I would like to enter the tournament...but I need to know what day and time?

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 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.

Dear Ed Trice,

I have reviewed your geocities posting cursorilly, and would like to say "thank you"
for that. It is something I have always wondered about, and now I need wonder no longer. An interesting observation is, that while my perview was hasty and superficial, I probably spent at least as long looking it over as your computer spent generating it in all its precision.

While I cannot claim to think as a computer does, it is nevertheless significant to me, and therefore worth the mention, that several points come to mind as I see your results:

1) The solutions for checkmate as given are mostly impossible to achieve in real life play. This does not detract from their value for the computer, however, for in view of the purpose of this list being to generate the answer to my question, I acknowledge and appreciate this fact.

2) The first 148 mates are with the bishop of one color, and then starting with #149 the bishop changes color. This infers that the following 147 positions are likely a repetition or mirroring of the first 148, and so on for the other 2 corners.

3) Of these first 148, only the first 65 are with the Black king in the bishop's color of corner, the rest are on the side of the board between corners, where nobody ever achieves checkmate when the defensive king moves correctly. Others, among the first 65, may be legitimate mating positions, but inasmuch as they cannot be arrived at in real play, they would also never happen in a live game. These in question are all, therefore, practically impossible.

4) The checkmates that Capablanca exemplifies in his writings (I am not aware of any in his actual games, but if anyone knows of one, please let me know!) are to be found at positions 2, 32, 151, 195, 338, 382, 501, and 531. They are all the same arrangement of pieces, however, placed in the 4 corners, right hand and left hand, as it were.

I have tried to arrive at an answer for your challenge to find the starting position for the longest possible checkmate for these 4 pieces, and it is a daunting task, to say the least. If I give you an answer now, it would be a shot in the dark, for I do not have time to think about it right now. After studying your 8x8 solution, it seems that I am not well prepared to render an educated conclusion in regards to this question.
Although, if you are giving us a deadline, I will put mine in, just to be a participant. Please let me know if there is a time limit on this.

And thank you, again, Ed, for your diligence. /Fx/

I, too, have looked at the daunting database and suspected the same as Felix. My thanks goes to him as he has done what I had hoped to do, but, I am sure, in a much more rapid process.

I think that the same applies to most of the stalemate psoitions, that they would not (some even could not) occur in actual games.

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.

<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.

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.

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

Okay, give me the initial position so I'll be able to prepare the database change for all related games.

Hi GothicChessPro

I am a little confused ... well, a lot actually. Are we to post here our proposed starting positions or are you going to set up one of the 245 40-move alternatives for us to solve by playing you? If we are to post here then I guess we should also post the solution which may have a number ways of getting there.

Cheers from one well-confused whisper :)

Now, now, now! Enough of this self-effacing rhetoric!! Anyone who calls himself an idiot and then promptly proceeds to demonstrate the contrary is, per se, a walking oxymoron; provided, of course, that he can walk.

So, if you will please stand to be corrected, Ed: you are obviously not an idiot, but a moron, that is, an OXYmoron.

O X Y M O R O N S O F T H E W O R L D, U N I T E!!! /Fx/

Hey! Hey! Hey! No fair giving away the answer to Fencer! If you guys wanna turn some shady deals, you'd better do it behind closed interfaces or whatever, 'cause it makes the rest of us jealous. /Fx/

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

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.

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

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

White: Ka8, Be8, Nj2
Black: Kc8

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

White: Ka1, Be1, Nj7
Black: Kc1

White: Kj1, Bf1, Na7
Black: Kh1

White: Kj8, Bf8, Na2
Black: Kh8

White mates in 37 moves.

So far he is the leader!

Okay, I had my guess early, but to put some positions on it:

White: Ka1, Ba2, Nb1
Black: Kj8
Black King has many posible locations but generally in that diagonally opposite corner.

White to move checkmates in 34.

Juan is still the leader with a mate in 37.

Well, here is my shot!

White Kc8,Ba1,Ni1
Black Ka8
Like Whisperz I needed to put something in!!

White to move checkmates in 25.

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.

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!

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#

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: 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#

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

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.

Whisperz
- Move 14 Kg6 clashes with move 12 Bg6 :(

Jaungrande
- Move 27 Kg4 but bishop is already here (move 23).
- Moves 29 to 36 are repeats, and why wouldn't King repeat Kj4 at move 37?
:)

Personal to Ed, the dyslexic wizard:

With all due respects, sir, while we all appreciate your posting of the solutions, we must ask for a reconsideration in Whisperz' case, for he said, "Black King on j8" and you provided a solution for mate in 34, however, it proceeds: "1...Kj2," which means that while you have acknowledged j8 as the starting position, you have somehow allowed the computer to register j1 (or i1, i2, i3, or j3) as the starting square. Ain't it nice you are among friends, who so joyfully tolerate your little foibles??

DSYLEXCIS FO TEH WORDL UNTIE!

