook and bishop (queen) on the other side. When the worth would be the same if you say ,what would be the worth of the chancellor (rook and knight) in gothic chess? It is sure a little bit stronger then a Janus and then a little stronger as a queen? i think no

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.

I have only just started playing and I find this discussion interesting. So far I have found the knight attribute extremely helpful and i think this is because it is the beginning of the game where there are more pieces and fighting is at closer range. I expect, as with the knight, the advantage will dimish slightly as the game progresses and the board becomes more open. I can see why the the Janus and Chancellor are closer in values than the Bishop and Rook as the Janus will not be restricted to one colour diagonals but I am not sure why it should be worth more as the Cancellor has the ability to cover an additional two squares.

juangrande ... i would be interested to know, from your previous research, the relative values of the rook, knight and bishop when they are on the board with the queen, janus and chancellor. I assume a pawn is 1.0

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.

Thanks, you have been most inciteful

I tested yesterday the values in Gothic Chess with "Zillions of games" and the result was that the values of the chancellor and the queen was nearly the same and the value of the archbishop was clear deeper. But the application is not very strong.
But I have another idea: Perhaps we can play both Januschess and Gothic Chess. There are only to make some small changes at the rules.
Who asks fencer?

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"?

Yes,sorry my english is not so good...
I know Omega Chess too and it would be great if we can play it here too. I informed fencer in the last month about "Januschess", but I can not ask him every week for another game.The best would be if you send him setup,rules and images of these games. That is sure the the best way.

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 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...

Does anyone know if there is a website that is the "home" of Gothic Chess? Or a website maybe with some tips or something?

Hi Juan,

You beat me to the first post! :) Sure, this is a good place to discuss piece values now. Should I show how to rederive them, or just list their values?

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. :-) )

The concept of a "safe check", i.e. a check delivered by a piece that cannot result in a trivial capture by an enemy king, was first used by Taylor in 1876. Taylor reasoned that the probability associated with delivering a safe check on an empty board featuring just the piece in question and the enemy king should be proportional to its strength.

Let's take a Rook for an example. Ok, place a Rook on a1,a2,a3...a6. It can safely check a king on a8. It cannot safely check a king on a8 when it is on a7, since Kxa7 violates "safe check".

You essentially "sum" these safe checks over the entire board, placing the king on each square, and computing the number of squares on which a rook resides. The ratio of safe checks to total arrangements on an 8x8 board is 1:6 for the Rook.

Bishops get a little messy in the computation (explanation is not too intuitive) but basically varying diagonal lengths as a function of bishop location and king placement make it very recalcitrant to derive. Knight computations are easy, so are the other pieces.

So, I set out to do the same for a board of dimensions Y by Z, not just a square board like Taylor did.

More on the algebra of the Rook computation in the next post...

To derive a nice formula for the strength of a Rook on a board of Y height and Z width, here is what you do.

First, examine the geometry of the board. You can see that from the 4 corners, the King can be safely checked a total of (Y - 2) + (Z - 2) times. Recall is a Rook is next to the king while delivering check (like Y -1 or Z - 1) then the king can just capture it.

So, we have 4((Y-2)+(Z-2)) so far.

Basically, in the corner, the king can recapture 2 of the rook checks.

Now move over one square for the king (b8) or move down one square (a7). The king would be able to recapture against 3 rook checks. In the case of the a7 king, it could capture a Rook checking on a8,a6, or b7.

You notice on any rectangular board, there are 4 pairs of squares where this is true. On the 8x8 chessboard these are b8/a7, g8/h7, b2/a1, and g2/h1. So, we have 4 instances of (Y-2) + (Z-1) and 4 instances of (Y-1) + (Z-2).

To 4((Y-2)+(Z-2)) from the 1st calculation we add 4((Y-2) + (Z-1)) + 4((Y-1) + (Z-2)).

Recall a probability is a quotient, that being these total squares of safe check divided by the entire population of arrangements. After placing one piece on the board, there are ZY - 1 slots remaining for the next piece. But the first piece can occupy any one of those ZY squares, so you get fractions in terms of ZY-1 and ZY(ZY-1) when you compute the probabilities.

