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Redistribution 3d Chess. Relatively small 3d variant with short-range pieces including Pasha family. (4x(4x6), Cells: 96) [All Comments] [Add Comment or Rating]
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?

Joe Joyce wrote on Wed, Apr 14, 2010 01:26 AM UTC:
Does this mean no? ;-)

💡📝Charles Gilman wrote on Wed, Apr 14, 2010 06:27 AM UTC:
Give me a chance to answer already! As it happens I've been offline analysing your analysis:

'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.' It is not rank-bound but rank- (and filestack- and level-) switching. It always moves from an odd to an even plane or vice versa in all three dimensions. Nor is it colourbound in the same way as the Ferz. It is in fact bound to one quarter of each Ferz binding, rather than half of just one. A Dabbaba binding (on a cubic board) is the intersection of a Ferz and a Viceroy one.

'The Eunuch is colorbound, rankbound, and filebound, and given the particular geometry of this board, can only access 3 cells by itself.' True, but as the rules specify, it can never actually be by itself in this game.

'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.' You're not, as the Baron, uniquely among two-component non-Wazir compounds, is unbound due to the Ferz and Viceroy bindings being independent. A Baron can reach an Elk square in two Ferz moves and a Viceroy one, without even interacting with another piece en route, e.g. a1-e2-j2-m1. Given that, are you now happy with the original array, or is your mind too blown to decide yet?

This all suggests that thinking of the Ferz, Viceroy, and Baron as variants of the same piece is not that helpful. Likewise for oblique directions the colourswitching 2:1:0 leaper, the 2d Knight, is a very different piece from a combined 2:1:1 and 2:2:1 leaper, let alone the compound of all three.


Joe Joyce wrote on Mon, Apr 19, 2010 02:24 AM UTC:
Lol, I'm certainly not the one to be serious about others taking a day or two to respond - look how long this took! Charles, it took me 2 days to come up with that slightly flawed analysis. Grin. Obviously I should have run it at least 3 days - I only looked 2 moves out. Would've helped if I'd used an actual board and pieces. Realized the Viceroy changed colors, but didn't adequately follow up, or I should have realized a third move would give the combination. [Moral of the story: don't try complex visualizations when you're sleepy, and always re-check the next day. Too bad I'm better at giving advice than following it.]

So you think my analysis is too reductionist [in using A' and F']? If it causes others to make the same mistake I made, I'll agree with you. But for now, I think it was just mental sloppiness. If the piece move is diagrammed, you won't have someone like me pointing into empty air with both hands while calculating which imaginary cells the piece can or can't move to. I was thinking on the odd levels that it's one color, and on the even, the other. Full descriptions of piece movement and movement potential should prevent others from falling into my error.

But it's easy enough to replace the F' with V and the A' with E. It's just that I think my version carries visual directional information [certainly it does for me] that isn't apparent using V and E. It's easier for me, at least. [And it saves letters, something I like.] Compare:

 [DWAF]  PASHA,  [DWAF]
  [FW]+[AD]     [FW]+[AD]
  [DW]+[AF]     [DW]+[AF] 
  [AW]+[DF]     [AW]+[DF] 

[DWA'F']  KHAN,  [DWEV]
  [WF']+[DA']   [WV]+[DE] 
  [DW]+[A'F']   [DW]+[EV] 
  [WA']+[DF']   [WE]+[DV] 

[AFA'F']  IMAM,  [AFEV]
  [FF']+[AA']   [FV]+[AE] 
  [AF]+[A'F']   [AF]+[EV] 
  [FA']+[AF']   [FE]+[AV]

One thing I do not do is think of the Baron as a variant of either the ferz or the viceroy; I've played enough compound pieces to know better. 

As for the setups, I still think mine is more immediately dynamic. If a piece on this board has to spend an extra turn or two to combine into pieces that are then left on the back rank, good development by the opponent should beat that tactic. However, if the pieces, as they move toward contact, can join on the way, in a good location on the very small board, then that would be even better, most likely. The only way to see how it goes is to try it out with a board and pieces. Game Courier has a large range of pieces. Do you have any preferences for a preset for R3D? The 2 setups should be played against each other, as well as against themselves.

