Comments by SamTrenholme
http://polgarstarchess.blogspot.com/Some general points:
- Small star shaped hexagonal board with 37 hexes
- Doesn’t have the “diagonal” movement most hex variants use, with the exception of the Knight
- The rook is a lance that can only move forwards and backwards
- The bishop is not colorbound
- The game has free setup of the pieces, a la “Pre Chess”
- The queen moves like the rook in most hex chess variants
The biggest issue I see with giving Joker80 support for this piece is properly evaluating the piece, and having it possible to have the pawn promote to this piece—is there a way we can give Winboard a subset of pieces which we only allow the pawn to promote to?
Given a setup where we have the two rooks in the corners, the king on the F file, two bishops on opposite colors, two Adjutants on opposite colors, two knights, and the queen, we have 216 possible setups.
One issue I have with the Adjutant on a 10x8 board is that there’s a lot of smothered mating threats in the opening. For example, in the RANBQKBNAR array (A = Adjutant), black can threaten Af4# by opening with 1. h4. Black’s only reasonable reply to this is 1. h4 e5; after 1. h4 Ng6 2. h5 Black loses his knight; 1. h4 c5 2. Axb8 Rxb8 and Black can no longer castle on the queenside; 1. h4 g6 2. hxg5 and Black loses a pawn; 1. h4 f5 2. Af4+ and Black loses castling privileges; so that leaves us with 1. h4 e5 2. Nd3 and now Black is probably best doing a Slav-style defense with 2. ... d6, though 2. ... Bxh4 also looks interesting. This Slav-style defense also works against other White threats like 1. h4 e5 2. f4 d6.
When I investigated six different Capablanca setups to see which one was most balanced for White, the one setup with a first-move mating threat scored really poorly; being fifth place out of six (White had a really strong advantage). We can also consider using the RBNAQKANBR array, which doesn’t have any first-move mating threats. Then again, it’s an open question whether RANBQKBNAR is better for white than RBNAQKANBR, or what the most balanced Adjutant array is.
OK, I think we should agree to disagree about Capablanca/Carrera chess’ value as a variant, well except to point out it has, short of regional variants like Shogi and Chinese Chess, the most computer engine support of any variant; it’s one of the few variants where I can readily have, after a couple of weeks, some 30,000 games played with a given array to study its opening. One thing I wish Jeff Mallett added to Zillions was the ability to have the engine automatically play hundreds or thousands of games at a given engine strength/time control, so more variants could be better studied.
So, a question: What is your favorite variant right now? What do you like about the variant in question?
Grande Acedrex. A large variant from 13th century Europe. (12x12, Cells: 144) [All Comments] [Add Comment or Rating]Also, it’s rather arrogant to take your dislike and Winther’s dislike of Capa variants and conclude from that that all modern chess variant inventors dislike these variants. Do you have evidence to back up your claim that these variants are uniformly disliked? If these variants were so disliked by modern inventors, why are there so many of these different opening setups using these pieces and board out there to play?
I wonder how strong this dislike of Capa really is with you. After all, Winther has made more than one Zillions preset that can play Capablanca chess, and I remember a couple of enjoyable games of Schoolbook chess with you.
Carrera's Chess. Large chess variant from 17th century Italy. (10x8, Cells: 80) [All Comments] [Add Comment or Rating]The best way to really study the opening of a given chess variant is to have a lot of games played with said variant, and analyze how the games went. Since no chess variant has traditionally had the popularity to have enough games played to say anything meaningful about the variant’s opening, H.G.Muller suggested having a chess engine play thousands of games with a given variant to get a sense of the opening.
After some 30,000 Schoolbook games, I got two significant pieces of data from all this simulation:
- Some strong black replies to certain opening moves by white. 1. f4 c5 looks good for black, and 1. e4 d5 2. exd5 Nb6 looks to equalize. It was somewhat problematic to find a fully satisfying reply to 1. c4, and, indeed, 20,000 of the games were played to see how to minimize black’s problems after white makes this move; I finally settled on 1. c4 Mh6. One line of research I was not able to complete in the timeframe I allocated this project was to see if black had a reasonable reply to minimize his problems after 1. c4 e6 2. g4 (1. c4 e6 2. Bc2 f5 equalizes for black, but we can not depend on white cooperating so); I was not able to find a fully satisfying reply for black.
