:-) 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!

The answer to all of your questions appeared in the April 2001 edition of Gothic Chess Review. The ending can be a forced win without expiring the 50 moves. Some of them just barely squeak by. Maybe I will compute this database. It will give me something to do.

The task of bringing checkmate upon a lone King with only a Knight and Bishop has always been a good exercise to learn coordination of the minor pieces. Capablanca highly recommends it in his Chess Fundamentals, bemoaning the fact that many otherwise excellent players cannot corral his King in the required 50 moves (no pawns to move). This ending translates somewhat to the 10x8 board, however, it seems to me that the time it takes to achieve the mate is longer than on an 8x8 board, assuming good play by the lone King, although 50 moves seems to be sufficient. It is more challenging to force him into the wrong-color-corner (the standard preliminary position) while eliminating his recourse to the long side, but it is possible to do as far as I can see. I would like to see this question explored empirically, for the fact of what works is the final test in this game. If the enemy king can slip out to the 10-square side, he is then able to somewhat double the number of moves required to mate. If he does escape once to the 10-square side, it looks like he can be somewhat contained at the opposite, wrong-colored-corner, inasmuch as prevented from doing the same thing again, for if he could repeatedly escape, the knight and bishop would be then incapable of winning, regardless of the number of moves. This second containment appears to have something to do with the coordination of the offensive pieces, and especially the pattern of the knight moves. A student of this ending will quickly discover that while the knight has some usefulness while located on a square opposite in color to the bishop's squares, the highest power is always obtained when the knight and bishop are on the same color squares. There are several consequences to this doctrine.

If there is anyone else as interested in this exercise as I am, I would suggest that perhaps a tournament could be set up using only these 4 pieces on a 10x8 board. A win for Black (or White?) would consist of escaping checkmate for 50 moves, while a win for White (or Black) would be achieving checkmate. We could call it the "Capablanca Memorial Endgame Tournament," because he pronounced the value of its rigorous study to improve chess at large, and he was given to dabble in 10x8 format. I would be interested to see how other players handle this ending.

It is my sincere hope that the question of whether or not the 50-move limit is sufficient to secure checkmate does not pose a problem for keeping control of the patent on gothic chess. We could find out that it takes a more skilled player to win in this larger format, but that does not necessarilly mean that the rules of the game need to be changed, for new rules would mean a new game, and a new game would not be covered by the current patent.

There is much to be gained by toying with this ending, and I would like to share my own fascination with gothic chess fans, if they are interested. /FX/

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

I started building the page discussing this strategy, a very important aspect of Gothic Chess.

Juan, the endings you mentioned would have to be some of the most treacherous possible! I could always write a program to solve the endings and report the results back so I would know how long the win would take from any position. I could then make this database avaialbe for everyone.

The problem is: the construction time is long and I would need to use about 4 computers to solve these endings.

My partner and I already generated large databases for the game of checkers. We have every solution for any endgame involving 8 pieces. That is roughly 111 billion positions!

We also have "distance to win" information for the 19 billion seven piece endings. This takes up 7 gigabytes on your hard drive in its compressed form!

So, just to let you know, I know how to solve endgames via retrograde analysis. Before we do something like A+P vs. R, we need to solve all of the endings such as:

A vs. R
AQ vs. R
AC vs. R
AA vs. R
AB vs. R
AN vs. R

Why? Because a pawn could promote to ANY one of those pieces, and we need to know the result of ALL of the conversion information before we can solve the pawn ending!

For this reason, it becomes a big task, but I am up for the challenge.

I have a web page at:

http://www.geocities.com/bow_of_odysseus/internat_open_01.html

I would like to know if I interfaced correctly with the web pages here, and if you can see your games using my page as a source.

Thanks in advance for any feedback.

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.

Ah ha, now I see our difference honed in upon, finally! OK, remember the original 10x8 board was 'Capablanca' which had Bishops on the d and g files, not c and h files. For this reason, I 'translated' the concept of the file name to the literals (a,b,c,d,etc) from the descriptive notation tying a piece to the back rank (rook pawn, knight's pawn, etc) since the descriptive notation would vary depending on which 10x8 board you used!

So, placing the pawns in the rook file on the 8x8 board was just transplanted to the h-file in Gothic.

I was caught in a catch-22: using descriptive notation would be different depending on your 10x8 style of preference, yet using hard coded literals should not be done by rote.

I did not re-translate the destination files when moving it onto Gothic.

But everything else was true :)

The draw I showed in 8x8 chess would be a win on the 10x8 board, moving the EXACT position as was shown.

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).

I updated:

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

to showcase an old speed game I found where my Archbishop checkmates on e7, all by itself. It is a cool game. Let me know what you think :)

Basically this ending (pronounced Lou-Chen-Ah) is a staircase procedure. As you mentioned, you would think the height or vertical distance from Rook to King would be the governing factor. But Lucena themes are numerous, and in one of them there is a sneaky "end around run" which the width of the board allows.

