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Joe Joyce wrote on Mon, Apr 12, 2010 03:33 AM UTC:

Charles, I spent some time putting your game into a format I could not only understand, but 'see'. I have a highly visual imagination and a complete inability to remember names. By the time I was halfway through, I could see you have effectively moved the ShortRange Project into the third dimension. 

This is your initial setup, copied from the rules:

 --------- --------- --------- ---------
|a Baron  |b Dybbuk |c Duke   |d Elk    |
 --------- --------- --------- ---------
|e Alibaba|f Vinnock|g Emperor|h Prince |
 --------- --------- --------- ---------
|i Prince |j Wazbaba|k Fearful|l Alibaba|
 --------- --------- --------- ---------
|m Elk    |n Duke   |o Dybbuk |p Baron  |
 --------- --------- --------- ---------

The 6 Atoms:

[W] WAZIR moves one step along any of the 6 orthogonals
[F] FERZ moves one step along any of the 12 standard (root-2) diagonals
[D] DABBABA moves exactly two steps along any of the 6 orthogonal.
[A] ELEPHANT moves exactly two steps along any of the 12 standard (root-2) diagonals.

[F'] VICEROY moves one step along any of the 8 nonstandard (root-3) diagonals, commonly called triagonals. Its name refers to its attachment to a King forming an Emperor.

[A'] EUNUCH moves exactly two steps along any of the 8 nonstandard (root-3) diagonals

Discussion: Extending Betza notation. The Viceroy is clearly a '3D only' ferz, just as the ferz in this game is a standard 2D only ferz. By using 'Ferz prime' and 'Alfil prime' to denote these 3D only pieces, we simplify things considerably. (A 4D only ferz would then be F'', a ferz double prime. And with the asterisk, we could have a fully N-dimensional ferz as F*, and a ferz that was 3D and higher only, not 2D, would be F*', etc.) And it's a very simple and natural notation for CVers. Others may vary, but I find it very descriptive.

If I'm looking at this right, the Viceroy is not merely colorbound, but also rank-bound, visiting only 1 in 4 cells on the board. The Eunuch is colorbound, rankbound, and filebound, and given the particular geometry of this board, can only access 3 cells by itself. 

The starting, small compounds (note the emperor is unique and isolate):

[FF'] BARON, compound of Ferz and Viceroy, can be combined only with the Elk
[DA'] DYBBUK, compound of Dabbaba and Eunuch, can be combined only with the Duke
[WF'] DUKE, compound of Wazir and Viceroy, can be combined only with the Dybbuk
[AA'] ELK, compound of Elephant and Eunuch, can be combined only with the Baron
[AD]  ALIBABA, compound of Dabbaba and Elephant, can be combined only with the Prince 
[A'F'] VINNOCK, compound of Viceroy amd Eunuch, can be combined with the Wazbaba or the Fearful 
[KF'] EMPEROR can move one step along any of all 26 radials compound of the FIDE King  and the Viceroy. It cannot be combined with other pieces. The royal piece.
[FW] PRINCE, compound of Wazir and Ferz, can be combined only with the Alibaba
[DW] WAZBABA, compound of Wazir and Dabbaba, can be combined with the Fearful or the Vinnock
[AF] FEARFUL, compound of Ferz and Elephant, can be combined with the Wazbaba or the Vinnock

The 3 large compounds, and their breakdown pairs of small compounds:

[ADFW] PASHA, compound of Wazir/Ferz/Dabbaba/Elephant, can be split into: 
  [FW]+[AD] Prince and Alibaba, OR  
  [DW]+[AF] Wazbaba and Fearful, OR 
  [AW]+[DF] Waffle and Fezbaba

[DWA'F'] KHAN, compound of Wazir/Viceroy/Dabbaba/Eunuch, can be split into:
  [WF']+[DA'] Duke and Dybbuk, OR  
  [DW]+[A'F'] Wazbaba and Vinnock, OR
  [WA']+[DF'] Wazzock and Vicbaba

[AFA'F'] IMAM, compound of Ferz/Viceroy/Elephant/Eunuch, can be split into:
  [FF']+[AA'] Baron and Elk, OR  
  [AF]+[A'F'] Fearful and Vinnock, OR
  [FA']+[AF'] Fezzock and Wilful 

Non-starting breakdown compounds:

[AW]  WAFFLE, compound of Wazir and Elephant, can be combined only with the Fezbaba
[WA'] WAZZOCK, compound of Wazir and Eunuch, can be combined only with the Vicbaba
[DF]  FEZBABA, compound of Ferz and Dabbaba, can be combined only with the Waffle
[FA'] FEZZOCK, compound of Ferz and Eunuch, can be combined only with the Wilful
[DF'] VICBABA, compound of Viceroy and Dabbaba, can be combined only with the Wazzock
[AF'] WILFUL, compound of Viceroy and Elephant, can be combined only with  the Fezzock

Discussion: A quick count shows 19 different pieces available in the game. My first thought was that this was just going to lead to mass confusion, with players being unable to keep track of how any of the pieces moved. Once I had the notation figured out and listed for each piece, however, the situation seemed far less chaotic, and the game now seems a good bit more playable, certainly worth looking at a bit closer. 