Let's see now that's, the Bishop changed color and it took a Capablanca fan to notice, you let the program stop at 64 plies without questioning its reason for stopping, and you provided a Whisperz solution for a position unlike Whisperz' entry. But who's keeping track? /Fx/

I am unquestionably thankful for your effort in putting out these solutions, Ed, and it will give me a good workout to study them in detail. In the interest of learning better chess, this is an exercise that can go a long way to filling a void in a student's tactical skill: the proper handling of Bishop and Knight, and more generally, the proper handling of two pieces of different powers.

While I delight in the prospect of gaining more proficiency on the board, it comes as a curious disappointment that I have found an obvious error in your move list. In the solution you have provided for Whisperz' entry, there is the following: 12.Bg6 is followed by 13.Kh6, and then 14.Kg6(*?*). This is impossible, because the King is moving to a square occupied by his own Bishop.

I trust this is an oversight and that you will soon locate the source of the error and fix it, for we are depending on you to get it right, eventually. That is, we can't rely on computer moves that would not win in real life games. /Fx/

This is no mate. It is a curious 5-fold repetition, which would have been a draw after the first 3. The computer did not recognize it as such, and neither did the programmer, aparently.

It seems to me that this mistake begins when the King moves to g4, already occupied by the Bishop. If we substitute a legal move, such as Kh4, the play could have played out to mate. But this mistake continues in the Knight moves, which instead should have continued the pattern already established, which would have then resulted in mate at move 37, anyway.

My question is rather on several of the previous positions, which have the Black King moving in ways that seem to facilitate his own demise. I am now wondering if the program was hastening toward a stalemate position instead of attempting to survive 50 moves? This latter objective is the principle subject of our investigation, after all. /Fx/

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.

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 tried to send this for the past 2 days but could not get this discussion board to activate. I got messages to the effect that BrainKing was being updated.

In case it still is possible to register my entry, here it is:

Wht: Ka8, Bg8, Ni1
Blk: Kc7, with Black to move. /Fx/

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

What happens when the Cancellors and Archbishops are traded off, leaving regular pieces and two additional pawns on a bigger board: are such games likewise faster than chess, or slower by the fact of a larger arena with more pawns? If faster, to what can this speed be attributed, to the greater difficulty of protecting opposite sides of the board, or some other aspect? /Fx/

Well it depends on what you mean by 'faster'. If two players of reasonable skill went up against each other, I would say that there are more options and possibilities due to the bigger board.

It is hard to define faster or slower, but if you are talking about pawns being promoted into Pieces, then it is a lot harder to keep track of everything going around the [larger] board.

I would say the game would seem faster if an expert was taking apart a beginner, but then that happens in chess too.

So no I wouldn't say that Gothic is faster than regular. Maybe more complicated, but certainly not faster [as a rule] because chess isn't about speed and we cannot define a short checkmate as being better than a prolonged checkmate.

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.

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

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

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

When I say "faster" I am talking about two things: obviously, the fewer the moves in a game, the faster it looks (recorded) on paper, and since most game lists do not include a time value for each move, that duration of the game is somewhat nebulous. Correspondence chess may have a different look to the moves, but I think it would take an eye with much experience or else some great talent to tell whether a given move list came from correspondence play, which takes many days between each move, or speed chess, which can consist of two or three moves per second. Even so, lightening chess played by great masters likely exhibits more profundity than correspondence chess played by amateurs.

Secondly, there is a tempo aspect to chess which is inherent in the moves regardless of the time it actually took to play them. When one side achieves checkmate by force, it is in fact necessary that the offensive pieces by virtue of their aggression, have the initiative, for without it, they would not be able to press the defense into a losing position. This initiative has a curious aspect in that it can be entirely gained or entirely lost again, in one move. The frequency with which this occurs is another way to say the game is moving "faster" or "slower".

In my own limited experience with gothic chess, it seems to me that tempos get trumped by opposing tempos, leaving layers of latent action which has not been seen in chess, as far as I can tell. This complexity carries a sort of speed of its own which appears to make the game end in fewer moves, if I am not mistaken.

Perhaps someone with better information can answer these questions. I have not made a very exhaustive study of chess theory and practice, but I am amused by the similarities and differences between the two games.

Someone brought up the concept of "distant opposition," maybe on IYT, and I do not know what that is, so I feel ignorant. It has to do with controlling the right and the left sides of the board from afar by placement of the King on the square which affords his potential movement the greatest effectiveness. If I could learn the basics of that theory, it may help me to find the answers I seek here, and then again, maybe not.

I was trying to identify in my mind the causes of gothic's speed, and in order to understand what is really happening here, I thought that separating the power of the pieces from the size of the boards would effect a clearer comprehension of what elements contribute to gothic's observed faster pace. I do not know if such knowledge would be useful, practically speaking, it's just this compulsion I have of wanting to penetrate the essence of a thing: in chess, it has been a journey of several decades for me, and now in gothic, I am facing the possibility that I may not live long enough to find the answers I seek.