Following is me quoting you quoting me... ? Anyhow, goes like this:
''The Eunuch is colorbound, rankbound, and filebound, and given the particular geometry of this board, can only access 3 cells by itself.' True, but as the rules specify, it can never actually be by itself in this game. '
So the eunuch only adds a couple moves to the piece it's part of, but gives it the potential to jump to a [somewhat] different area of the board. This adds to the 'chaos potential' of the game, but to a limited extent given the max move is 2. And given the tiny size of the 3D board, with only a 4x4 cross-section, the jump moves of the elephant and viceroy may provide needed maneuverability. 

I've been comparing and contrasting our pair of 3D games while trying to put this reply together. The similarities are strong; thus the differences should be instructive. The differences include: simple vs complex pieces, pawns vs no pawns, and a tight board vs a looser one - a lot of little questions for the theory boys to play around with. But what are the odds anyone will play either of these games?

💡📝Charles Gilman wrote on Mon, Apr 19, 2010 06:09 PM UTC:
I still prefer my original array, as there is a method behind it, and will gladly give authorisation for an implementation based on this.

As for your notation, why not go the whole hog and start from the orthogonal with Ferz as W', Viceroy as W'', Elephant as D', Eunuch as D'', and so on?

Joe Joyce wrote on Tue, Apr 20, 2010 08:44 PM UTC:
Okay, I'll put a preset together. Do you have any preferred piece icons, or shall I just do it, then we can discuss possible substitutions? [If we play our cards right, we just might suck someone in to playtest our 2 games in a compare and contrast mode, which might be some kind of record for this site. Have we ever had 2 higher-D games looked at together this way?] 

As for the notation, be careful! You've got me thinking... Seriously, the simpler the notation you can describe things in, the deeper the understanding you might get. [There's a branch of math where you start with 0, then the next number is the successor to zero: S0, and the next is the successor to the successor..., so that 3 is written SSS0.] As you might have imagined, I'll be happy to discuss notation with you, too. The problem with using an 'orthogonal prime' as a 'diagonal' in your game is that 'orthogonal prime' is not appropriate for that, in your game. W' is most logically a 3D wazir, not a 2D ferz. The way your pieces work, you want, for ease of handling, a way to look at 2D and 3D components of both orthogonal and diagonal moves. My notation is a compromise between your simple and unambiguous but directionless notation and something that only a math major could love.  

Now, in 3D Great Shatranj, the W' and D' notation are far more useful, because my 3D elephants are just 3D warmachines rotated in 2 of 3 dimensions, and have 'exactly' the same moves otherwise. Weak analogies to particle physics are noted, as the rotation of the 3D wazir splits it into 3 3D elephants, breaking symmetry... and now I gotta run. Enjoy.

💡📝Charles Gilman wrote on Thu, Apr 22, 2010 05:49 PM UTC:
Feel free to go ahead. If you can find images that echo the components - or at least 2d-compatible ones - of the pieces in some way.

Joe Joyce wrote on Fri, Apr 23, 2010 02:25 AM UTC:
Okay, I've started: http://play.chessvariants.org/pbm/play.php?game%3DRedistribution+3d+chess%26settings%3DRed3d
Some pieces are easy, if you accept the 2D version. Others are going to likely be a little strange. [We need a piece artist onsite.] Figure I'll go with some of the crown-like and odd bishop-type icons for what I haven't got, except for the Elk, which apparently is going to a a sort of mooselike pawn. And the Dybbuk is likely to be a hydra or griffin or somesuch.

💡📝Charles Gilman wrote on Sun, Apr 25, 2010 06:41 AM UTC:
Regarding piece images, so far so good. I look forward to seeing the rest. Having a list of all possible images below is a bit confusing. One problem is that you appear to have letterd the ranks. I could understand files being relabelled aa-dd or ea-hd or wa-zd, but the convention of numbering ranks and ranks alone is one that I have tried to observe in all my face-to-face 2-player cubic variants.

Joe Joyce wrote on Sun, Apr 25, 2010 09:47 PM UTC:
Okay, Charles, step 1 is done, tentatively. I wanted a dabbaba with a black crescent moon on its side for the DA'/DE. No joy, so I went with some sorta bishopy type pieces to complete the basic setup. Those 3 pieces, the MI, PA, & 1M, I originally thought I might save for the remaining pieces in the game, and I may need them for those other pieces yet. 

