Comments by Robert Price

The game Edge Chess, by Mitch Martin, might be added to this discussion. In that game, a piece that can move to a (single) square is also allowed to 'expand' and occupy surrounding spaces as well. In this way, any piece on any move can become what appears to be a twofold or fourfold piece. An enlarged piece is vulnerable (since it can be captured on any of the squares it occupies) and maneuverable, having the ability to use any of its occupied squares as a departure space. Effectively, the piece shrinks to normal size, then moves, then has the option of expanding again, which is an alternative behavior to the two- and fourfold pieces described in this article. As a result of the size-shifting, Bishops are not colorbound, and Pawns can move unusually quickly across the board by always expanding into the next square forward.

Also, the large variant Microorganism Chess by Mark E Hedden and Bryan Weaver contains an Amoeba piece (of which each player has two). To quote:

They move either as a bishop or jump 3 spaces like a rook. But, it has one unique characteristic. It can expand from being a piece that takes up 1 square to a piece that takes up two squares orthoganally next to each other. However, both of these squares must be empty in order for it to be able to expand. Once expanded, it can take two pieces in the same turn, and generally be very dangerous. Also, it can, once expanded, contract back to its original size.

I presume that the entire width-two path of the expanded Amoeba has to be unoccupied when it wants to move as a bishop. So, the Amoeba in its expanded form is an example of a true twofold piece.

Right, the 'illegal move' consists of picking up one of your pieces and moving it to any empty space, or using it to capture any enemey piece other than the King. All that extra verbage is just to prevent you from inventing a move that has the convenient side effect of slaying multiple enemy pieces (like the atomic bomb from Tank Chess, for example). <p> Anyway, it just occurred to me today what I found interesting about this variant when I wrote it up a year ago. The <a href=http://www.fide.com/official/handbook.asp>FIDE Handbook</a>, as a document that regulates tournament play, has a twofold job. First, it must describe the rules of the abstract game Chess with mathematical precision, so that for any board position that can possibly occur, it is unambiguously known what moves are available to the player. Secondly, it has to provide <i>procedures</i> to resolve disputes of a more 'human' and imprecise nature. <p> In particular, the handbook needs to say what to do if a piece is physically moved in a way that is not 'possible' in the abstract game (and is detected before the end of the game is declared). What I suddenly realized is that Cheapmate Chess came from modifying one of those <i>procedural</i> rules, and leaving all the abstract rules of Chess alone. In a perfect world, the procedures of chess playing would be completely separate from the abstract game. But it seems that this is a case in which they are inextricably related. No matter how precisely the rules are defined, the problem of <i>enforcing</i> them is still an imperfect matter of procedure. When I removed that last part of article 5.1a of <a href=http://www.fide.com/official/handbook.asp?level=EE101>Laws of Chess</a>, the problem of enforcement spilled into and altered the abstract game.

That's a great idea. I've seen the <a href=http://www.chessvariants.com/multiplayer.dir/4players.html>Four-Handed Chess Variants</a> on plus-shaped boards criticized for their wide-open spaces and slow action (the Cincinnati 4-way article makes this criticism, for example). But, as the setting for an epic tale, the vastness and slow opening would be part of the charm. <p> I would consider Dessau (described in the Four-Handed Chess article) first. It has a plus-shaped board consisting of an 8x8 center to which four 3x8 rectangles have been appended, with the familiar Chess armies standing on the first two rows. The Ring would have to behave a little differently, since White needs to carry it sideways instead of forward. Instead of granting White the power to move one space straght or diagonally forward, it could be one space straight or diagonally toward Mordor. <p> I don't think I like how some of White's pawns are so much closer to the final goal than others. Maybe the Ring can only be destroyed on the far half of Mordor's back rank. <p> If I had more friends, I'd try it out. Thanks for the insight.

