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Mathematical definition of a chess piece?
Garth Wallace wrote on 2018-11-20 UTC

Because of the "inside-out rook" problem, I started trying to define equivalence for pieces in terms of what conditions (relative piece positions) a move can be performed under, until I realized that this was a much better way of defining moves in the first place. the inside-out rook demonstrates that the sequence of steps is entirely irrelevant, only which squares relative to the starting square can it be blocked on and how.

So at this point, I changed my approach. Instead of a path being a sequence of steps, it becomes a destination vector and a set of "tests", where a test is a pair of a vector and a state that must be true of the square that vector away from the starting square for the move to be legal.

A welcome byproduct of defining everything in terms of vectors from the starting square, instead of vectors from the previous step in a sequence, is that "exotic" board topologies become much easier to deal with. The sequence method was fine for hex boards (it's just a different set of basis vectors), but trying to define, say, a bishop on a moebius strip board was weird (try it!). But if all vectors are treated as having the same origin, there's nothing special about it.

Nice, right? Oops, forgot about divergent captures. Okay, instead of just a destination vector, we have a set of results, a set of "things that happen when the move is taken", which can include a destination and/or capture vectors. The Chu Shogi Lion's igui capture can be expressed as a move with a capture vector but no destination vector, since the Lion doesn't move; a null-move like the Lion's jitto is a move where the result set is the empty set ∅. Promotions? Another kind of member of a result set.

There's still a problem with promotion though. We need to know when it's an option. All moves are relative, but pawn promotion happens at a certain absolute position. Let's say that there is a "promotion zone" state for squares, and any pawn step onto a square with that state is a move with a promotion result. En passant can be defined in terms of a capture move to a "just stepped over by a pawn's double move" state. Of course hte problem here is that "state" is very vague. A promotion zone is permanent, but the en passant square only exists for one turn, and there's no way of specifying that sort of thing within this system yet.

Another important thing has been left out: black and white, or more generally sides. At this point I'd been mostly ignoring them and was thinking in terms of just e.g. "knight" rather than "black knight" and "white knight". I was more or less treating captures as explicitly affecting the opposite side. But that's not very flexible (it disallows, say, a hopper that can only use friendly hurdles, or a piece that can capture friendly pieces). Abstracting away the actual human players (who may not even exist, e.g. in a chess problem), what is the distinction between the sides? Alternating turns! Counting from the beginning of a game, white pieces move on odd-numbered plies and black on even-numbered plies (and neutral on all). So we should include, as part of a move's condition (set of tests), which plies it may be performed on, in most cases some number modulo the number of sides. Together with obligate promotion, we can even define oddities like Petkovian half-neutrals, which change sides when moved. Now that we've introduced a time dimension, we can even include that in our test vectors, allowing us to define en passant more concretely in terms of the previous turn's position instead of hand-waving an "en passant square" state.

I'll get into royal status, mimics, what a "state" really is, rethinking captures, and generalizing to almost everything later, but it's getting late and I have work tomorrow.

Garth Wallace wrote on 2018-11-20 UTC

For a while now I've been playing with the idea of defining chess pieces in strictly mathematical terms. Originally this was meant as a more flexible/descriptive alternative for Betza Funny Notation, perhaps as a way of specifying pieces for chess-variant-playing AIs, but there is also the possibility of defining operations and functions over them, and maybe even proving some things algebraically.

My early attempts were to define pieces as sets of possible paths, where paths are sequences of steps, and steps are vectors; notation would use the Kleene star for unlimited equal steps. So a wazir, for example, would be {(0,1),(1,0),(0,-1),(-1,0)}, and a rook would be {(0,1)(0,1)*,(1,0)(1,0)*,(0,-1)(0,-1)*,(-1,0)(-1,0)*}. Since most pieces are symmetrical it would make sense to parameterize this as a kind of shorthand, but since some pieces aren't symmetrical it shouldn't be assumed (in the way that "a 1,2 leaper" usually implies the (1,-2), (2,1), etc. leaps). This works for the usual steppers, leapers, and riders, and even bent riders; it's basically how people usually think of chess moves, just in more formal terms.