It is a draw on an 8x8 board. Move it to a 10x8 board, it is a win.

First, a typical Lucena win. White king on e8, white pawn on e7, white Rook on f1, black King on g7, black Rook on d2. This is on an 8x8 board.

Lucena published a manual in 1497 (a mere 5 years after America was ‘discovered’ by Christoval Colon, a.k.a. Christopher Columbus) wherein certain endgame techniques were mentioned, but, curiously, the critical position was not in that tome! In truth this endgame is an age-old one, but an Italian author named Salvio was the first to document the winning technique for White in the year 1634, and even he attributed the composition to a previous mentor named Scipione Genovino. That historical tidbit aside, White can win independent of the side to move by using the “staircase” technique.

1. Rg1+ Kh7 2. Rg4! (placing the Rook far enough away from the enemy King to avoid a trivial banishment while allowing for the quickest check-intervention block as the King marches towards the Rook. Playing 2. Kf7 at once achieves no gain since the Black Rook delivers a long sequence of harassing checks.) 2...Rd1 3. Kf7 Rf1+ 4. Ke6 Re1+ 5. Kf6 Rf1+ 6. Ke5 Re1+ 7. Re4 and the win is trivial now.

Let's look at another theme.

White king on h6, white pawn on g6, white Rook on a7, black Rook on b8, black King on g8.

This position represents another common 8x8 endgame where White’s g-pawn is functionally useless. It appears Black’s Rook is serving a purely passive role, but a draw is all White can hope for with 1. Rg7+ Kh8! 2. Rh7+ and now Kg8 draws. Black needs to avoid only 1...Kf8?? which loses to 2. Kh7!! Rb1 3. Rf7+ Ke8 and now the pawn promotes.
Transplanting the drawn position onto the Gothic chess board results in a win.

Black loses the Rook at once after 1. Ri7!! since mate is threatened immediately with Ri8# if the Rook moves. After 1...Kh8 2. g7+ Kg8 3. Ri8+ Kf7 4. Rxb8 Black is toast. Black likewise does not have the resource 1...Kf8 2. Ri8+ Ke7 3. Rxb8 which loses even quicker.

I hope this analysis is accurate, I am doing this without sight of a board.

in group 2

gothicchesspro has scored another victory and stands first with the 100% score of 3/3. Schaakhamster is second with 2/3. The other big fish in group 2 appears to be pawnchucker (question to gothicchessspro: do you know who he is??). Although he hasn't finished any games yet he holds a huge advantage in 2 games and also has an advantage against Schaakhamster. He appears to stand equal against gothicchesspro (at first glance)

In group 1

Juangrande drew first blood by defeating tonyh from England.

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).

One way to think about the piece values subjectively is to imagine what you are discussing in an ending against a lone enemy king. While it is true the Archbishop is stronger than a Rook, would you like to try and win Rook vs. King or Archbishop vs. King?

:)

I posted a mate in 8 for Archbishop vs. King at:

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

It is a real brain teaser of a problem to mate with the Archbishop on an empty board!

One way we can compare something like a Bishop Pair to an Archbishop is to try and find "Longest Wins" in the endgame. I know in chess, the Longest win from a Bishop Pair is about 67 moves. That was on an 8x8 board.

But in Gothic Chess, examine the ending of King vs. Knight + Bishop. It is almost a draw! Whereas in chess the N+B will mate in either of two squares, those of the same color as the Bishop, in Gothic, you can only force mate on one of the squares! The square of the same color as the Bishop that is closest to the enemy king vertically (not horizontally across the files) is the only one the mate can be forced in.

So, we need to look deeper at the discussion of piece values in the endgame, because in Gothic, even things like the Lucena Rook and Pawn vs. Rook ending need complete rewriting.

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... :-) )

And another aside that I have heard is that a bishop pair is worth more than the sum total of the two bishops individually, that is, taking the first bishop is worth more than taking the second. Any thoughts on this?

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.

I have seen this happen a few times. The first I published and annotated in the July 2000 issue of Gothic Chess Review. There is no corollary associated with play other than the knockout punch.

Here is the other game:



David Vales vs. Biju Samuel

1. i3 d5

Dave often plays i3 at the start of the game to invite the Pawn push that reveals the Bishop’s attack on the Rook. It is a short-lived attack.

2. Nh3 h6

The geometry of Knight-Pawn spatial relationships indicates that any singular push of a Pawn one rank from the starting position will functionally disable an enemy Knight’s ability to advance two ranks closer on the next move. White’s Knight on h3 is so stymied by Black’s h-Pawn.

3. Bi2 i5

This is a favorite Pawn push of Biju’s, aimed at dislodging the Knight on the h3 square. With the exposure to the King created by ...h6, White crafts a plan to use the tempi lost by Black in dispelling the Knight to move it closer to the King, then “hope”....

4. d3 i4
5. Nf4 c6?

Black is missing the point. The dislodging of the Knight was not a positive realization, and it is most dangerous.