- Over 100 mating positions, which can be downloaded and looked at in Winboard; go to http://samiam.org/schoolbook to download them. I hope to one day make an inexpensive book with nothing but Schoolbook mating problems, a la Reinfeld’s classic 1001 Brilliant Ways to Checkmate (without the tactical errors the original book had)
The nice thing about the technological age and the ready availability of powerful home computers (did you know that an inexpensive netbook has as much computational power as a then start-of-the-art Cray XMP from 1984?) is that we can research information that previous generations could never dream of. I would like to thank H. G. Muller for making all of the software freely available so I could do a meaningful in-depth study of a chess variant. Indeed, I have coined 1. c4 in Schoolbook the “Muller attack” since it was his software that first showed me how powerful this line is for white.
The help command should summarize the changes done, or point to a help topic that explains stuff like the variant ICS server always using style 12, moves needing to always be entered in c2c4 format, examine being broken, and what not.
There’s a lot of cruft in the FICS client from the days when a lot of people didn’t have chess clients—this was back when a lot of people didn’t have computers at home (a decent computer cost $2000), and installing game software on shared lab computers was problematic. Cleaning up this cruft is understandable but should be documented to reset the expectations of us who do remember the old-school FICS client.
Hey, it looks like you never telnetted in to a Chess server.
Basically, a client like xics or winboard is a pretty GUI front-end; one would telnet in to the Chess server (either with or without a GUI client). There, you could shout with other players, chat in channel 1 or any other channel, flirt with the few girls who would show up—or play chess.
It was possible to play chess on the server using crude ASCII graphics, with an ASCII diagram for the board (R=Rook, etc.) if you were using a simple telnet client and didn’t have a graphical client—I even played ICS chess using dumb terminals back in the day, before the big mid-1990s FICS-ICC split.
The clients came later, allowing people to have an attractive looking board to play chess on their screen. There was also an ICS-like server for people playing Chinese chess, one for people playing Go, and I think even one for Shogi.
If you have a telnet client around, telnet in to your server and see what it’s like. Some basic commands:
- help RTFM is easy on the FICS server.
- match player, where player is the player you wish to play
- examine examine a game already played
Schoolbook. 
8x10 chess with the rook + knight and bishop + knight pieces added. (10x8, Cells: 80) [All Comments] [Add Comment or Rating]Some general impressions I have gotten from this research:
- 1. c4 looks to be white’s best first move.
- 1. c4 Mh6 looks to be black’s best reply.
- Black should reply to f4 with 1. f4 c5 (The “Winther defense”) and e4 with 1. e4 d5 2. exd5 Nb6
This is just one of many, many possible opening setups for the Capablanca pieces—there are some 126,000 possible setups if we use this set of pieces (two each of rooks, knights and bishops, one each of the strong pieces), force the bishops to be on opposite colors, and the queen to be left of the king. There is a nearly endless land to explore with just Capablanca chess and the many, many possible setups.
But, real life is calling me and this will be my last look at Schoolbook for 2009. Well, except to finish up the game with Wolff.
As an aisde, I have 132 games where one side thought they were even or ahead, but the other side found a mating combination to win the game:
http://www.samiam.org/schoolbook/
2 Queen Rocky Horror Lycanthropic Chess. Featuring pieces that automatically flip into wyrd and not so strange counterparts. (10x8, Cells: 68) [All Comments] [Add Comment or Rating]This game can be played with a real board using checkers with pictures of the piece on each side of each checker.
Like I said before, it looks like pretty much any simple piece a Chess Variant can have has been thought up before. Maybe it’s time to devote less energy to trying to come up with new pieces and opening setups, and more energy to coming with with ways we can develop opening theory for setups, figuring out how to make a Chess variant that comes as close as possible to having high depth, short games, no draws, and no advantage for the first player (or deciding how important each of these four factors are), and finding ways to come up with opening theory, endgame theory (which pieces can mate the king, etc.), and what not.
I’ve actually been working on opening theory for the one variant I have “officially” invented; White has about a 7% advantage and I’m trying to come up with ways Black can equalize. 1. e4 d5 2. exd5 Nb6 equalizes things for Black and Black has a better game after 1. f4 c5; I’ve been spending the last two weeks looking for a good reply to 1. c4 (right now, 1. c4 Mh6 looks like the most equalizing line for Black; 1. c4 e6 is refuted by 2. g4).