The massive piece listing is Alfaerie: Many, and that is what I am looking through to find the game pieces. When I've found them, I'll drop all the unused ones. Fergus has provided a nice little check-box for that purpose. And I changed the letters and numbers. If you see anything you like in the list, let me know. 

Now I have to come up with the 3 combo pieces, and the 6 remaining breakdown pieces. I'll put those icons in the middle of the preset, and have them  removed when the game starts.  http://play.chessvariants.org/pbm/play.php?game%3DRedistribution+3d+chess%26settings%3DRed3d

💡📝Charles Gilman wrote on Tue, Apr 27, 2010 06:17 PM UTC:
Right, so that redistributing of letters and numbers seems not to have worked. How about going back to letters across the bottom and numbers down the side, but show each level as a block rather than each rank. That would also make the whole display more balanced and lessen the need to scroll (eliminate altogether for a really big screen), as it would be 6 rows by 4 lots of 4 columns rather than 4 rows by 6 lots of 4 columns.

💡📝Charles Gilman wrote on Wed, May 26, 2010 06:31 AM UTC:
Joe, have you given up on the implementation or are you just very busy with other things? It would be nice to know whether it's still a possibility.

Joe Joyce wrote on Wed, May 26, 2010 08:27 PM UTC:
Charles, my apologies. I have been quite tied up with various things, and have not had the mental energy to try to push past the current block with the preset, which is that I have 3 pieces where I need 6. Part of the answer might lie with the Duke and Elk. There is an unadorned crown in the piece set called 'Duke' [I first saw it in Rennchess], which is appropriate, and there is also a pawn with antlers that could double for the Elk. The remaining problems are that I'm still short 1 piece, and our elk will look suspiciously like a pawn with moose antlers. 

As for the slowness, several family health issues have flared up in the past months which often eat up all my free time. I am hoping they will resolve soon, but I'm not expecting it. Thus my lack of obvious presence onsite. It is not from lack of desire.

Joe Joyce wrote on Fri, May 28, 2010 08:07 PM UTC:
Hey, Charles, these seem to be our choices. Do you have any preferences? http://play.chessvariants.org/pbm/play.php?game%3DRedistribution+3d+chess%26settings%3DRed3d
The Duke is the trapezoidal crown by the all too obvious this-is-not-really-an-Elk piece.

💡📝Charles Gilman wrote on Sun, May 30, 2010 06:50 AM UTC:
Now I'm confused. I understood that the array pieces - including the Duke and Elk - were the ones displayed on the end ranks. Are you using different images for array and non-array Dukes, Elks, et cetera? If you are, I see no reason to do so.

Any news on whether you're taking up my idea to arrange the cells in the form

.... .... .... ....
.... .... .... ....
.... .... .... ....
.... .... .... ....
.... .... .... ....
.... .... .... ....

instead of 

.... .... .... .... .... ....
.... .... .... .... .... ....
.... .... .... .... .... ....
.... .... .... .... .... ....

to get the ranks as numbers and files as either letters or pairs of letters and reduce the need to scroll?

Joe Joyce wrote on Sun, May 30, 2010 01:54 PM UTC:
Hey, Charles. The Duke and Elk are now as shown in the set-up on the 2 end boards [labeled 'an' and 'fn'], but we are short 6 pieces for the breakdown products of your combo pieces. I was theming the pieces as best I could, sharp angles being ferz-type pieces, crescent moons being the trigonal 2-space leapers, that sort of thing. But that's busted with the last 6 pieces. I can replace the current Duke and Elk with the crown and moose pawn, but that just offends my sense of aesthetics so much I'd want to bring the squirrel in, so we could have a moose and squirrel combo, and then maybe a Boris and Na...ahh, well, I may just look for the 6 least-offensive pieces and stick them in. Might swap the Duke pieces, so I could free up the one currently used for one of the 6, if it looks better that way. Any suggestions you may have, from ditch the moose to having a specific Boris piece to use, I will take at this point. If something becomes too annoying, it can be changed. 

