Comments/Ratings for a Single Item
Complementarity - Part I. With Short Range Project in mind, list of a highly specific set of pieces defined by simplest compounds.[All Comments] [Add Comment or Rating]
Joe Joyce wrote on Sat, Aug 25, 2007 01:36 AM UTC:Good ★★★★31 short-range pieces
I will briefly look at 31 possible 1-2 square short range pieces that are on a square board. Basically, here is an ASCII diagram of the five possible places where a given piece may or may not be allowed to move:3 2 1 2 3 2 5 4 5 2 1 4 . 4 1 2 5 4 5 2 3 2 1 2 31 is the Dababa; 2 is the Knight; 3 is the Alfil (Interesting fact: 'Alfil' is the Spanish word for what we call a Bishop); 4 is the wazir; and 5 is the ferz.
Here is a look at all 31 combinations of these possible moves, or, if you will, 'atom' pieces:
D N A W F 1 2 3 4 5 Name Colorbound N N N N Y Ferz 2-way N N N Y N Wazir No N N N Y Y Guard; Commoner No N N Y N N Alfil 8-way N N Y N Y Alfil-Ferz 2-way N N Y Y N Waffle; Phoenix No N N Y Y Y Guard + Alfil No N Y N N N Knight No N Y N N Y Knight + Ferz (Augmented knight) No N Y N Y N Knight + Wazir (Augmented knight); Vicar No N Y N Y Y Crowned Knight; Centaur No N Y Y N N Knight + Alfil (Augmented knight) No N Y Y N Y High Priestess No N Y Y Y N Alfil Knight Wazir No N Y Y Y Y Crowned Knight + Alfil No Y N N N N Dababa 4-way Y N N N Y Ferz + Dababa 2-way Y N N Y N Woody rook No Y N N Y Y Guard + Dababa No Y N Y N N Alibaba; Deacon 4-way Y N Y N Y Alibaba + Ferz 2-way Y N Y Y N Alibaba + Wazir No Y N Y Y Y Mastodon No Y Y N N N Knight + Dababa (Augmented knight) No Y Y N N Y Knight + Dababa + Ferz No Y Y N Y N Minister No Y Y N Y Y Minister + Ferz No Y Y Y N N Squirrel No Y Y Y N Y Squirrel + Ferz No Y Y Y Y N Squirrel + Wazir No Y Y Y Y Y Lion NoThe power of these pieces depends on the size of board we are using. The Alfil is clearly the weakest piece; probably worth less than a pawn. The Lion is clearly the most powerful piece; probably worth about two queens. Seven of the pieces are colorbound; an 8-way colorbound piece needs eight of the piece to cover the entire board, a 4-way colorbound piece four pieces to cover the board, and a 2-way colorbound piece needs two pieces to cover the board (such as the Bishop in FIDE chess). There is one 8-way colorbound piece (the Alfil), two 4-way colorbound pieces, and four 2-way colorbound pieces in our mix. The other 24 possible pieces are not colorbound.
The pinwheel piece
You may observe that the knight is a unique 'atom'; all other four 'atoms' can move four squares; the knight can move eight squares. One possible way to divide up the knight in to two 'subatomic' pieces is to make what I call 'pinwheel' pieces. There are two possible pinwheel pieces; the two pinwheel pieces combined make a knight. Here is a diagram of the 'left-handed pinwheel':. X . . . . . . . X . . * . . X . . . . . . . X .And the 'right-handed pinwheel':
. . . X . X . . . . . . * . . . . . . X . X . . .In other words, the 'left-handed pinwheel' can, from e4, go to d6, g5, f2, and c3. The 'right-handed pinwheel' can, from e4, go to f6, g3, d2, and c5.
Each 'pinwheel' piece is 5-way colorbound; you need 5 pinwheel pieces to cover every square on the board. However, its colorboundness is unusual and a pinwheel combined with any one of the other atoms (Ferz, Wazir, Dababa, Alfil, or even the other Pinwheel) becomes a non-colorbound piece.