But this starts to get awkward where pawns are involved (and a way of describing chess pieces that has trouble with pawns is seriously flawed!). First off, we need to separate passive moves from captures. That's not too bad; we can even do so by introducing a "capture step" distinct from a passive step, which must be to a square occupied by an opposing piece, and this lets us do fun things like define the Chu Shogi Lion and the Locust. Then there's the initial double move, and promotions. We can introduce a new kind of "step" that is a promotion to another piece type to deal with these: the initial double-step can be implemented by defining a "starting pawn" that has it, where every move ends with a "promotion" to a "basic pawn" piece that doesn't. The promotion step is also strange, because it always happens at the end, but if you define operations that derive pieces from other pieces (like a "double move" operation that derives a Hook Mover from a Rook) in terms of sequence concatenation, you can end up with a promotion in the middle, or even more than one. So we've unfortunately introduced a distinction between "well-formed" and "ill-formed" pieces, and a need for some sort of normalization.

Introducing hoppers also complicates things. We have to introduce another step, one that requires a hurdle like the capture step but doesn't capture it. But now we've introduced the possibility of moves that "collapse": after all, what is the difference between a (1,2) knight move, and a pair of a regular mao-move and a mao-move over an obligatory hurdle?  Or between the latter and a pair of a regular moa-move and a moa-move over an obligatory hurdle? Equivalence is a mess.

I never found a satisfying way of dealing with en passant, or castling. Defining a piece in terms of the path is travels doesn't lend itself to a move where two pieces are repositioned.

Finally I realized that this approach fundamentally allowed for pathological alternate definitions of pieces. For example, take the rook. One or more equal orthogonal steps, right? Now let's define an "inside-out rook": a piece that leaps orthogonally directly to the square right next to its final destination, then slides by orthogonal steps until it reaches its starting square, then finally leaps directly to its final destination. This piece behaves exactly like the basic rook. It's entirely equivalent: any square it can reach, a standard rook can also reach under the same conditions, and vice versa. Yet it is considered a different piece. While the example is obviously contrived, similarly weird things could be produced by operations that concatenate or interpolate paths.

Chess 2. Different armies, a new winning condition, and duels. (8x8, Cells: 64)
Ben Reiniger wrote on 2018-11-19 UTC

Sorry for the confusion.  That page is under the "Related Pages" menu, but maybe the different name muddies things.  I'll try to add a link to the page contents when I get home.

Sirlin's Chess. Alternative presentation of "Chess 2 - The Sequel". (8x8, Cells: 64)
Anthony Viens wrote on 2018-11-19 UTCAverage ★★★

Sirlin's Chess2-the Sequel

I agree that name reeks of hubris.  However, that page has all the discussion about the game on it.  I would be great if this page were linked to it in the main body of text.

Chess 2. Different armies, a new winning condition, and duels. (8x8, Cells: 64)
Anthony Viens wrote on 2018-11-19 UTC

Immediately after I posted the two previous long comments, I did a search for something else and discovered:

Sirlin's Chess

Someone already posted all the rules to Sirlin's Chess2!  Auuuugggghhhh.....I just wasted a couple hours trying to make sure the rules were saved on CV.  Sigh.

PS.  Like most people, I consider the name Sirlin chose for his chess variant--Chess2, the Sequel--to be full of hubris.  Probably part of the reason never caught on with chess fans.....

Anthony Viens wrote on 2018-11-19 UTC

The third thing Sirlin did was make 5 new armies in addition to the classic one, in the vein of Betza's Chess with Different Armies.

This is the part I thought was super cool, as there are some very different armies contained, completely unlike Betza's. I had thought I could just port the armies over against Betza's, but that doesn't completely work, as Sirlin balanced his with the midline invasion and dueling rules.  In addition, the tremendous amount of play they got on the steam game before it was largely abandoned proved a few other holes.  The Reaper army has difficulty winning against Nemisis or Two Kings, but can feel overpowering sometimes against other armies.  Sirlin commented Reaper was very difficult to balance, and it appears it still isn't quite right.

Quoting the rules:

The Six Armies

I) Classic (balanced)
It's regular old Chess. This is the only army that can castle.

II) Nemesis (favors pawns)
The queen is replaced with a new piece: the nemesis. The nemesis piece moves as a queen, but cannot capture or be captured except by the enemy king. (It can check and checkmate a king, and a king can capture it.)