When you collect all such terms for the rook, you get:

P(safe check) = Z + Y - 6/(ZY - 1) + 2(Z + Y)/[ZY(ZY-1)] for the probability that a Rook can safely check a king on any such size board.

Plug in Y = Z = 8, and you get:

8+8-6/63 + 2(8+8)/64(63) =
10/63 + 32/64x63 =
640/64x63 + 32/64x63 =
672/4032 = 1/6

So my results match Taylor, I just computed it a different way since Gothic Chess has a rectangular board.

in gothic chess yet??? (yup I want fame :))

That's interesting question. Ed, what do you know about that?

then I claim a hamster-opening (don't know which moves yet but that is a detail) =)

There are a few. The first was the Gothic King's Indian, a natural extension of 8x8 chess. I decided to name the variations after cities, so there is a Philadelphia System with some variations. But I do not want to copy the existing chess names to Gothic like the "Gothic Reti" for example. These should be named after the pioneer in Gothic Chess who molds it into a formidable system.

I only want one opening named after me.

1. Nh3 is Trice's Opening :)

I know that one will be around for a while.

Are these available for review anywhere? HAve they be anaylised and annotated?

Various issues of Gothic Chess Review showcase them. Also, there are some animated games online at http://www.geocities.com/bow_of_odysseus/index.html if you click on the SAMPLE GAMES link. I am in the process of cleaning up the website substancially.

thanks, I have had a look at that site and the games are fun to watch, but go too quickly for me. It would be good if there were some controls on them, but enough bitching, I think it is great to be able to see them at all. I also like the initial commentary. I shall follow up the Gothic Chess Review in due course. For me, the what I find hard to determine (in my game) is which is going to be the best move in any given position. Thanks :)

Well if you figure out some way to determine the BEST move in ANY given position, then you MUST, and I mean MUST, tell me how the heck you do it!!! :)

Dear Mr. Trice,
Far be it from my expertise to question your mathematics, but it seems to me that in the message from which I derived this reply opportunity (St. Patrick's Day, March 17th), in paragraph #6 you made an error, saying "b2/a1" when you should have said "b1/a2". The math does not change as a result, because it seems to presume the latter terms, anyway. /Fx/

I continue to play and can assure you tath I am regularly NOT choosing the best move available, or so I find out a few moves later ... hence my need for (a lot of) assistance :)

When pawns are promoted, are there any new trends developing as to favorites, or are players still favoring Queens, over Chancellors or Archbishops, perhaps due to their abiding insecurity about the new pieces' versatility and/or staying power?

Note: I intend to imply a relationship between the apparent inherent speed of development in any position and the necessity of considering the chances that, since the very character of the position may well change rapidly with the advent of a Chancellor or Archbishop upon promotion, perhaps their value should be accordingly adjusted (up!) over the alternative of adding (even a second!) Queen.

Comments welcome! /Fx/

P.S. Is it time to think of a new name for "queening"? Would something like "crowning" or "electing" or "raising" catch on? I suppose we can forget "knighting" right away! (Or...should we?!) They talk about someone having been "created Cardinal" on a particular day. Could a pawn be "created Chancellor" or "created Archbishop"? That could be abbreviated "c/C" or "c/A," instead of "p/C" or "p/A".

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.

Underpromotion is what the term is called in chess, which would be promoting to a knight since this is the only piece that a queen cannot move like. It stands to reason that in Gothic Chess that if you underpromote it would be the Archbishop for the same reason. It makes no sense to promote to a Chancellor or any other piece since the Queen already has that advantage.
The reason for underpromoting would be to deliver a check when promoting the piece (Knight or Archbishop) or winning a piece with a fork thereby giving you a winning or drawn game that promoting to a Queen would not of given you.

Wow, I am impressed! You are correct and you have a keen eye. I did transpose the nomenclature regarding the b2/a1 note. Thanks for being so thorough.

I agree with my old Gothic Chess friend the chesscarpenter. It seems a bit harsh to transfer the label "underpromotion" to the Chancellor and Archbishop. In chess, there are only two major pieces, the Queen and the Rook. Promoting to anything but the Queen represents a significant "under" promotion, but in Gothic, with a Chancellor being so close in strength to a Queen, I think it can be associated with a promotion. Heck, from the pawn's point of view, everything is a promotion, is it not? :) Even if delegated to the ranks of "middle management" and being made an Archbishop is still a promotion!