Dividing up the knight in to the two pinwheels, we now have 64 possible short range pieces, 54 of which are not colorbound.
Other ways of dividing up the Knight
The pinwheel is a very unusual piece. It does not preserve left-right symmetry, which means it will not be as popular with chess variant inventors. The only widely known Chess Variant I know of with left-right asymmetrical pieces is Tori Shogi. However, it is far more common to have pieces that do not preserve forwards-backwards symmetry, including Chess' pawn, and Shogi's lance, silver and gold generals.There is one way of breaking up a knight in to two moves-to-4-squares atoms that preserves both left-right and forwards-backwards symmetry, and two ways to break up the knight in to 4-square atoms that only preserve left-right symmetry.
All three ways of breaking up a knight have already been discussed by Betza. To summarize:
Sub-knight atoms #1: Narrow and wide knights.
Narrow knight:
. X . X . . . . . . . . * . . . . . . . . X . X .Wide knight:
. . . . . X . . . X . . * . . X . . . X . . . . .Both of these pieces are 4-way colorbound.
Sub-knight atoms #2: Crab and Barc
Crab:
. X . X . . . . . . . . * . . X . . . X . . . . .Barc:
. . . . . X . . . X . . * . . . . . . . . X . X .Betza liked these sub-Knight atoms the most; they are unique in that, unlike other symmetrical sub-Knight atoms, they are not colorbound. He preferred the Crab over the Barc, since it encourages one to attack the other player.
Sub-knight atoms #3: Forward knight and Backwards knight
Forward knight:
. X . X . X . . . X . . * . . . . . . . . . . . .Backwards knight:
. . . . . . . . . . . . * . . X . . . X . X . X .These pieces are not very useful by themselves until combined with other atoms; the forward knight is probably the more useful atom to add to other pieces.
Joe Joyce wrote on Tue, Aug 28, 2007 12:44 AM UTC:Sam, that is very nice, and looks like a fairly exhaustive list of 1 and 2 square movers. Good job. Everyone seems to look at the knights in this context, because they are special pieces here, being the only inclusive compound piece in the group, rather than an 'atom', as are the other 4 pieces, and thus hit more squares. So the 8-square knights are broken into 2 4-square parts, more closely matching the other 'atoms'. What leaped to mind when I was looking at your backwards and forwards knight components was adding a dabbabah move in the opposite direction. Then I thought that adding east-west dabbabah moves to the narrow knight and north-south ones to the wide knight would be nice. And round it off with forward dabbabah jumps for the barc, and backward ones for the crab, making them sort of star-shaped pieces. I like the stuff you and Jeremy are doing enough to ask you if you'd be willing to move a copy of TSRP and your works to the CVwiki, and put together a revised and updated work where we could all get our fingers into the pie. You both have added to the original, and additionally, others who have or wish to do stuff can add original material or links to relevant material. The wiki is an ideal spot for this sort of thing. What do you say?
Adding the Sideways Dabbabah to the Narrow Knight will achieve nothing important. The piece will be able to triangulate, but that's all there is. It's still 4-way colorbound. However, adding the Forward and Backwards Dabbabah makes the piece 2-ways colorbound, but unable to triangulate. Betza used the Ferz+Forward Knight (Fibnif) with success in the CwDA. The piece is as powerful as the knight, even though it's slower while moving from one wing to the other.
