Theoretical wins are achieved more quickly. That is, a win takes fewer moves in general. When your opponent elects to resign is a different matter.

The reasoning stems from endgame fundamentals. Look at the concept of "the square" in king and pawn endings. Now the board is rectangular, which means, by default, you can swap down even from all minors to just pawns and be in an instant win. Usually, n chess, you have to manuever a great deal, play on for a long time, then get the opposing king out of the square to promote a pawn. No longer true in Gothic, in fact, you can even sac a piece to force the king to recapture, getting him into the rectangular area outside of the square, then you can promote at will.

Hi Felix,

I was having trouble as well. I am also recomputing the database and trying to resolve the errors in it. Once this is done, I will announce the winner, but up to that point in time, anyone can enter.

--Ed

Some of you had contacted me privately regarding the opportunity to get the Gothic Chess Federation moving. As you know, pieces already have been produced, but getting people to quit their day jobs in this economy has not become a reality.

I had put some numbers together concerning raising private capital (banks give you a nice low rate, but they want your house as backup. Venture Capitalists give you lots of money and collect lots of interest, and they want the rights to the company. I am offerening very high dividends and "votership" in the enterprise, a great middle ground) and these conservative estimates are posted online at:

Investor Inquiries for those of you who are interested.

I have been committed to Gothic Chess since 1998, and I left my full time job in 2001 to make this a reality. Basically, if everyone on BrainKing gave as little as $500, we could start this as an international enterprise tomorrow!

Feel free to read it and offer any comments. For those who have $1000 or more to invest, think about what the stock market could deliver, versus the 20 times investment dividend you could have over the course of the 6-year investment tenure.

I was so happy to see the thing finally able to put out text, I did not check any of them other than the first mate in 40, which looks like a mate in 40.

However, there are two areas that are suspect.

1. The database could be fine and the translation to the output text could be wrong.

2. The database could be garbage.

Just as an FYI, this is a database generator, and it does not apply the "50 move rule" to any such position. It solves all of the checkmates and draws on the first pass. Then, it backs up one move at a time, seeing which play is forced, and which is not forced.

It works its way backwards, from checkmated to mate in 1 to mated in 2 to mate in 3, etc.

Since I do most of my coding from the hours of 9 PM to 2 AM, I need to double check this stuff.

For now, consider all posted solutions to be on hold, subject to further review.

I will concentrate on verifying the databases today. With so many of those solutions featuring checkmates with a Knight, I am not 100% sure they are entirely accurate.

Interesting that even the mate in 37 by Juan featured a knight checkmate, not a bishop checkmate! This could mean that given a wide variety of choices, the unforced loss was just as long as the forced loss. Or, the database could need to be scrutinzed more fully.

If you want to go over any point in the analysis shown here, I will do so and check whatever you woud like checked out.

--Ed

White: Ka8, Be8, Nj2
Black: Kc8

Mate in 37

Nh3 Kd8
Bc6 Kc8
Bf3 Kd8
Kb7 Ke7
Kc7 Ke6
Kc6 Ke5
Kc5 Kf6
Kd5 Kg7
Nf4 Kh6
Be2 Ki7
Ke6 Kj8
Nh5 Ki8
Bd3 Kj8
Bf5 Kj7
Kf6 Kj8
Kg7 Kj7
Kh6 Kj8
Ng7 Kj7
Ni6 Kj6
Bi8 Kj5
Ng5 Kj4
Bf5 Kj5
Bg4 Kj6
Nh7 Kj5
Kh5 Kj4
Kh4 Kj5
Kg4 Kj4
Nj8 Kj5
Nh7 Kj4
Nj8 Kj5
Nh7 Kj4
Nj8 Kj5
Nh7 Kj4
Nj8 Kj5
Nh7 Kj4
Nj8 Kj5
Nh7#