Your pawns can move as normal pawns, or alternatively they can make a nemesis move, which is a move one space toward the enemy king. (Imagine a box drawn around your pawn and the enemy king; moving inside that box is a nemesis move. That move can be toward your back row if the enemy king is behind your pawn). Nemesis pawns can only capture pieces (or threaten a king) the same way normal pawns can: diagonally forward. Your pawns cannot move two spaces at the start of the game.

Despite what the rules say, Nemisis is not really about the pawns.  This army is focused on the Nemisis.  You can run the Nemisis right into the thick of things, unworried about loosing it.  It's quite a good army.  The ability to move your pawns out of the way of your rooks to develop them early also changes things in interesting ways.

Betza calls the whole class of pieces that cannot capture except the king nemisis pieces, from the first piece of that type he came across.

I'm not sure how easy this is to integrate with Betza's Chess with Different Armies. It might be close.

III) Empowered (favors knights/bishops/rooks)
While a knight, bishop, or rook is adjacent (diagonals do not count) to another knight, bishop, or rook on your team, each piece gains the movement powers of its neighbor in addition to its regular movement powers. (King, queen, and pawns cannot gain movement properties.) To compensate for this power, the queen can only move as a king. Example: if knight, bishop, rook are in a line, adjacent to one another, then knight can move as knight+bishop. Bishop can move as knight+bishop+rook. Rook can move as rook +bishop. The knight does NOT gain rook movement in this example, nor does the rook gain knight movement.

Sirlin doesn't acknowledge any influences for Chess2, but this is almost exactly like one of Betza's ideas.  I can't find the page right now, but Betza had the powers relayed when pieces were within the movement range.  (A rook that was a knight's move away from a friendly rook would also be able to move as a knight.)  This becomes especially apparent when you read the forums on the Sirlin games website--David Sirlin posts there he had to reduce their empowerment range to only orthogonally adjacent pieces; playtest proved that anything more was too powerful.

In my opinion, this army could be made a standard part of Betza's Chess with Different Armies.  It is not too much affected by the midline invasion or the dueling rules, and it has gone through a considrable amount of playtesting and balancing.

IV) Reaper (favors queen)

The queen is called a reaper. It can teleport and capture anywhere on the board except the enemy's back row. The reaper cannot capture a king.

Also, the rooks are ghosts that can teleport to any open square on the board. The ghosts cannot capture or be captured.

The Reaper army is really awesome—it plays very very different than anything else. Unfortunately, it is balanced with midline invasion and dueling. Dueling keeps the Reaper from running amok....the player needs to worry about what he takes. And the Reaper army really needs midline invasion to win-- they only have bishops and knights to create checkmate.

Betza talks about teleporting pieces lower down in the same article about the nemisis right here.

If midline invasion was allowed for only this team, it might be transportable to Betza's Chess with Different Armies without too much modification.

V) Two Kings (favors kings)

You have no queen, but instead have two kings called warrior kings. If either one is checkmated, you lose. To win by the Midline Invasion method, BOTH warrior kings must cross the midline of the board into enemy territory.

A warrior king can move and capture the same way as a regular king, though it also has the option of doing a Whirlwind attack. For this, the warrior king stays in place and destroys all adjacent pieces—friendly and enemy—including diagonally adjacent pieces. You cannot Whirlwind if your other warrior king is adjacent.

After each of your turns, you may (optionally) take a special king-turn where you only move a warrior king. On your normal turn, there are no special restrictions. You can move either warrior king, or some other piece, whatever you want. During your king-turn, you may ONLY move a warrior king or perform Whirlwind with a warrior king. It doesn’t matter if you moved that warrior king or not during your normal turn.

Helpful hint: whenever you choose to skip this extra king-turn, it would be helpful if you tap one of your warrior kings as a signal to your opponent that he can take his turn.

Two Kings is also very different. The whirlwind attack is very powerful, but it requires you moving your king/s out in front. The delicate balance between attacking with and keeping your kings alive is a very different and fun experience!

I don't recall hearing anything like this in any of Betza's articles.