And in the greater picture, as far as this discussion goes, the world may not last long enough for ANY of us to get all the answers we hope to find! /Fx/

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

From Juan:

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Ed (GothicChessPro) claims that it would be faster because more games would be decided by an outside passed Pawn due to the increased width of the board. I find that hard to believe.
-----

Nowhere did I discuss the specific ending theme of outside passed pawns.

My exact remarks were:

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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.
-----

The concept of "the square" is not limited to outside passed pawns. Keyword: concept.

If the board was populated entirely by minor pieces, one miscue in Gothic, and a flurry of swaps could leave you in a King + Pawn ending that cannot be drawn because your own King would be too distant to reach a square where a breakthrough could be initiated or an opposition would need to be contested.

I have been in countless speed games and done this to chessplayers who would make comments like: "But this is a bishops of opposite color draw" to which I replied: "If you remove any two files on this board and make it an 8x8 board you are correct. But it is 10x8, so I win."

In the future, if there is something that is written that needs additional elaboration, just ask me and I will explain in more detail. As was seen in this case, and in the Juan/Felix discussion, it is possible for us to have "different understandings" of what was being discussed.

Well, I am still following the thread, although you guys have lost me with all that technical gobbledygook. Maybe I should go get some coffee first :)

Better make that strong coffee ... and black ... and add some chocolate to help stimulate the brain ... it'a a little beyond me too :)

65th and Whisperz, it is not my intention to overwhelm you with esoteric nonsense. The terms we are using have specific significance, and this discussion is of genuine interest to me. Please do not think anybody is attempting to pull a fast one here, but if you decide this is too exhausting to follow, perhaps you would do well to go back (when you have had some rest-- a luxury for some these days!) and simply look for the word or words which appear mysterious, and look them up in a good dictionary. I am not kidding. You may well be amazed at how much less stressful it is to correct misconceived notions which begin in one word. I look forward to reading the links that Juangrande provided on the Opposition and on King and Pawn endings. These are two subjects regarding which I am quite pleased to find, there are real people who are willing to think about them, for I have never met such a person in real life. While there are books written, most chess players regard these topics as too boring to bother with. I believe that their frustration (perceived as "boredom") is due to not understanding the principles at work in these concepts, which is the root cause of their boredom, for once they're understood, a player suddenly finds he has a new appetite for studying King and Pawn endings (or Rook and Pawn endings, or Bishop and Knight vs. King endings, etc.) and he has a change of heart. On the internet, I have run into people who have experienced this change, and they are happier chess players as a result! If I can help people find happiness, that is its own reward.

These concepts are not for everyone, however, and a good chess player need not feel left out or inadequate for not caring to study these rare endings. Not everyone is interested in helpmate compositions, for instance. I am one of those. But I do not therefore think that someone who does appreciate them is somehow less of a chessplayer. In fact, if I ever meet someone who is a fan of helpmates, I look forward to asking them: what makes them think that way? Maybe I just have not had the right explanation.

In any event, I am glad you are participating in the discussion, for your disquiet is duly noted, and I will please try to be more discreet with my ramblings, so as not to appear presumptuous.

Eschew obfuscation! /Fx/

This is exactly what I was talking about when we started the B+N vs. K contests. The spirit of putting the theories to practical test is the key issue. We can hurl e-mails at each other 'till the cows come home, and it won't prove anything. We have to test it in the lab. Ed Trice claims to have played the streets in this question of pawns outside the square, and that is precisely the wisdom that is required. We are dealing with a 10x8 board, and it OUGHT to come as no surprise that there may be some differences in play rooted in the fact of two more files on the board.

We are touching on things that could become hot topics of dispute in the chess world very soon, for it seems that people are just now starting to warm up to the idea, that to the greatest intellectual board game ever devised, a viable alternative now exists.

Furthermore, Drueke, and such manufacturers of high quality, tournament size chessboards, ought to wake up to the imminent demand for 10x8 boards, because it won't be forever that serious gothic chess players are willing to make do with roll-ups, or (like me!) post-its on the right and left borders of their walnut and maple solid boards.

--Unless, of course, the War Effort has placed reservations on the supply of seasoned hardwood lumber, in which case we are facing delays, not excluding those caused by War Protestors who impede shipment of materials... /Fx/

I finally finished the page with the mathematical derivation of the piece values. Each step is explained in great detail. Take a look at:

Piece Values

for more information. I came up with these values for the approximate piece weights. Feel free to discuss this, argue with it, defend, attack, or modify these values as much as you want online here.

Pawn 1.00
Knight 2.50
Bishop 3.00
Rook 4.75
Archbishop 6.50
Chancellor 8.25
Queen 8.75

Okay, but if we have pillow fights, can we use feather pillows in the street on a windy day?

Seriously, Ed, your Piece Values web page is quite informative. At first look, it appears to be mathematically correct, which is a welcome development. I have to wonder how much time it must be taking you to assemble all these parts to your platform? Fortunately, you seem to have the general footing secure in the way things work, so we can continue to blithely play our gothic games without wondering if it will ever catch on: of course it will!

And the feathers will be scattered by the wind for sure.

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

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