I personally think the Rhino makes more sense on a hexagonal board. Here is how a hex-Rhino would move:
. . . . 1 2 . . . . . . . 1 . . . . B C . . 1 2 . . 3 B B C . 1 . 3 3 4 . . B B 1 2 3 4 . . . . A # 4 . . . . . A 9 8 6 5 5 . A 9 9 . 7 . 6 5 5 9 9 . . 8 7 . . 6 . . . . 7 . . . .Here, we see the hex-Rhino (This may also be considered a hex-crooked-Rook) travels like the usual piece people use as a hex-Bishop, but stops at the squares in between, and can take two paths for each of the six directions it can go in a straight line, resulting in 12 total paths.
Speaking of Hex chess, I never liked the idea of the “bishop” as normally implemented in Hex-chess, nor the knight or the queen.
I used to play hex-based wargames with my dad when I was a kid and, in those games, there is no “diagonal”; the only movement allowed is to one of the six fully adjacent hexes; some pieces could move two, three, or more hexes, but never diagonally.
This is akin to a Knightrider, but unlike a knightrider, it doesn’t hop over any squares.
A picture is worth a thousand words:
. . 1 . . . 2 . . . . . 1 . 2 . . . 8 . . 1 . 2 . . 3 . 8 8 . 1 . 3 3 . . . . 7 # 3 . . . . 7 7 . 5 . 4 4 . 7 . . 6 . 5 . . 4 . . . 6 . 5 . . . . . 6 . . . 5 . .Or on the edge of a board:
1 . . . . . . . 2 . 1 . . . . . 2 . . 1 . . . . . 2 . . . 1 . . . 2 . . . . 1 . . . 2 . . . . . 1 . 2 . . . 8 . . 1 . 2 . . 3 . 8 8 . 1 . 3 3 . . . . 8 # 3 . . .This piece is in the same general class as the crooked rook, crooked bishop, rose, and other sliders that change direction as they slide: The piece goes out one square orthogonally, then turns 45 degrees to the left or right, goes out one square diagonally, then turns 45 degrees back to go outwards orthogonally again, goes one square, turns diagonally the same direction, etc.
Another way of looking at this piece is that it’s a “bent queen”, instead of going from its origin 0 degrees, 45 degrees, 90 degrees, etc., this piece goes from its origin 22.5 degrees, 67.5 degrees, 112.5 degrees, etc. Since Chess is quantized to its squares, the move is a little more awkward-looking on the grid.
There are, of course, a lot of ways of making other pieces based on this idea. There is the same piece starting with a diagonal instead of an orthogonal move, there can be versions of this piece whose rotation from the queen’s move is not 22.5 degrees, but some other rotation. We can have a “Betza Crab” version of this piece, etc. There are the forms of this piece that are “Bent rooks” or “Bent bishops” which are not left-right symmetrical. There is the possibility of combining this piece with other leapers and sliders. And so on.
2 Queen Rocky Horror Lycanthropic Chess. Featuring pieces that automatically flip into wyrd and not so strange counterparts. (10x8, Cells: 68) [All Comments] [Add Comment or Rating]Jeff Mallett seems to agree with me; in Zillions of Games, it’s somewhat difficult to program a variant with multiple royal pieces where the goal is to capture all of them (you need to add complex rules where the royal piece is off of the board until the player is at their last royal piece, at which point you put it on the board), but simple to program it so capturing any of the royal pieces win (just change the setup to put multiple kings on the board).
And oh, to be a pedantic Sheldon, while there is a transvestite in The Rocky Horror Picture Show, there is no werewolf. :)
While I’m being pedantic, pieces that change their move after being moved have been done before. This change was optional in Flip Chess/Shogi, and flipping is mandatory after every move in the 1976 game Kyoto Shogi (Wikipedia link which will work as long as some deletionist twit doesn’t succeed in deleting the article)
And, of course, there’s all the variants with rotating pieces out there; to the extent of my knowledge, the first variant with rotating chess pieces was Ploy, and, like Warlock chess, you lose a tempo when you rotate a piece (newer rotating variants have it so you rotate after moving the piece). Warlock looks to be new in the sense that the piece changes its nature that’s not merely rotating at the cost of a tempo.