I'm not sure how much Two Kings relies on the midline invasion rule to be balanced. I don't think it matters much and can be directly ported over to Betza's Chess with Different Armies. But I might be very wrong on that!

VI) Animals (wild card)

Knight -> Wild Horse. Moves as a knight, but can capture its own pieces.

Bishop -> Tiger. Can only move up to 2 squares diagonally, but does not move when it captures (immediately jumps back to the square it attacked from).

Rook -> Elephant. Can only move up to 3 squares orthogonally. It can capture both friendly and enemy pieces, even multiple pieces in one move. If it captures a piece, the elephant rampages and must move its maximum distance, capturing everything in its path. Also, the elephant cannot be captured by a piece more than 2 squares away. (Draw a 5x5 box with Elephant in the center. It can't be captured by pieces outside the box.)

Queen -> Jungle Queen. Can move as a rook or as a knight.

This is a really delightful army, it takes a little bit to develop but is powerful. I really like both the Elephant and the Tiger—they push the envelope differently than Betza's pieces.

In my opinion, this can be moved over to Betza's Chess with Different Armies as-is. The pieces are about as strong as their FIDE counterparts one-on-one, so it should slide seamlessly in.

And I have a few more quotes from the official rulebook on miscellaneous stuff:

Players choose their armies in a simultaneous, double-blind fashion at the start of each match. It’s permitted for both players to choose the same army. Though players will likely specialize in playing only one army, in a multiple-game match, the loser of a game may switch to any army for the next game. The winner of the previous game may not switch.

Promoting Pawns
When one of your pawns reaches the last row, you must promote it (not optional). You can promote to any piece that’s part of your army other than a pawn or a king (or a Warrior King). For example, a pawn on the Animals team could promote to a Tiger piece, but an Empowered pawn can’t promote to a Tiger because Tiger is not part of its army. When you promote a pawn, your opponent does not get a stone.

Dueling Ranks
For purposes determining if you have to pay 1 stone to initiate a duel against a higher ranked piece, the only possible ranks are 1) pawn, 2) knight/bishop, 3) rook, and 4) queen. In other words, all special queens count as queens, even though the Empowered queen is rather weak. Elephants count as rooks. The wild horse and the tiger count as a knight/bishop. Nemesis pawns count as pawns.

Draws
There are no stalemates in Chess 2. The other types of draws from Chess 1 still apply here, though they are much more unlikely because of the Midline Invasion rule. The types of draws are: threefold repetition (when the same position occurs three times), the fifty-move rule (when the last fifty successive moves made by both players contain no capture or pawn move), and impossible checkmate (when neither player has sufficient material to checkmate, and Midline Invasion is not possible).

Other Notes

All pawns on all teams have the ability to en passant.

Pieces cannot pass through the Reaper army’s ghost rooks or occupy the same square as a ghost rook.

A warrior king’s Whirlwind cannot destroy a ghost rook.

Even the reaper cannot take an elephant if its more than 2 squares away

Anthony Viens wrote on 2018-11-19 UTCAverage ★★★

I've played a fair bit of Sirlin's Chess2, so I'm going to make a bunch of posts to move the rules onto CV website, in case the game is ever abandoned by Sirlin games.  I will also comment on the game in general.
Sirlin's Chess2 is quite balanced, and has clearly gone through a lot of playtesting.  Being developed by a modern boardgame company owner clearly shows here!

First, Sirlin's Chess2 adds 3 things:

1)win by centerline invasion
2)dueling stones; possible loss of an attacking piece
3)different armies.

Quote from offical rules:

New Win Condition: Midline Invasion
You can still win by checkmate, but you also win if your king crosses the midline of the board. Each move has added significance, because you must weigh how much it helps or hurts each player’s chances of winning by king crossing the midline in addition to the usual considerations of furthering a checkmate.
Just like in Chess 1, it’s illegal to move into check, so to win by Midline Invasion, your King must land on the 5th rank without being in check. Unlike Chess 1 though, there are no stalemates. If you have no legal moves, you lose the game.  While stalemates are common in Chess 1, they aren’t needed in Chess 2 because the Midline Invasion rule provides an even stronger option that a player can aim for when he’s down on material.