White: Ka1, Ba2, Nb1
Black: Kj8

Mate in 34

Kb1 Kj2
Nd2 Kj3
Nf3 Kj4
Kc2 Kj5
Bb1 Kj6
Kd3 Kj7
Ke4 Ki7
Kf5 Kh6
Kg4 Kg7
Kg5 Kf8
Ne5 Kg7
Bg6 Kh8
Kh6 Kg8
Kg6 Kh8
Nf7 Kg8
Bh5 Kf8
Kf6 Kg8
Bi6 Kf8
Ne5 Ke8
Bf3 Kd8
Ke6 Kc7
Nd7 Kd8
Kd6 Ke8
Bh5 Kd8
Nc5 Kc8
Bg4 Kd8
Ne6 Kc8
Kc6 Kb8
Nc5 Ka7
Kc7 Ka8
Kb6 Kb8
Na6 Ka8
Bf3#

White Kc8,Ba1,Ni1
Black Ka8

Mate in 25


Ng2 Ka7
Kc7 Ka8
Ne3 Ka7
Nc4 Ka8
Nb6 Ka7
Bd4 Ka6
Nd5 Kb5
Ne3 Ka5
Kc6 Ka6
Nd5 Ka5
Bb6 Ka4
Kc5 Kb3
Ba5 Ka4
Bd2 Kb3
Ne3 Ka4
Bb4 Kb3
Kb5 Ka2
Kc4 Kb2
Ng4 Kc2
Ne3 Kb2
Ng4 Kc2
Ne3 Kb2
Ng4 Kc2
Ne3 Kb2
Ng4#

I found one of the mates in 40 moves would be a draw for black to move, without capturing a piece on the first black move! Now that must be, by definition, one of the hardest positions in the database!

of course these results have to be verified, I have yet to hook up the output to show the winning line. I will be able to do this tomorrow.

White to move checkmates in 25.

White to move checkmates in 34.

Juan is still the leader with a mate in 37.

White mates in 37 moves.

So far he is the leader!

I looked at my numbers again from the database run:

Mate in 1 move: 2400 positions
Mate in 2 moves: 1324 positions
Mate in 3 moves: 3247 positions

I thought that was strange that the mate in 2 numbers went down from the mate in 1 counts. I would have thought that this number should steadily climb until reaching a saturation point, then it should taper down as fewer positions are resolveable near the end.

But, on second examination, this make sense.

The mate in 1 count is artificially high since it includes all of the mates in 1 executed by a Knight. Recall this mate cannot be forced, but clearly the weak side can walk into it. Fewer of these Knight mates can be forced in 2 moves, much fewer than the additional number of Bishop mates that can occur by move two.

Then the count rises again, etc.

FYI.

First, Dyslexics of the World, Untie!

:)

To whisperz: There are actual two contests going on here.

Contest # 1: Post the position featuring B + N vs. lone king that you believe is the longest white to move and win. NO ANALYSIS. Just the position. I will query the database and whoever has the longest win, wins :) The winner will receive a Gothic Chess Mug once they pay for the shipping.

Contest #2: I sent to Fencer one of the 245 longest win positions. He is setting up special, private games where people can play the winning side against my database. Whoever wins the position most quickly will win a free Gothic Chess set, again, for the price of shipping.

So, the deadline is approaching. Get your entrants for contest #1 to me by Friday. We will start the tournament for the Gothic Chess set prize thereafter.

I should have the graphical user interface hooked up to my database by then.

--Ed

Now that I have the database code working (I still need to verify my latest computation) it appears that the longest win is a mate in 40 moves. In 8x8 chess, the longest win is 33 moves.

OK, the contest for guessing the longest win can officially start. Post your guess here. The person who submits the position resulting in the longest number of moves for white to win will receive a stainless steel Gothic Chess mug for the price of shipping.