- If you transform the pieces so you have no royal pieces on the board, you instantly lose
- If you have only one royal piece on the board, the other piece is unable to transform
Schoolbook. 8x10 chess with the rook + knight and bishop + knight pieces added. (10x8, Cells: 80) [All Comments] [Add Comment or Rating]Here are some interesting ideas I have made public on this server (it looks like Google doesn’t index things very well here, so I’m making some public bookmarks):
- 31 short-range pieces
- The 16 basic sliders that can traverse the entire board
- The “Sage” (Camel + Bishop) piece
- A discussion of various piece ideas
- A discussion of some Capablanca opening setups, along with a little of the discussion about the “Sage” piece.
- An idea I had to have Rook + King, Knight + King, and Bishop + King on an 8x10 board After playtesting this idea, I didn’t like it: Not enough tactical fireworks
The issue I have is that having to place bishops on opposite colors reduces the number of possible setups. There are 126,000 possible Capablanca Chess setups where the queen is to the left of the king and the bishops are on opposite colors. There are, however, 226,800 possible Capablanca Chess setups if we allow bishops to be on the same color of squares—something we can only do if we allow the bishops to shift colors.
Speaking of strong colorbound pieces, in addition to the Adjuntant (Bishop + Dabbah-Rider), there is the Sage (Camel + Bishop), and The Way of the Knight has a piece called the 'FAD' (Camel + Ferz + Alfil + Dabbah). There’s also, if you want a really powerful colorbound piece, Sage + Dabbahrider (or think of it as a Adjuntant + Camel), or even the diagonal hook mover I recently mentioned (a very ancient piece, older than Mad Queen Chess).
(Edit: 226,800, not 453,600 possible setups because the queen should be to the left of the king—we shouldn’t count mirror images)
- Has a simple move
- Has not been, to the extent of my knowledge, thought of before
This magic piece can change movement capability by using up a move to transform itself. A Warlock rook can change into a Warlock cannon by turning the rook upside down, or vice versa. The Warlock cannon uses Korean Cannon movement: it moves as a rook after having jumped a piece. If it cannot jump then it cannot move. As such, it is somewhat weaker than a knight, but its tactical capacity is great. In any case, the Warlock cannon can always transform itself back into a Warlock rook. After the piece is transformed it must make a move before making yet another transformation. So it's not possible to stay put and make continual transformations on the same square.OK, this is something I haven’t really seen before: A piece that can, at the cost of a tempo, change its nature. We can have all kinds of pieces of this form: bishops that can become knights and vice versa, Jumping Marshalls (Korea Cannon Rook + Knight) that can become Queens, as just two examples. This is best for pieces that are strong, but don’t develop very well in the opening, or pieces that alternate between two pieces of about the same value (bishops becoming knights on an 8x8 board, or bishops becoming augmented knights on larger boards).
The only time I’ve seen something like this before is Betza’s “Weakest chess”, where a piece has to lost a tempo to go from a moving piece to a capturing piece (and vice versa). Here’s an idea for people who want a game that computers do not play well: Multi-move weakest chess!
This is a question that is, by nature, a subjective impression. One person’s simple is another person’s complicated.
OK, let me try to prove myself wrong. I think one simple type of piece is a piece occasionally seen in historical Chess variants:
- The “hook mover” in Dai-Dai Shogi (and some of the other really huge Shogi variants) There are two versions of this hook mover; one that moves like a rook, then can, at any point, bend 90 degrees and continue its movement; the piece can go to any square on an empty board. There is also the “bishop” form of the hook mover that can go to any square of its color on an empty board.
We don’t have the complete rules of Dai-Dai Shogi here, but the Wikipedia is your friend; you can also play this game in Zillions (yes, Jeff Mallett deserves your $25 to register the game if you haven’t done so already)
- The “griffion” in Grande Acedrex. This piece moves out one square diagonally, then turns 45 degrees and moves any number of squares like a rook. A picture is worth a thousand words:
. . | . | . . . . | . | . . - - X . X - - . . . # . . . - - X . X - - . . | . | . . . . | . | . .