Gentlemen,
It is an honor to be counted among such esteemed company as yours, and it is my sincere hope that such pleasant and reasoned discourse may prosper and increase.

I am contemplating the significance of promoting to a Newpiece in leiu of a Queen, and not merely for its immediate effect, but for what follows thereafter. Sometimes the game continues for more than a few moves after promotion, but also, the promoted piece becomes an immediate target. I am thinking about the added element of uncertainty which now accompanies promotion. It seems that the same acceleration that the Newpieces add to the game at large are added to the act of pawn promotion.

I am also curious about the decision to make the new board 10x8. Was there much experimenting done with other formats, or was it a conclusion quickly arrived at because it simply works so well? I have played 4-corner chess with my kids, and it is a real jungle out there! Two other people move after the one that follow your move, so the board changes in wild ways before each move, and there tends to be a r-e-a-l l-o-n-g t-i-m-e between successive turns.

I looked at the website that shows games in action, and the play is exhilaratingly rapid, but that is what the mind needs in order to absorb the spirit of the game.
Surely my observation of games in action will go far to answer my concerns, but it seems I enjoy the wonderment of anticipating consequences and the making of valid generalities. I have always found such pleasure in the moves of chess: wondering what will be coming next; which is near to the heart of mental combinational calculation (computers are heartless!) and the thrill of taking a risk with informed confidence, that one's opponent could not have seen a better move...or could he? It seems to me that it is the learning of when to be sure of one's next move and when to recognize that instinctive voice warning of some vague danger ahead, that makes playing chess (and now gothic chess!) worth the effort.

There is always a thrill to be had when one's play improves, and now with gothic chess, a genuinely new element is added which promises a geometric increase of the very pleasure which makes chess advocates love their game. I expect that by learning both games well, one can use each to expand his skill at the other.

This is the first variant of chess that has held any interest to me, for the others have seemed to be cheap knock-offs of the best game ever devised in recorded history (my own bias). This is different. It's kind of like putting a turbocharger on a hemi. You get more power, and the ride is more exciting. But it's not necessarilly the best format for everyday use. I cannot imagine ever losing my love for chess, and as much interest as I may develop in gothic chess, I expect to always return to the reliable standard, at least from time to time! Having to face a grand prix speedway is more intense than driving down the freeway. But who would want to commute to work every day in a formula 1 car? Okay, some would. /Fx/

Very excellent post sir! I am in the process of "rebuilding" the tattered remnant of the website into something more worthwhile. I will share the trials and tribulations of 'discovering' how the 10x8 board with this setup was the one that seems to finally "work". There was a quest of sorts, starting way back in 1986 when I was programming The Sniper (my chess program which eclipsed 2200 shortly after Ken Thompson did it with his Belle hardware). There were many interruptions, and the quest began again in 1998....read more at:

http://www.geocities.com/bow_of_odysseus/index.html

it should be ready by Saturday or Sunday.

Dear Mr. Edward Trice,

The story of your quest is of great interest to me, as you can see by my explanation of what makes chess, itself, interesting. In a way, your decision to apply for a patent using the 10x8 format is an exponentially great chess move, per se. You must have been rather anxious in hopes the patent office would not reject your application. I would love to hear your story some day about how that came down, and what your reaction was when you were given the news of being granted the patent. In case you can't tell, you have a ready-made fan club, here! /Fx/

I completed one of my web pages. Feel free to take a look at:

http://www.geocities.com/bow_of_odysseus/why_change.html

Make sure when you copy and paste the link that you remove all of the spaces that might appear as a result of the line breaks here.

Felix, the US Patent office rejects 90% of all applications the first go around. My own experience with them is that this is largely undeserved. They basically force you to retain legal services. I personally called my examiner (a big "no no" once you assign power of attorney) and I questioned him thoroughly. I spent 100 hours on my application, and his "102 rejection" was clearly way off mark. He basically admitted to me that he was advised to reject the application and see how we (me+attorney) would respond. Well, I gave him an earful, and I mentioned who I would contact at the press and arrange for a nice interview for him! Amazingly, the SECOND revised application was put through rather quickly.