And here are some stats of the latest run, assuming everything verifies properly when I do the test tomorrow:

Mate in 1 move: 2400 positions
Mate in 2 moves: 1324 positions
Mate in 3 moves: 3247 positions
Mate in 4 moves: 16136 positions
Mate in 5 moves: 49640 positions
Mate in 6 moves: 60757 positions
Mate in 7 moves: 78414 positions
Mate in 8 moves: 58897 positions
Mate in 9 moves: 57946 positions
Mate in 10 moves: 60434 positions
Mate in 11 moves: 110168 positions
Mate in 12 moves: 168635 positions
Mate in 13 moves: 254549 positions
Mate in 14 moves: 294188 positions
Mate in 15 moves: 261796 positions
Mate in 16 moves: 213463 positions
Mate in 17 moves: 171700 positions
Mate in 18 moves: 179002 positions
Mate in 19 moves: 193550 positions
Mate in 20 moves: 275013 positions
Mate in 21 moves: 421860 positions
Mate in 22 moves: 618981 positions
Mate in 23 moves: 743712 positions
Mate in 24 moves: 793462 positions
Mate in 25 moves: 768425 positions
Mate in 26 moves: 880231 positions
Mate in 27 moves: 1022307 positions
Mate in 28 moves: 1397010 positions
Mate in 29 moves: 1849137 positions
Mate in 30 moves: 2444455 positions
Mate in 31 moves: 3131093 positions
Mate in 32 moves: 3661812 positions
Mate in 33 moves: 3506075 positions
Mate in 34 moves: 2590711 positions
Mate in 35 moves: 1388359 positions
Mate in 36 moves: 482325 positions
Mate in 37 moves: 101621 positions
Mate in 38 moves: 13804 positions
Mate in 39 moves: 1788 positions
Mate in 40 moves: 245 positions

Of course my database stopped after 64 plies worth of iteration! I am an idiot!! In each byte of data, in which there are 8 bits (8 digits of 1 or 0) I needed to use 2 bits for win, loss, draw, or unknown.

unknown = 00
win = 01
draw = 10
loss = 11

That leaves only 6 bits available for distance to win, and 2 to the 6th power is 64!

So, as the database looped around, after iteration 64, nothing further could be resolved, so it stopped!

Now, either this is extremely coincidental, or I need to recompute this thing. I can get the distance to win up to 128 plies using a trick. I just divide the distance to win by 2 when I write it into the byte. If the win-loss-draw bits indicate a win, I double this number and add 1. If is it a loss, I just double the number. All wins are odd (mate in 1 ply, mate in 3 plies, etc.) since the winning side makes the last move.

Stay tuned folks, I will recompute the database today, this time doing it properly.

<This might be of interest to some of you. In generating a database, you have to map out all of the positions, and determine if they are wins, losses, or draws for each side to move.

Since there are 80 squares and 4 pieces, most people think you just create an array with four placeholders, one for each piece. Such an array would contain 80 x 80 x 80 x 80 entries, which is 40,960,000 positions per side to move.

This might not seem bad, but such a primitive scheme contains wasted entries. By making 80 slots available for each piece, basically you are allowing two or more pieces to be placed on the same square! For example, element 3,6,23,23 is a valid array index, but not a vaild over-the-board arrangement. Likewise element 12,4,4,31 is invalid, as well as 59,59,1,2....59,59,1,3....59,59,1,4 so you see there is a great deal of waste!

There is a technique to reduce this to setups where pieces are never on top of each other. This is called a sparsely-populated matrix. In this case, there are 80 x 79 x 78 x 77 entries per side to move = 37,957,920. It is smaller, but it makes the "lookup" procedure to locate your position a little more difficult.

In my case, the order I placed pieces on the board were black king (bk), white knight (wn), white bishop (wb), then white king (wk). So there were 80 slots for the bk, 79 remaining for the wn, etc.

So, my "indexing function" is now a formula. The result for any given position on the board is :

i = [(bk - 1) * 79 * 78 * 77] + [(wni - 1) * 78 * 77] + [(wbi - 1) * 77] + wki.

Notice we have an "i" on the end of all terms except the black king. These are "index" terms, not the actual square numbers. More on that later...