('#' is the piece, and it can move to any square marked 'X', '-', or '|'; the lines are used to show the piece moves like rook in these directions)This is, if you will, a limited subset of a hook mover; unlike a Dai-Dai Shogi hook mover, its hook rotation is 45 degrees, not 90 degrees, and it can only make the hook after moving precisely one square
. . . \ . / . . . . . . . X . . . . . . . . | . . . . \ . . . | . . . / . X - - # - - X . / . . . | . . . \ . . . . | . . . . . . . . X . . . . . . . / . \ . . .This hook mover is a variation on the Griffion; instead of starting with a diagonal move, it starts with an orthogonal move. If the piece moves more than three squares, it must bend 45 degrees on the third square it moves to, then move outward diagonally.
Here is the same piece’s move if it’s on the edge of an 8x8 board:
. . . . . . / . . . . . . / . . \ . . . / . . . . \ . / . . . . . . X . . . . . . . | . . . . / . . | . . . / . - - # - - X . .Like other sliders, this piece can have its move blocked.
How valuable is this piece? Somewhere between a rook and queen in value.
There’s also the diagonal version of this piece:
. | . . . . . | . - X . . . . . X - . . \ . . . / . . . . . \ . / . . . . . . . # . . . . . . . / . \ . . . . . / . . . \ . . - X . . . . . X - . | . . . . . | .Which is probably a little less valuable than the orthogonal version shown above.
Is this a simple piece? I’m not entirely sure. When I first saw the Griffion in, as I recall, New Rules For Classic Games (or was it Murray’s A History of Chess) I was very confused by this piece, but today it makes perfect sense to me.
We can have versions of this piece that bends after moving only square (the Griffion in the diagonal form), after two squares, after four squares, etc. We can have a version of this piece that bends 90 degrees instead of 45 degrees (the diagonal version of this piece is colorbound). We can limit the range of the piece. Etc.
Jose: Since you mentioned Ajax Capablanca Chess as a game with simple moves (add a non-capturing king move to the pieces), may I suggest Ajax Schoolbook. I should add that as a variant to the Zillions preset for Schoolbook. I really like the bishop + non-capturing Wazir piece; it nicely solves all of the headaches one has coming up with a board setup for colorbound pieces.
Schoolbook. 8x10 chess with the rook + knight and bishop + knight pieces added. (10x8, Cells: 80) [All Comments] [Add Comment or Rating]Move PV ----- --- e5 73 Ng6 69 f6 40 c6 13 e6 10 d6 51. c4 e5 looks to be Black’s best reply, but 1. c4 e5 2. Bc2 is dangerous for black if not handled properly. Here are the win/lose/draw ratios for White after 1. c4 e5:
Opening moves Win Loss Draw Games played --------------- -------- -------- -------- --- 1. c4 e5 2. d3 100% 0% 0% 3 1. c4 e5 2. Bc2 53.0997% 35.0404% 11.8598% 371 1. c4 e5 2. f3 48.2456% 37.7193% 14.0351% 114 1. c4 e5 2. h3 47.619% 44.7619% 7.61905% 105Black’s win/loss/draw ratios to various replies to 2. Bc2:
Opening moves Win Loss Draw Games played ------------------- -------- -------- -------- --- 1. c4 e5 2. Bc2 a6 100% 0% 0% 2 1. c4 e5 2. Bc2 Cj6 100% 0% 0% 5 1. c4 e5 2. Bc2 Ch6 71.4286% 28.5714% 0% 7 1. c4 e5 2. Bc2 g6 58.2915% 31.1558% 10.5528% 199 1. c4 e5 2. Bc2 f6 50% 37.5% 12.5% 24 1. c4 e5 2. Bc2 Be7 48.3871% 38.7097% 12.9032% 62 1. c4 e5 2. Bc2 Ng6 42.3077% 44.2308% 13.4615% 52 1. c4 e5 2. Bc2 Ad6 26.3158% 47.3684% 26.3158% 19 1. c4 e5 2. Bc2 Ni6 0% 100% 0% 1It looks like Black gets creamed here because Joker80 often does 2. ... g6 when 2. ... Ng6 appears to give much better results (Update: Further research shows Ng6 isn’t that great for Black: c4-e5-Bc2-Ng6 Win: 50.365% Loss: 39.4161% draw 10.219% Total 274)
More research has to be done, including looking for a reasonable Black reply to 2. f3.