After 18 months of work, receiving the actual patent letters (as they are called) was a bit of a anticlimax, but I found a way to celebrate. The real party will be this summer, and anyone who wants to make a pilgrimage to Philadelphia is invited!

I just finished the Game of the Month page on my site.

http://www.geocities.com/bow_of_odysseus/gotm.html

is the link.

I annotated the game, furnished diagrams, and other interesting tidbits. I would appreciate any commentary, and would like to do this on a monthly basis.

great really sweet; gonna print it and look at it =)

The Archbishop is fairly formidable in knight/bishop situations. He's able to change color as a bishop with each knight move, and wherever he goes as a bishop, he threatens to move as a knight.

But as formidable as he is, the Chancellor is absolutely awesome. He is able to zip around like a rook, and land on sqares from which he immediately issues proclamations of "fork!" in 2,3,4,5 or even 6 locations, which a Queen can do as well, but not on the squares that the Chancellor does: his forks are like the knights and rooks combined. /Fx/

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.

One thing which surprises me is the relative value (on 8x8 board) of the rook to the queen. In my early days I learnt that a queen was worth two rooks, and more lately that rooks might be 5 and a queen, 9. This is significantly different!

The safe check formula was used to get approximate values for the pieces way back in 1876 when it was not widely known how to rate the pieces for exchange purposes. I am glad Juan's numbers so closely mirror my numbers that I published in Gothic Chess Review in the year 2000. Now I have an independent verification of my work.

One of the drawbacks you will notice is that a Queen is worth a Rook + Bishop EXACTLY, as are the other new pieces that combine two into one.

Also, saying a Rook was worth exactly two knights did not seem to make sense. So here is what I did to my numbers.

Chess players consider a Rook to be worth LESS than two minors, so that exchanging two minors for a Rook is discouraged. Minor pieces play a more active role in the opening and middlegame, and you can get into trouble playing something like Bxf7+ Rxf7 Nxf7 Kxf7 on an 8x8 chessboard against black's castled king. Black can get a more active attack going, winning more material with minors than you can defend with your unmoved rook pair.

So, chessmasters have scaled a Rook down to 5 points on the 8x8 board. But, as you see, we do not have to do this, since a Rook turns out to be less than two minors in Gothic.

But, we still have to "borrow" something from the 8x8 chessmasters. In knocking the Rook down to 5 pawns, the Queen was worth 8, not 9, as is the standard value in use today. What they did was add a one pawn bonus to the Queen since it could perform the R + B moves on only one square instead of two.

They basically multiplied the queen by 9/8ths on an 8x8 board. I just used the same scalar value and multiplied the Archbishop by 9/8ths. Doing this for our Q and C with the unscaled Rook would over-exaggerate their worth.

So, leaving the Rook alone in Gothic, and adding merit for the Archbishop only, you get:

Archbishop = 5.54 x 9/8 = 6.2325

Reinserting this into the list, we have:

Knight = 2.51
Bishop = 3.03
Rook = 5.67
Archbishop = 6.23
Chancellor = 8.18
Queen = 8.70

This has the nice result of the Archbishop being worth more than a Bishop pair, which is something I think we can agree is true. And, I would not trade my Archbishop for a Rook, and this correction fixes this as well.

So, the 8x8 chessmasters had to "tweak" values for their Rook and Queen, and we only had to "tweak" the Archbishop, so I think our model is fairly sound.

http://www.geocities.com/bow_of_odysseus/sets.html is a picture of the Gothic Chess board. I set up a position I had against juangrande in the picture.

http://www.geocities.com/bow_of_odysseus/why_change.html now contains new information about how Gothic Chess got started, including the famous "Frying Pan Set". Check it out, let me know what you think :)

Read through your discourse on how Gothic Chess came to be ... very interesting indeed.

Let us hope it does not go the way of the "Beta" video tape.

I finished another web page tonight.

http://www.geocities.com/bow_of_odysseus/deadly_arch.html

I will try and carve out one or two pages a day.