In practice, against reasonablely competent players, the majority of games will end by midline invasion.  For one thing, whoever is winning can typically move his king up before he checkmate's his opponent.  The big change, however, is when a player starts to loose, he will usually make a quick attempt at midline invasion win.  This makes the transition between the mid- and end-game very chaotic.
Most non-chess boardgame players will find this a very exciting change; instead of a long slow grind as one player increases his advantage, the the game ends in an explosion of desperate dashes-for-the-midline.  While the player who is in a better position will still usually win, there is more hope for the loosing player.  Having more on the line, it is more exciting for both players, despite the fact that the game still usually ends as expected.
This also esentially eliminates the chess endgame--which most casual players consider the most boring.  Once a player has a significant advantage, chess tends to grind toward an inevitable conclusion.  This is why experienced chess players will conceed when the game gets past a certain point--going through the motions is just a waste of time.
As a side affect, Sirlin's Chess2 games tend to be shorter.  Modern boardgames (not chess variants) tend toward shorter is better, so non-chess enthusasts would generally consider this a good thing.

This is where Sirlin's modern boardgaming design experience is showing....he has designed a change that appeals to the masses (more exciting desperate chance of a win) and eliminated the masses least favorite part of chess (the grinding endgame) and shortened the game in one simple rule.

There is just one problem.
MOST CHESS PLAYERS DON'T LIKE IT.
I don't like it either!!!
Effectively getting rid of checkmate just feels WRONG.

Sum it up=theoretically a good change that appeals to casual players, but chess enthusists won't like it at all.

Dueling
Quote from offical rulebook:

Dueling

Dueling allows you to spend a new resource called stones to threaten to destroy a piece that takes one of your pieces. Try to trick the opponent into wasting his stones because if he runs out first, you automatically win any further duels.

You start with 3 stones and gain 1 stone each time you capture an enemy pawn, up to a maximum of 6 stones.

Whenever you would capture any piece, the defender can initiate a duel. If your piece is higher rank than his (ranks: pawn -> knight/bishop -> rook -> queen), he must pay 1 stone to initiate a duel. To duel, you each put 0, 1, or 2 stones in your closed fists, then simultaneously reveal them. All stones revealed are destroyed. The winner of the duel is the one who showed more stones--ties go to the attacker.

If the attacker wins a duel, he takes the piece in question as in normal Chess. If the defender wins, he still loses his piece, but the attacker ALSO loses the piece he attacked with.

Initiating a duel and bidding 0 is a bluff to make the opponent waste stones. The attacker calls your bluff by bidding 0 himself. He wins because attacker always wins on a tie and in addition, the attacker can choose to gain 1 stone or cause the defender to lose 1 stone. (A player can't have more than 6 stones.)

Kings cannot be involved in duels because they have "Diplomatic Immunity." (They can't initiate a duel or be dueled.)

Players with 0 stones cannot initiate duels, but they can be dueled against. When you duel against a player with 0 stones, you must bid 1 and you automatically win the duel. If you lose a pawn in a duel, your opponent does gain a stone.

Dueling is another change designed to switch the game up.  Normal chess has a very mathmatical quality to it--good players can predict moves very far in advance.  The farther forward you can think, the bigger your advantage.

Dueling changes this.  Now, sometimes you won't keep a victorious piece.  Consequently, there is only so far out it is practical to predict moves, leveling the playing field a little bit.
Dueling accomplishes this WITHOUT resorting to chance.  The number of stones each player has is public knowledge, and he who correctly reads the importance of the current board position and his opponent will win the duel.  (And the attacker has the advantage, so ties in skill will result in the same board state as if no duel occured.)  However, this requires a very different set of skills than chess.

Consequently, it is possible for someone who is really really good at typical chess to be beaten by a player who is better at reading his opponent and bidding accordingly.  Someone who is bad at bidding may be winning--until they run out of stones.  This gives the othe player a big advantage.

By broadening the useful/necessary skills to win AND lowering the ability to look ahead, a larger variety of player types can be effective players.  Plus each duel is a mini-game, which gives flashes of excitement in the middle of the game.

Again, Sirlin's skill at designing modern boardgames shows.  This is a rule that should appeal to the masses and create some excitement, while lowering the necessity of mapping out future moves.