As an aside, I get a lot more pretty mates when I have Joker80 play at 40-moves-in-4-seconds than when I use slower time controls.
Dimachaer Chess
. Introducing the Dimachaer, a bifurcation piece that always lands on the diagonal second leg (zrf available).[All Comments] [Add Comment or Rating]What I see with pieces like this is that all of the simple pieces a Chess-like game can have are already invented, and that we’re having to come up with some pretty convoluted moves to come up with new piece types.
The simple Chess pieces seem to be:
- Simple leapers (Such as the knight and the king) I wrote, a couple of years ago, an essay describing 31 such leapers
- Simple sliders, such as rooks, bishops, and queens. There are, as I recently posted, 16 symmetrical sliders that can traverse the entire board if the board is a bounded square; there is also the bishop and Shogi’s lance
Once we move past these simple pieces, things get complicated and the learning curve goes up. One relatively simple piece is a piece that captures differently than it moves; a piece that, say, moves like a knight or captures like a bishop.
Betza covered the “crooked rook”, “crooked bishop”, and “rose”—sliders which change their direction every square they slide.
Chinese Chess, of course, has the “Cannon”, which has inspired all kinds of pieces that leap before moving or capturing (or a combination thereof). Speaking of leaping pieces, I’m surprised no one has recently discussed having a checker’s king in Chess: A piece that moves like a Ferz, but captures by jumping over an adjacent piece, and can (optionally) capture multiple times in its move. We can, of course, have a wazir (horizontal and vertical) form of this piece, or combine it with any other chess piece.
So, yeah, it looks like pretty much any kind of piece chess can have with a simple move has been discussed here, so we’re moving on to complicated pieces that don’t seem very intuitive to me.
In terms of bifurcators, I assume we’re taling about a piece that:
- Moves in a straight line, either orthogonally (rook-like) or diagonally (bishop-line).
- Hits another piece, either friendly or enemy
- Changes direction, either 45 degrees or 90 degrees upon hitting the other piece
- Finishes its move
. . . . . 2 . . . . 2 . . 2 . . . 2 . . . 2 . . . . . 2 . . 2 X . . . 2 X 2 . . . . . X 2 . . 1 2 2 2 . . 1 . . . . 2 2 2 1 . 1 . . . . . . 1 . . . 2 . . . . # . . . . . 1 1 # 1 1 1 X . . . 1 . 1 . . . . . . 1 . . . 2 . . 1 . . . 1 2 2 2 . . 1 . . . . 2 1 . . . . 2 X . . 2 . . . 2 . . . . 2 . . . . 2 . . . 2 . 2 . . . . . 2 . . . . X 2 2 . . X . . . . . 2 X . . . 1 . . . . . 1 . . . . . . . 1 . 1 . . . . . . 1 . . . . 2 . . . # . . . . . 1 1 # 1 1 1 X . . . 1 . 1 . . . . . . 1 . . . . 2 . 1 . . . 1 . . . . . 1 . . . . . 1 . . . . . X . . . 2 . 2 . . . . 2 . . . . . 2 . . . . 2 . . . . . 2 . . . . . 2 2 2 . . X . . . . . . X . . . X . . . . . 1 . . . . . . . 1 . 1 . . . . . . 1 . . . . 2 . . . # . . . . . 1 1 # 1 1 X 2 . . . 1 . 1 . . . . . . 1 . . . . 2 . 1 . . . 1 . . . . . 1 . . . . . 1 . . . . . X . .Here, we see three types of these bifurcators:
- The piece bounces just before the other piece’s square (first row)
- The piece bounces in the middle of the other piece’s square (second row)
- The piece bounces just after the other piece’s square (third row)
- The piece can move to an empty square on the first leg of its move (the second leg is not used)
- The piece can capture on an enemy-occupied square on the first leg of its move (the second leg, again, is not used)
- The piece can move to an empty square on the second leg of its move.
- The piece can capture on an enemy-occupied square on the second leg of its move.
I’ll pull a Betza and create a notation so we can quickly describe a bifurcator. O means we start with an orthogonal move; D means we start with a diagonal move. B means we bounce just before the other piece, M means we bounce in the other piece’s square, and A means we bounce afterwords. 1m means we can end our move on the first leg, 1c means we can end our capture on the first leg, 2m means we can end our move on the second leg, and 2c means we can capture on the second leg.