The original starting setup in modified Betza notation:

 --------- --------- --------- ---------
|a [FF']  |b [DA']  |c [WF']  |d [AA']  |
 --------- --------- --------- ---------
|e [AD]   |f [A'F'] |g [KF']  |h [FW]   |
 --------- --------- --------- ---------
|i [FW]   |j [DW]   |k [AF]   |l [AD]   |
 --------- --------- --------- ---------
|m [AA']  |n [WF']  |o [DA']  |p [FF']  |
 --------- --------- --------- ---------

Discussion: Comparison of the initial setup with the allowed combinations seems to reveal a minor error in the setup. The Baron [FF'] and the Elk [AA'] can never get together to form their one allowable compound, the Imam, if I'm figuring the moves properly. A lot of the initial compounds are extremely limited in what they can reach. The Alibaba [AD] can reach 12 cells, 4 on each of 3 levels, as can the Dybbuk [DA']. It's the Wazir-containing compounds that have the mobility in this game, and they don't combine with everyone. I will take the easy way out, and suggest a slightly modified setup, rather than figure out what other compounds you could use here to keep this setup and make it fully useful. Switch the Barons with the Alibabas.

Suggested possible starting setup:

 --------- --------- --------- ---------
|a [AD]   |b [DA']  |c [WF']  |d [AA']  |
 --------- --------- --------- ---------
|e [FF']  |f [A'F'] |g [KF']  |h [FW]   |
 --------- --------- --------- ---------
|i [FW]   |j [DW]   |k [AF]   |l [FF']  |
 --------- --------- --------- ---------
|m [AA']  |n [WF']  |o [DA']  |p [AD]   |
 --------- --------- --------- ---------

I hope that others find this analysis and the proposed notation useful. 

Charles, would you consider allowing an updated version of this to go into the active [well, active sometimes] ShortRange Project in the CVwiki as the beginnings of the 3D project?

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Comments

Redistribution 3d Chess. Relatively small 3d variant with short-range pieces including Pasha family. (4x(4x6), Cells: 96)

💡📝Charles Gilman wrote on Sat, Jun 12, 2010 06:21 AM UTC:

The array looks correct now. The place I was talking about non-array pieces being missing was beneath 'Available Pieces - This table shows you what pieces belong to the piece set you are using.' I wasn't suggesting showing them on any kind of artificial extension to the board - although during play they would of course appear on the board itself through fusion and fisson. I hope that this clarifies things further.

Joe Joyce wrote on Fri, Jun 11, 2010 04:55 AM UTC:

/play/pbm/play.php?game%3DRedistribution3d%26settings%3DR3d2

I still need to do the chart of pieces and how they work. I might just put the combo and breakdown pieces on the side of the preset, in islands of board, as both visual reference and icon code for the pieces.

💡📝Charles Gilman wrote on Thu, Jun 10, 2010 05:47 PM UTC:

Here are the four symmetries. Note that kv and KV are the Emperors.

1: The way I wrote the rules page was with mirror symmetry:

fv de wv ae | da ve kv wf | wf wd fa da | ae wv de fv
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
FV DE WV AE | DA VE KV WF | WF WD FA DA | AE WV DE FV

2: Here is vertical-axis rotational symmetry:

ae wv de fv | wf kv ve da | da fa wd wf | fv de wv ae
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
FV DE WV AE | DA VE KV WF | WF WD FA DA | AE WV DE FV

3: Here is horizontal-axis rotational symmetry:

ae wv de fv | wf wd fa da | da ve kv wf | fv de wv ae
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
FV DE WV AE | DA VE KV WF | WF WD FA DA | AE WV DE FV

4: Here is rotated mirror symmetry:

fv de wv ae | da fa wd wf | wf kv ve da | ae wv de fv
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
-- -- -- -- | -- -- -- -- | -- -- -- -- | -- -- -- --
FV DE WV AE | DA VE KV WF | WF WD FA DA | AE WV DE FV

💡📝Charles Gilman wrote on Wed, Jun 9, 2010 06:09 PM UTC:

On the plus side the cells are now arranged the way that I anticipated, and the White pieces are correct. As I wrote it, however, all Black pieces should match the White one on the same rank, not just the Alibabas and Princes. A rotationally symmetric version might be interesting as well, but the Black pieces aren't set up for that either. There are four possible symmetries, which I could outline when I've had time offline to write them all up. Finally, the off-board list of possible pieces should include non-array as well as array pieces.

Joe Joyce wrote on Wed, Jun 9, 2010 05:34 PM UTC:

Charles, is this preset closer to what you want?

/play/pbm/play.php?game%3DRedistribution3d%26settings%3DR3d2

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