Each element, bk, wn, wb, and wk is a number in the range from 1 to 80. There is still one other thing to do before applying the formula. Since not all 80 square are available for the pieces based on the order the board is occupied, you need to "collapse" the indices associated with every piece other than the first one on the board.

That is, start out by letting every index element equal the corresponding square of the piece on the board.

wni = wn
wbi = wb
wki = wk

Then, if:

wn > bk, wni = wni - 1
wb > bk, wbi = wbi - 1
wk > bk, wki = wki - 1

wb > wn, wbi = wbi - 1
wk > wn, wki = wki - 1

wk > wb, wki = wki - 1

The logic is that if a piece is placed on the board AFTER some other piece, if the new piece is on a square which is greater than the square of a previous piece, the previous piece is "taking away one slot" from the new piece. There is 1 less square available for the new piece since the previous piece has already been put on the board, but this slot is only "robbed" when the new piece is greater than the old piece. If it is on a square less than the old piece, there is really no interference.

That being said, there are still ways to reduce the size of the database. In reality, the first king need only be placed on 20 squares for pawnless databases. Any position on the board with one king constrained to the rectangle a1,e1,e4,a4 can be rotated and flipped to produce ANY position on the board with the king unconstrained.

Place a king on a8. place the other pieces anywhere you want. If you flip the board vertically, setting the rank of each piece to 9 - current rank, you will have the king on a1 and all other relative relationships the same.

King on j8? Flip the board horizontally, the king is on a8. Flip it vertically, it is on a1. This can be done for any square outside of the rectangle.

You gain a 400% reduction in the database with the offset of a more difficult lookup scheme, but in this case, the gain is worth it.

There are two other types of reduction that can be performed.

One is to constrain the king pair to eliminate adjacent king positions. These are still elements in the database, although illegal over the board.

I can generate an array of 20 x 80 elements that enumerate the legal king arrangements, 1,2,3,4...etc. I can then use this as the precursor to the indexing function formula, which would be modified slightly.

The next, and final compression that can be done is called RUN LENGTH ENCODING. This technique requires creating another database listing just the wins, losses, and draws with no move to win information. This database will compress very well in this case, where it is mostly wins and losses. This technique will allow me to throw away the drawn positions from the move to win database, which are one byte per entry. It will also allow me to throw away the adjacent kings, and every position where it is white to move and black is already in check!

This should give excellent compression results in the end. I will only have distance to win data for legal chess positions, and distance to win takes up the most disk space.

So, I will work on this during the week, and maybe the resulting databases will be small enough to be placed online here for everyone to play against.

Felix made some interesting observations with his post. Regarding the "impossible" or should I say "impractical" checkmates in the corner other than the one of the Bishop's color -- true it is that in real live play they would most likely not occur against a strong human. However, from the perspective of the computer, they must be solved, of course! While the mate in 1 scenario can be recognized, I could post the most distant win where it spirals into such a checkmate, and even from a few moves away the solution might not be readily apparent to a human. I mention this because a computer will always find the QUICKEST path to a victory. If the human player makes an imprecise move, the program will not care a whit about whether to force the knight mate or chase the king into the correct corner with the bishop (a much longer task, usually.)

So, should a human make one miscue, he could find himself embarrased at being mated by the knight!

I had not made Felix's observations about the Bishop color -- that the database switched colors and generated a whole class of mates that are otherwise virtually identical! I will have to consider this as I compress the database and make it available for others when I write the program to probe it.

Currently, there are two files, a white to move file, and a black to move file. Each one is over 36 megabytes, but I can reduce it by more than a factor of 4 when I create a better indexing scheme.

I solved B+N vs. K today. If the database is solved correctly, it mirrors the 8x8 domain in difficulty, without a longer win. Black to move can lose in 64 plies, requiring 32 moves for both sides.

I will verify the database for correctness by probing the entire set and making sure all of the wins in "N" lead to positions that lose in "N-1" for the other side. Any break in the chain means there are errors lurking. If everything resolves, I think I did it properly.