OK, so where do Winther’s pieces fit in this Betza-esque scheme? Like this:
- Gladiatrix OB2m2c
- Crossrook DA1m2c
- Crossbishop OA1m2c
- Murmillo DB1m2c (also can bounce off the edge of the board)
- Secutor OB1m2c
- Provocator DB2m2c (also can bounce off the edge of the board)
- Diamachaer OB2m2c
- Sagittar DA2m2c
- Venator OA2m2c
- Laquear DB1c2m (also can bounce off the edge of the board)
- Essedar OB1c2m
- Gaul DA1c2m (not allowed to end its move in the square immediately after the second piece)
- Thraex OA1c2m (not allowed to end its move in the square immediately after the second piece)
OK, there are some other pieces that don’t fit in this scheme, but this makes a reasonable introduction to these types of pieces.
Schoolbook. 8x10 chess with the rook + knight and bishop + knight pieces added. (10x8, Cells: 80) [All Comments] [Add Comment or Rating]These types of positions are actually quite rare; in the 5,000 games or so I have had my computer play to research Schoolbook, only 24 mates of this nature were found; a mate like this happens about once every 200 games.
These mates (in addition to the script that data-mines the .pgn files to find these kinds of positions) can be found here:
f3 Win: 51.462% Loss: 35.0877% draw 13.4503% Total 171 c4 Win: 48.5075% Loss: 38.0597% draw 13.4328% Total 134 c3 Win: 47.6923% Loss: 38.4615% draw 13.8462% Total 130 e4 Win: 46.9965% Loss: 40.636% draw 12.3675% Total 283 f4 Win: 45.6522% Loss: 43.1159% draw 11.2319% Total 276 h3 Win: 41.6667% Loss: 50% draw 8.33333% Total 12 Total Win: 47.6143% Loss: 39.8608% draw 12.5249% Total 1006Here is the same chart when we give Joker80 90 seconds to play 40 moves (per side):
j3 Win: 100% Loss: 0% draw 0% Total 2 f4 Win: 54.7945% Loss: 31.5068% draw 13.6986% Total 73 e3 Win: 53.8462% Loss: 46.1538% draw 0% Total 13 c4 Win: 48.1663% Loss: 36.6748% draw 15.1589% Total 409 f3 Win: 47.4576% Loss: 45.7627% draw 6.77966% Total 59 e4 Win: 46.9444% Loss: 40.8333% draw 12.2222% Total 360 c3 Win: 42.5926% Loss: 42.5926% draw 14.8148% Total 54 g4 Win: 36.3636% Loss: 63.6364% draw 0% Total 11 h3 Win: 31.5789% Loss: 52.6316% draw 15.7895% Total 19 b3 Win: 0% Loss: 100% draw 0% Total 1 g3 Win: 0% Loss: 100% draw 0% Total 1 Total Win: 47.505% Loss: 39.4212% draw 13.0739% Total 1002So, the question is, can Black equalize if we give him a small opening book?
It would appear he may be able to.
For example, I have had my computer play a lot of 40-moves-in-16-seconds games, starting with either 1. e4 d5 or 1. e4 d5 2. exd5 Nb6 (here, White can not hold on to the pawn). Here are the results:
e4-d5-exd5-Ad6 Win: 100% Loss: 0% draw 0% Total 1 e4-d5-exd5-f6 Win: 55.6604% Loss: 33.0189% draw 11.3208% Total 106 e4-d5-exd5-f5 Win: 54.1353% Loss: 37.594% draw 8.27068% Total 133 e4-d5-exd5-Nb6 Win: 45.4765% Loss: 41.9783% draw 12.5452% Total 1658 Total Win: 46.6807% Loss: 41.1486% draw 12.1707% Total 1898We can see that, with this defense, we reduce White’s advantage after playing 1. e4 from around 6.5% to around 3.5%, helping equalize the game for Black; Joker80 doesn’t do any reply besides exd5 after 1. e4 d5.
My theory is that we can find equalizing replies for Black to other White first moves in the Schoolbook opening array. For example, preliminary research suggest that the position after 1. f4 c5 strongly favors Black (but I’m putting this line of research on hold because I’m currently playing a Game Courier game with this opening).
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