There is just one problem.
MOST CHESS PLAYERS DON'T LIKE IT.
I don't like it either!!!
Effectively making it uncertain if you are keeping a piece just feels WRONG.

Sum it up=theoretically a good change that appeals to casual players, but chess enthusists won't like it at all.

Kevin Pacey wrote on 2018-11-19 UTC

Apparently with Game Courier you can create your own piece set (i.e. a collection of images), which could then be used with GC or Diagram Designer (which uses pieces sets currently available from GC), but if you wish to upload images to this website (for use by GC/DD, at least) you ought to ask Fergus or perhaps another editor to do that for you, I gather from the following GC instruction sub-link (I've never tried to create my own piece set as yet, and it may be beyond my current know-how if I ever wished to do so):

CHECK 11 ~ Original Vision ~. 11 different original factions, chosen secretly, each with extra powers when few pieces remain.
Anthony Viens wrote on 2018-11-18 UTCAverage ★★★

I strongly encourage continuing work on this....I love the idea of 'choosing different armies'!

Sirlin's Chess2

Betza's Chess with Different Armies

Fantasy Grand Chess

And your idea of a one-time enhancement Trance (spell) appears to be an excellent idea of something different while not being too powerful.

However, I think the rules need some clarification.
In particular, the army 'Hologram' appears underpowered rules-as-written.  You gain the ability to suicide your queen to teleport your king.  Useful, but only so much.  You can't use it offensively (teleporting your king to the front lines is not smart) and if you use it to get the king out of check you're already in a bad way, and probably only delaying the inevitable.
Meanwhile, you loose the ability for the queen to capture--but it can still be captured, apparently.  So the queen is essentally useless.  (The rules specify only that the queen cannot capture.  All other rules being the same as chess, that means the queen can be captured.  A queen that cannot capture or be captured is useful as a blocking piece--is that what you meant?)
The Trance is not that powerful, only allowing the queen the ability to capture kingwise.  (If the queen is uncapturable, this is very powerful.)
I'm left with the conclusion that you must have meant the queen cannot capture or be captured.

Crazy 38's: The Knight. Missing description
Anthony Viens wrote on 2018-11-18 UTC

Ben Reininger, thanks for linking that image.  I should have done that initially.
Your comment also made me realize something I missed....if you count the knight move as 2 sq ortho/1 sq ortho to the side OR 1 sq ortho/2 sq ortho to the side.....then the knight can reach b5, c6, and d7.  So yeah, it looks like he just used a standard definition (1 ortho, 1 dag outward) and then counted the squares differently for the example.

H.G. Muller, interestingly enough, I don't see a confusion with 'outward'.  I just see it as 'away from starting square'.  But you are correct, everything has to be defined very clearly on this crazy board.

Which now leaves us with a conumdrum.....how do knights move?  Apparently we cannot use the offical way (1 ortho/1 dig outward) without contradicting the offical example.

My opinion; use both the definition and the example as offical, as the inventor probably had to spend more time and effort constructing the example than writing the definition, so it probably reflects his desires.

So, I say:

The knight can move on notated spaces, either 1 othogonally then 1 diagonally outward (outward is away from the starting square) OR 2 orthogonally then 1 orthogonally to the side, OR 1 orthogonally then 2 orthogonally to the side.

Note this does not use the inaccessable (non-notated) spaces, but I believe it can reach all squares that could be reached by using the inacessable spaces.

H. G. Muller wrote on 2018-11-18 UTC

I don't know anything about GC. But if it allows the use of off-site image files for the pieces (like http://...) it would also be possible to put the URL of the SVG generator there, requesting the desired piece. If the requested 'FEN' is 1x1, it will be rendered with transparent background, as the generator will assume you just want an individual piece to be used in a larger image. This is what I actually did below.

I know this works for the Interactive Diagram. This is what I actually used in the 'Board Editor' posted in the Alfaerie comments; it uses an Interactive Diagram to let the user set up the desired board position, and it uses the SVG generator to supply the individual pieces in it.

Kevin Pacey wrote on 2018-11-18 UTC

That's quite nifty, then. The only problem at the moment for CVP users would seem to be if Game Courier somehow does not yet allow for the use of SVG generated figurines in presets (i.e. for use in actual play on GC), but rather GC users still must use the kind of piece sets found on it, which are also found on the diagram designer.