Don't worry folks, I still have the entire graphical user interface to write for this database. Once I have it, I need to be able to write code for the program to probe it, generate moves, find the best defense, and make that best move.

I am not even there yet!

But if you want to help, I will post all 532 checkmates on the web at:

BishopAndKnightDB

sometime this evening. I am sure you will all review every position carefully and make sure all positions are checkmates and no possible configuration is ommitted!

:)

I do not know what the exact position is as of yet, but when I do, yes, I will play the losing side of sole king, and everyone else will play the strong side with B+N. We may switch sides if they want a demonstration of the winning technique. I am still a ways from this. I just ran a test last night on the code to make sure everything is in place.

In the 37,957,920 positions in the database, only 9,489,480 are unique, the others are reflections and rotations. I ran the test over all of them just to make sure.

It found 532 checkmates and 17,576 stalemates. These results are both encouraging since they are a multiple of 4, and the board will produce 4 mirrors of every pawnless endgame in Gothic Chess.

I can reduce the size of the database by 400% when I get a more sophisticated lookup scheme, but for now, I just want to compute the data.

It took 15 seconds to do this first pass, which is the quickest pass. Each subsequent pass will take about 1 minute with database lookups and move generation. So, once everything is in place, it will only take about an hour to solve the database.

Then I have to write the code to look it up and translate the best move to a move on the board.

Suppose I said place a white Bishop on a2, a white knight on j5, a white king on a1, and a black king on j6. Could you do something like that?

I will up the ante, if Fencer can accommodate. I will start to compute the B + N database on Saturday. When it is done, I will need a day to hook it up to some form of graphical user interface. I will probe the database for the most difficult position.

Any who wishes may enter the contest to try and win most swiftly against the database from the hardest position.

Whoever wins the quickest will receive a Gothic Chess set for the cost of the postage.

This is provided that

a) Fencer can provide some sort of temporary interface to set up positions for the purpose of this contest

b) the games remain private

c) those involved before other participate do not give away the position.

On a final note, I reserve the right to change the position if there are more than one arrangement taking the same length to win.

Is anyone interested? Send me an email to GothicChess@aol.com if you are, tell me your nickname on here, and I will post the official entrants online.

Fencer will verify that each name is unique, and that someone is not using more than one handle from the list.

--Ed

I would like to thank Pawnchucker for the kind words. Had I known who Paul was when I first started playing, and that he had access to GCR, I certainly would have embarked on a different opening plan in our game :)

I am in the process of sifting through some of the old GCR issues and making the material available online. There are some other interesting items presented here as well. Here is what is up and running so far:

A discussion on the evolution of chess, including some interesting tidbits about the early days of Gothic Chess.

Why Change Chess?

An interesting attacking game, showing the hairline that separates over aggression and proper defense. Ending with an Archbishop sacrifice and a nice combination.

Game of The Month

One of the first strategic notions I uncovered early on was that a Chancellor + Bishop attack could take every piece off of the board. Here is a discourse on this lesson, ported directly from GCR.

The Chancellor's Vortex

A photo gallery from the year 2000 Championship, our largest over-the-board tournament ever. Hopefully many more events will be hosted in the future!

National Championship 2000

I will gradually bring more items online, especially if I start computing database results for endgames.

That's all for now.

--Ed

By the way, my partner and I have already done this for the game of checkers. The longest win we have takes 253 plies to finish! We verified it is impossible for any program on the planet to play it properly! Our program, called World Championship Checkers, comes with an 11-CD installer, and these CDs are compressed! Now that's a lot of data!

Felixe mentioned:

"I would like to know, how can you be sure that a program can find all the best moves for the defensive king?"

The database starts by placing the pieces on every square and asking the simple question: Is the side to move in checkmate? Yes, identify this as a loss in 0. No? Is the side to move in stalemate? Yes? Identify this position as a draw. No? Can the side to move win one piece? Yes? identify this position as a draw. No? There is not enough informaiton to resolve the position yet, keep looping.