I would love to help in coding Nemoroth in Zillions, just as soon as I can convince myself that it's possible at all. <p> As I understand it, piece <i>attributes</i> can not change the <i>appearance</i> of a piece, so a petrified Basilisk, for example, must be implemented as a different piece-<i>type</i> from an ordinary Basilisk (if you want them to look different), even though their non-voluntary behaviors are identical. <p> A far greater concern is multiple-occupancy. The usual approach is to declare a piece-type for every <i>combination</i> of pieces that may coexist on a space. Add to that the need to distinguish between petrified and fleshy, friendly and enemy (because such strange bedfellows may indeed come to share a space). And realize that pile-ups of more than two may easily arise... All of a sudden, Octi's library of 256 piece-types (<a href='http://www.zillions-of-games.com/games/octi.html'>http://www.zillions-of-games.com/games/octi.html</a>) is looking downright trivial by comparison. <p> From the game-logic standpoint, I intend to investigate the possibility of treating each of the 64 spaces similarly to a <i>prison</i> in the ZRF for Shogi. From the graphical standpoint, we can't afford simply to divide each square into a 3x3 grid of positions as I did for <a href='http://www.zillions-of-games.com/games/edgechess.html'>Edge Chess</a>, or people will need a magnifying glass to see the great graphics someone's going to make for the pieces. Instead, the cells of my prison will overlap, and with a well-defined order of precedence. I learned from <a href='http://www.zillions-of-games.com/games/platformchess.html'>Platform Chess</a> that the later-defined space will have its contents drawn before a sooner-defined space. This works perfectly. The front cell of the prison will dominate most of each space, with four more behind it kind of peeking in from the corners. Clicking-and-dragging a piece from the prison works as expected; if you grab a pixel that belongs to two spaces, Zillions assumes you mean the one it drew out in front. So if you want to move your Human that someone's gone and pushed a Basilisk statue onto, you can click on the visible portion of his puny form and command him, exactly as if two pieces really were present on the same space at the same time. <P> <b>Anyway,</b> multiple occupancy is what struck me as the big difficulty. Besides that, the non-simultaneous nature of the Go Away shout may not be pretty. One solution is to present a big pop-up menu consisting of all possible orders in which to push the victims (or only those which are substantially different due to the presence of basilisks). I would hate to have to use one move per push, because that's the sort of thing that weakens the computer opponent. <p> The evaporation of ichor is something that will just have to be managed by a ?Moderator who is programmed to scan the board and decrement all the ichor-plies by one. This raises another point... in order for ichor to be visible, it has to be a piece-type. I could do that by making a position behind each prison, where the ichor would sit. If the graphics designer wants to make ten different pictures of ichor, that's great, because each ply of ichor is going to be a different piece-type, and when the board is covered in broad sweeps of the stuff, the players are entitled to know which ichor is ickier. <p> Compulsion is tough to describe - it's slightly more complicated than the move-priority construct which in Checkers requires you to jump if able. But it is definitely doable. A piece is never compelled to make any <i>particular</i> move, only to make a <i>legal</i> one, provided the 'legal' constraint handles the details like preventing a piece within 2 of a Ghast from moving-without-fleeing. (note the beauty in Nemoroth on this point: The same *legality* constraint appies whether the Ghast is friendly or enemy; the only difference is that a piece within range of an <i>enemy</i> Ghast is compelled during its move generation.) Imposing move-priority and also (somehow) verifying that either a compelled piece was moved, or no compelled piece remains (after the immediate effects of the move have happened) comes very close to fitting the bill. <p> This sounds like an extraordinary game, and it certainly was presented in a marvelous way.

Since a properly-functioning SIR unit is colorbound, I am guessing that the author intends that a SIR unit is 'Berzerk' if and only if there is no friendly Invader (bishop) on the board occupying the same color of square. If this is the intention of the rule, then phrasing it this way handles situations that can arise after promotions.

I can think of three ways to restore a Berzerk SIR unit to normal operation:

1. You move your Berzerk SIR unit moves to a square of the opposite color, and under the command of your remaining Invader
2. You promote an Irken Soldier to Invader on a same-colored square
3. You are playing Invader Zim Bughouse (!) and you drop an Invader onto a same-colored square

I had the same question of whose king goes on the left or right, and I was about to suggest an alternative: The author calls for you to push two half-boards together by rotating one into place above the other. I was about to suggest reflecting it into place (and inverting the checkered coloring) instead; now you can let everyone's king start on the e-file but the two-player case is still just like FIDE chess.

Joining by reflecting is not so contrived. Imagine constructing the half-boards out of stiff cardstock or plastic, checkered on both sides so that the bottom-right square from each perspective is light. Use magnetic chess pieces in pairs so that they attract each other through the material. Bind several of these half-boards together with loops of string along the joining edge in an arrangement just like the illustration that opens the article. Now you join half-boards by flipping to two pages and ignoring whatever happens to lie in between.

But I said I was 'about to suggest'. That's because this arrangement causes the act of moving a bishop from the Green half-board to Orange, and then later to Blue, and then back to Green, to have the consequence of changing the Bishop's colorbinding because it has effectively been reflected an odd number of times. I still like the idea somewhat, but I think it is more important to have colorbound bishops than a symmetrical royalty-seating arrangement.