H. G. Muller wrote on 2018-11-18 UTC

> It seems it would be great if the SVG generator supplements or is the successor to the diagram designer on CVP at some point. I assume most any shade of colouring can be used for the SVG figurines.

Well, it is there for you to use it. Just type the FEN after the f= in the link I gave. Indeed you can use any color for the pieces or shade for the squares; for details see the discussion in the comments on the Alfaerie piece set.

Kevin Pacey wrote on 2018-11-18 UTC

It seems it would be great if the SVG generator supplements or is the successor to the diagram designer on CVP at some point. I assume most any shade of colouring can be used for the SVG figurines.

Again an aside: For the variant idea I had in mind, it involved  using the RA piece type (besides the BD and QAD types, along with NP, and K) for an 8x8 variant involving eight sergeant pawns per side, but the idea looks like it's not going to pan out, if only because the RAs apparently could be swapped off the board on the flank files early in a game, at little cost to either player. Using RD (plus BA) instead would be no better, on 8x8, for that reason, but on a 10x8 board with the BD's not guarding the RA's in some setup with an extra piece type I've yet to decide on, with the seargent pawns and QAD thrown in, all the ingredients in question might work together better. The toying continues...

H. G. Muller wrote on 2018-11-18 UTC

You can get compound pieces of any kind with the SVG piece generator:

( http://winboard.nl/my-cgi/fen2.cgi?f=e-r )

Draws
Aurelian Florea wrote on 2018-11-18 UTC

I'd like to add something on this topic, especially for you HG.

A while ago, around 2 years, when starting the design of the apothecary games, you had recommended me extra major pieces (it was actually not extra minor pieces but towards the idea that a higher percentage of strong pieces leads to clearer outcomes). This for the simple reason that in the endgame best moves become much more specific especially when it comes to trades with strong pieces. When the board is empty but the material is very strong, tempo matters a lot :)! I still don't like ridiculous strong pieces. I tend not to use amazons, for example in my game ideas.

I think in designing chess variants this makes the drawing chances smaller. With perfect play it will still be a draw as long the rules allow it (in Arimaa obviously this is not possible). That for studying purposes.

This becomes more interesting when studying games that can be strictly longer then omega0 (the smallest infinite ordinal). But we don't have many such games probably, I know of no good one :(!

Other nicer finite cases are games with different armies. Spartan is a very good example. With perfect play I think it can be a black win. Here Zermelo's theorem (https://en.wikipedia.org/wiki/Zermelo%27s_theorem_(game_theory)) does not apply in it's classic sense as the players have different moves, but it can probably (although I have not did it) easily be proven that the game is either a win or a draw.

Kevin Pacey wrote on 2018-11-17 UTC

In case anything can be done, I'd note that the Diagram Designer's Alfaerie: Many piece set seems to be missing any symbol to represent a plain Alfil+Rook compound piece figurine, which I happen to be thinking I might use sometime, since I'm toying with an invention idea. The closest symbols are for either elephant rider versions of that compound piece, or else for versions where the rook component is restricted to moving up to just 4 squares. I'm thinking the latter would be a less confusing substitute (if one is necessary) for a plain Alfil+Rook piece, unless something more unrelated like e.g. an upside-down rook figurine would be less confusing than even that. I suppose CVP editors take accepting such emergency substitutions for diagram figurines on a case-by-case basis.

As an aside, oddly enough, Diagram Designer's Alfaerie: Many piece set does have a figurine for the plain Dabbabah+Bishop compound piece, as well as for the (plain) Alfil+Dabbabah+Queen triple compound piece. The latter I recently noticed is a piece type used in the patented 10x10 Big Battle commercial variant. No indication on the CVP page for Big Battle that that piece type is patented, nor is there anything about the QAD type being patented that I could easily find elsewhere on the internet. I know e.g. the Champion piece type (aka WAD) in (commercial) Omega Chess is used liberally in games found on this website alone. On the other hand, every aspect of e.g. Arimaa is patented/licensed (including the piece type names for that, if I recall correctly).