Eventually, it finishes "pass #1" and has identified all of the losses and draws. Then, by definition, every position on subsequent passes must be either play into: a pre-resolved win, a pre-resolved loss, a pre-resolved draw, or remain undetermined.

In order to resolve a win, only one move for the winning side need to lead to a win. In order to resolve a loss, EVERY move for the losing side must lead to a win for the other side.

As you loop around, doing pass after pass, you have a variable that indicated whether or not you resolved something on a particular pass. After so many loops, there may be nothing left to resolve. By definition, any of the UNKNOWN positions must be draws, so you mark them as draws then you are done.

Why you consult the database in a position, here is what you do:

1. Determine if you are in a win, loss, or draw to start. This is stored in the db.

2. Generate all legal moves from the position.

3. If in a win, look up the # of moves to lose for the other side to move. Pick the smallest number you find, and make the move leading to that position.

4. If in a loss, look up the # of moves to win for the other side to move. Pick the largest number you find, and make the move leading to that position.

5. If in a draw, make sure you do not move into a loss! (It is impossible to select a move leading to a win, or it would not be a draw.)

In this fashion, the program can always play the best defensive move for the weak side, and fastest winning move for the strong side.

Hi Felix,

Just so you know, the longest win on the 8x8 board for B+N vs. sole K does not occur with the pieces on the perimeter in the 4 corners!

The longest 8x8 win is as follows:

White King = a8
Black King = c8
White Bishop = e8
White Knight = h2

Solution with Black to move and lose:

1... Kd8 2. Bf7 Ke7 3. Bc4 Kf6 4. Nf3 Kf5 5. Bd5 Kg4 6. Kb7 Kf5 7. Nd2 Kg4 8. Nc4 Kh3 9. Be4 Kg4 10. Kc6 Kh5 11. Nd6 Kh6 12. Ne8 Kg5 13. Kd5 Kf4 14. Nf6 Ke3 15. Nh5 Kf2 16. Kd4 Ke1 17. Bd3 Kd2 18. Nf4 Kc1 19. Kc3 Kd1 20. Bc2+ Ke1 21. Kd3 Kf2 22. Bd1 Kg3 23. Ng6 Kf2 24. Bh5 Kg1 25. Ke2 Kg2 26. Bg4 Kg3 27. Bf3 Kh3 28. Kf2 Kh2 29. Bd1 Kh1 30. Be2 Kh2 31. Bf1 Kh1 32. Ne5 Kh2 33. Ng4+ Kh1 34. Bg2#

Here is a link for the year 2000 Championship. testing the link feature from within here...

Year 2000 Championship

There is a bulletin board in England where there are a few people who do not like me too much. But, the checkers program that my partner and I created, the strongest one in the world, has a reputation.

For those looking for a laugh, read the first line of the post:

http://checkersolutions.co.uk/cgi-bin/board/messages/7119.html

I was not the one who posted it, it was just brought to my attention :) P.S. My programmer partner is Gil.

I can start working on the code for the BN vs K database tonight. It will not be slick, nor fast to execute, but I can get it up and running in no time. I think the longest win is about 38 moves (for one side) so it will need to loop around 75 times (38 times for the winning side, 37 for the losing side) and I am not sure how long each iteration will take to complete.

If I generalize the code to solve any db configuration, I would need to spend at least a week making it very fast.

OK, now for a contest:

Try to set up the most difficult position for a knight and bishop to mate a lone king.

So, tell me the location of:

White King
White Bishop
White Knight
Black King

For the longest white to move and win position you think there is. The winner I will give a free stainless steel Gothic Chess commuter mug, complete with thermal lid.

Post your submissions, one per customer, with the subject heading "B+N vs. K Contest"

OK?

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.

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.

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.

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.

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.

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#

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.

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.

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.

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!

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.