Joe Joyce wrote on Tue, Aug 28, 2007 01:43 PM UTC:Adding the opposite-sense dabbabah moves to the wide and narrow knights does absolutely nothing for their range, the pieces still visit exactly and only their 'original' squares. What gets added is speed and attacking power. Each piece goes from attacking 4 to attacking 6 squares per turn, and the pieces may now move twice as fast in their original 'non-preferred' direction. I'd say that should increase the piece value roughly 75%. [And decrease their annoyance value about 50%.] This represents the unusual case where taking a piece with a specific move and adding another piece with a different move does not change the original movement pattern, but only augments the original piece's speed/power. Other examples are adding the alfil move to the bishop or dabbabah to the rook. Amazing how good you can make the rationalizations sound for doing something when the real reason you did it was that it looked 'prettier'. And finally, we need some better terms for 'colorbound'. [Only Jeremy and the guy that made Rainbow Chess actually color boards that way. ;-) ]
Take care,
- Sam
I have signed up on Wikidot and have just sent a request to be a part of the ChessVariants wiki. Can a member there approve me? (Cue 2002-era nightmares of wanting to be a part of LiveJournal, but couldn't because I didn't know anyone who was a member there. Today I have a MySapce account instead)
- Sam
Joe Joyce wrote on Tue, Aug 28, 2007 05:54 PM UTC:Sam, The ShortRange Project paper is now on the wiki, but isn't yet hooked into anything so here's the URL: http://chessvariants.wikidot.com/the-shortrange-project Happy to have you looking at this stuff. There is a very simple code to register that David Howe set up that I can't remember [might've been the date the wiki started???], and I can't find it in the comments. Can anybody help? David told us in a comment here, somewhere...
Just a comment on Sam's 31 short-range pieces comment: I noticed he mentioned the lion as worth 2 queens. Perhaps, on a very crowded small space, but I don't see how this can be on a large open board. In my game Asylum Chess, the piece Insane Ninja Knight has the moves of a lion (and double capture too).I say its worth slightly less than a queen in this game on an open board. I don't see any clear description of the lion except in Cho Shogi game (and they are some differences). (In fact, I initially thought that the ninja knight was never seen before in any form!) I have yet to see the Lion used in any other game. Perhaps, it is assumed that a jumping piece should not be too powerful or the gameplay would not be balanced?
Sam. Another way to split the knight is left/right. Seems a better piece than a backward knight and is a great piece ih a game where pieces can begin in the middle of the board. 'Right Knight' ...X. ....X ..K.. ....X ...X. 'Left Knight' .X... X.... ..K.. X.... .X...
An example, posted by you. http://www.chessvariants.org/index/listcomments.php?subjectid=Super+Chess+1993
I changed the itemid for this page from MPcomplementarit to MScomplementarit, since the MP prefix is for Game Courier presets.
A while ago, I looked at 31 possible short range pieces. I have now expanded this research.
I have written a small C program which looks at all 16,777,215 possible leapers that move at most two squares. Some findings:
- I expected around half of all possible pieces to be colorbound in some way. Wrong. 16,452,080 (over 98%) pieces are not colorbound.
- There are 104 non-colorbound pieces with three moves, 2,512 pieces with four moves, and some 2,696,337 pieces with 12 moves.
- Only 2,944 possible pieces are Bishop colorbound: These relatively few pieces can go to the same 32 squares a Bishop can go to.
With some 16,452,080 non-colorbound pieces, if we replace the knight, bishop, and queen with a random non-colorbound short leaper, that gives us 4,453,099,898,116,838,912,000 which is, what, 4 hextillion possible variants, and that’s keeping the king, pawns, and rook.
OK, if that’s not enough possible variants, we can also add the ability for a given random piece to be able to be a rider in any direction it can leap (e.g. a fers-rider is our bishop; a wazir-rider is a rook, and a knight-rider is, well, a knightrider), where we randomly choose, from all the moves a given leaper has, for it to be able to ride in a random number of directions. For example, if we look at the wazir, then randomly choose which directions it moves like a rook and which directions it can only move one square, we get 16 possible pieces. If we do this for all 16,452,080 non-colorbound short range pieces, we get some 282,232,643,280 possible pieces, just over 2 to the power of 38 (2^38 or 2 ** 38 in Python notation).
This means an 8x8 board with random non-colorbound pieces and using a standard chess set has some 6,344,961,231,517,063,209,074,884,200,517,463,972,290,560,000 possible variants (the pawns and kings can keep their moves), just over 2 to the power of 152.
16 comments displayed
Permalink to the exact comments currently displayed.