6. Cf3!

A very, very sneaky move! White has set up the deadly revealed check.

6 ----- Nj6??
7. Ng6#

Just reviewed this game and it does rely heavily on your opponent not moving the e, f or g pawns. How often have you come across this type of opening? I would have thought most players would move at least one of these pawns to activate the diagonals? Is there a corollary which builds on this opening in these instances?

Hi Felix, you must have been online the same time as me, and editing your previous post, since I saw 3 or 4 versions of it. I am a speedreader, and I could swear the text changed immediately after I read it...then read it again, then it changed again! I started rubbing me eyes and blinking!

Anyway, I am in the process of doing "Dog and Pony Shows" to attempt to procure capital to fund the next stage of the venture. I do have boards and pieces already made, I think I mentioned that. A picture of one is now on the webpage at:

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

The pieces are high quality, the boards are machine washable and never wrinkle (made out of something akin to mouse pad material.) The patent is becoming international, extending the umbrella from Europe to Hong Kong. I am not so much concerned about wheel barrow sales as I am about software distribution. If somebody creates a Gothic Chess program, I will have no choice but to go for the throat.

I intend to use the patent for licensing agreements. Parker Bros. or Hasbro or Ideal Toys want to make sets, fine with me, pay an annual flat fee plus a small % of the sales, provided I get to write the accompanying documentation.

Anyway, more on this later, I have to finish my 159th version of the Business Plan :) Why can't the banks just give me the 2.2 million dollars and trust me??

The "Dual Steed Smother" is one of my favorite Gothic Miniatures. In it, you place your Chancellor in the f-file, make one strange knight move after having baited your opponent to activate his Bishop to chase your Chancellor, and on the very move you are so threatened, you mate with the Knight.

If you go to archived game 57339 you will see this in action.

http://www.BrainKing.com/game/ArchivedGame?g=57339

is the link. It should be noted that you can execute this in 4 moves, but I had to "challenge" the potential placement of his bishop on the long diagonal, or else the miniature cannot be accomplisged.

All this talk about relative values is great. I would never have guessed that I would be interested in it, but here I am reading every word: and LOVING IT!! Even the decimal point values don't get me worn out, because I can see that there are logical reasons for using them. It rather comes to mind that the tendency for sticking with single-digit values in chess has always seemed a bit fudged. Maybe with the broader perspective of a more complex game, rethinking the chess piece values for 8x8 games won't be such an impossible task. At least we may find new reasons to corroborate the same values that the past greats agreed on. In any event, this new perspective cannot do other than expand our appreciation for chess as it has been all along. And what about when the appreciation level starts to impress the general public? What are people going to be saying in Peoria, IL, come October 2003?

I can't help but wonder what is going to happen when chessplayers start to catch on to the idea that gothic chess is a new frontier that they, with their race horse mentality in chess already, are well poised to enter; that it makes for a playing experience that is every bit as enthralling as chess, but in the process, you get whiter knuckles? (The larger playing board will make a better sized table for coffee and doghnuts, and besides, with the new plasma TV monitors coming out, a wider board will fit more beautifully on the screen...)

I don't know much about tournaments, because I've never played one (my current entrance in the BigBadWolf's 5-day is my first of any kind!) but it seems to me that there may be a lurking popularity explosion in the near future with this game. I am so glad for Ed Trice that he has secured a patent. I get the feeling he is going to be stretching that puppy to its limits. Therefore, I wonder what preparations would be prudent for the advent of tens of thousands of people all wanting gothic board sets all at once? It takes a few months to get production up, and it takes a good bit of diligence to enforce the protection of patent violations. When stuff is made in -well, let's face it- China, the black market for patented items is bigger than the legitimate market. If overseas sales of gothic board knockoffs proliferates, it will be pretty hard to enforce any kind of control over importation of cheater sets into the swap meets and flea markets. How can you bust a guy pushing a 3-wheeled cart in Chinatown?

Another field in which I have no experience is marketing, but I do know that it can get expensive to have a marketing firm do a contract for your new product. I've heard of guys going broke just trying to keep up with preliminary expenses. It seems to me that using the internet here, Ed could ask people to take a sample board and (four extra?) pieces into local coffee bars where chess groups meet (I've heard of one in Glendale, CA, where Armenians get quite serious about their national pastime, chess) and set up a board to have a little fun. We could answer questions, suggest visits to this website, and report back to Ed without running up any marketing expenses for him! I would not be surprised one iota if within a week, men start walking in with homemade boards and handcarved pieces! Just be sure you have a place to duck when the arguments erupt!!

But presuming all these details get worked out, has anyone considered what to do if this gets popular by summer or even the big rush next Christmas? /Fx/

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.

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.

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 :)

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.

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.

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!

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 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/

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

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.

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!

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/

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.

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/

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!

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.

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.

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.

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".

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 :)

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/

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!!! :)

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 :)

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.

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

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.

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

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