Draws
H. G. Muller wrote on 2018-11-16 UTC

In computer self-play without opening book Capablanca Chess has only about half the draw rate of orthodox Chess (about 16%, vs 32%). These are all games that start well within the draw margin, though. So as play approaches perfection, they should eventually get a 100% draw rate. A large body of opening theory can be viewed as an attempt to play perfectly at least for the first 20 moves, or so, reducing the game phase in which result-changing errors can occur accordingly.

James Zuercher wrote on 2018-11-16 UTC
Does FisherRandomChess (Chess960) produce fewer draws than regular Chess when opponents are about equal in strength? How about Capablanca Chess?

Crazy 38's: The Knight. Missing description
H. G. Muller wrote on 2018-11-15 UTC

Ah, OK, he uses 45-degree rotated coordinates.

In that case, that the example that shows a Knight can move from a8 to c6 indecates that the blue areas should merely be considered inaccessible squares, i.e. like they are occupied by an uncapturable obstacle that cannot be moved by either player. But as a Knight jumps, it will ignore such obstacles, and moves as if they were normal, unoccupied board squares.

Although it is obvious what orthogonal and diagonal means in this board topology ('through sides' or 'through corners'), it is not so obvious what 'outward' means. After all, a Knight cannot make just any move that consists of an orthogonal plus a diagonal step. One could use the generalization that the diagonal step must go through a corner of the cell that was not an end-point of the side through which it entered the cell; this would allow it to go straight ahead in a triangular cell. Another generalization would be that the diagonal step can only be made throug the corner(s) farthest away from the side through which it entered; for cells with 2less than 3 or more than 4 corners this would make a difference.

Ben Reiniger wrote on 2018-11-14 UTC

The board notation is available elsewhere in the game's pages:  notation page

I agree that the presentation is unclear in this case.  My impression is that the author just used a standard definition for knight, not recognizing the problem caused by the gaps (or assuming the diagram made it clear).

Four Towers. Irregular board with special tower squares upon which pieces can combine with each other or detach from each other. (Cells: 85)
Anthony Viens wrote on 2018-11-14 UTCBelowAverage ★★

I've got to comment on this....a crazy lot of ideas in this game.

I think they need to be refined, but I am attracted to the unusual.
This is definitly unusual!

Crazy 38's: The Knight. Missing description
H. G. Muller wrote on 2018-11-14 UTC

I have no clue what you are talking about. The image on the page on which you comment doesn't show any coordinates, so I have no idea what you mean by a8, c6, etc. You must be looking at a completely different picture.

Zillions of Games. Game package for Windows that allows you to play nearly any abstract board game or puzzle in the world.
Anthony Viens wrote on 2018-11-14 UTC

I tried a few weeks ago and could not.  :-(

I was really looking forward to playing a few against the computer, too.
That said, I've been having a great time with game courier!

Crazy 38's: The Knight. Missing description
Anthony Viens wrote on 2018-11-14 UTC

H.G. Miller, I'm sorry, I missed your response.

Here is my problem: the move is specifically defined as 'one square orthogonally, then one square diagonally outward.'

My assumption (possibly/apparently incorrect) is that spaces without notation are not squares, do not exist, and therefore cannot be used as part of any piece's movement.

The white knight is in a8.  The only spaces that appear to be orthogonally adjacent are a6 and c8.  Diagonally outward from those spaces yields only b5 and d7.

I don't see a path to c6......without counting the quarter-circle empty space within a8 as orthogonally adjacent to a8.  Diagonally outward from that empty space yields c6 as the destination.  But I wouldn't think the empty space would be used as part of the path, at least without directly mentioning it; such as 'the knight can leap over non-existent squares.'

(If the Knight's movement was defined as one space diagonally, then one space orthogonally outward, it makes sense.  The white knight starts in a8, diagonally moves to b6 or d7, and then moves orthogonally outward to one of b5, c6, or d7.  The white knight would actually have two routes to c6.  But the movement path of the knight is specifically defined as 1 orthogonally, then 1 diagonally outward.)

Basically, Ben Good went through the trouble of specifically defining the leaping knight's move (something I consider necessary to avoid questions on this crazy cool board) and then his example does not seem to match the defined move!

If there is a path I am missing, please show me.  But the only one I see is using the non-existant quarter circle within a8.