Alright, I see what you mean now by the board configuration. You want me to cut the board the same way, but spread it out north to south [up and down on the screen] instead of east to west [right to left]. Is this correct? The reason I did it across is to get the biggest possible board on the screen, and there's more room side to side. The pieces are kinda small now, and if I shrink the board any more, I, if no one else, will have problems distinguishing them. What I can do is turn your whole array sideways, like I did for 3D Great Shatranj. It looked and felt ugly to me in the raumschach-type configuration. 
http://play.chessvariants.org/pbm/play.php?game%3D3D+Great+Shatranj%26settings%3D3D+GtS+1
http://play.chessvariants.org/pbm/play.php?game%3D3D+Sideways+Great+Shatranj%26settings%3D3D+SGtS+1

Please give me the specific alphanumerics you want for your up and down layout, and I will rotate them also, so that if you turn your monitor on its side, the gameboard will be laid out and numbered the way you want. To lay out the board up and down and have it fit on one screen, I'd have to shrink everything around 20%. It's doable, should you wish.

Joe Joyce wrote on Sun, May 30, 2010 04:20 PM UTC:
A couple quick comments. First, I just expanded both 3D shatranj boards to give the largest possible size on my screen. I'd originally had the 'scale' setting at 49, but kicked it up to 65. If that takes the board off the side of your screen, you should be able to reduce the scale back toward 49, or whatever size fits your screen. But now, I'd have to reduce the size of the boards 40% anyway, to stack them top to bottom on one screen. [No, I don't have a Mac with a rotatable screen.]

Second, I'm curious about something. The 2 3DGtS presets are exactly equivalent, but I believe that people would play them a little differently, that they would sometimes make different moves from the same starting positions, because the boards look different. It seems to me that this is one way computers and people would have to be different; a computer's 'thinking' is not channeled by appearances [only by algorithms].

💡📝Charles Gilman wrote on Mon, May 31, 2010 06:07 AM UTC:
'You want me to cut the board the same way, but spread it out north to south [up and down on the screen] instead of east to west [right to left]. Is this correct?'
No, if you look at the diagram you will see that it is still spread out in the same direction, but each block is a level rather than a rank. The numbers will thereby exclusively represent ranks.
'It looked and felt ugly to me in the raumschach-type configuration.'
As Raumschach has a 5x5x5 board, this could serve as an illustration of the effect of my suggestion on scrolling. For a Raumschach board it would make no difference. For a Redistribution board 6 blocks 4 high and 4 wide are replaced by 4 blocks 6 high and 4 wide. Does this clarify things?

💡📝Charles Gilman wrote on Wed, Jun 2, 2010 06:26 AM UTC:
Regarding images for piecs, on the whole I think that the component-based images as currently shown on their starting spaces work best. For example, stick with the elephant marked witha crescent for Elephant+Eunuch and no need for the antlered Pawn image. Short-range as the pieces are, none of them are really Pawn-like. A Rocky & Bullwinkle theme to the images doesn't grab me, as my comment on the Squirrel piece demonstrates my lack of familiarity with that series. If you tell me which six pieces you're struggling with I'll have a look and see if any image strikes me as especially suiting it.

Joe Joyce wrote on Thu, Jun 3, 2010 03:00 PM UTC:
Okay, I think I get the board config. It will have 4 white pieces across the bottom and 4 black pieces across the top of each 4x6 rectangle. You want the board cut perpendicularly to the way I did it. [I gotta be closer, at least, with this one...]

As for the pieces, much as I loved Rocky and Bullwinkle, I agree they don't belong in this game. I will use the pieces we have available, but they will not fit the patterns established by the other pieces.

With luck, I'll be able to put this together over the weekend.

💡📝Charles Gilman wrote on Thu, Jun 3, 2010 05:55 PM UTC:
Yes, that's correct.

George Duke wrote on Fri, Jun 4, 2010 04:11 PM UTC:
Which CV or two of Gilman does he recommend seeing played someday for posterity? At Next Chess to be re-continued, Aronson gave replacement CV in Not-Particularly-New for his Transactional, and I have Gifford's down to couple choices. They and Gilman are next on schedule. Expecting no reply from Charles, who like pure mathematician cares nary whit for utility, I intend to just plug in tentative AltOrth Hex the ongoing line-up, making it the first hexagonal there. Neither is there at NextChess project a 3-d yet like Redistribution.

Joe Joyce wrote on Sat, Jun 5, 2010 10:45 PM UTC:
Charles, check out the preset now. The pieces are done, if you like them enough. Now all I have to do is rewrite the preset an entirely different way.

💡📝Charles Gilman wrote on Sun, Jun 6, 2010 06:06 AM UTC:
To Joe Joyce: it looks to me as if the pieces are shown as follows:
	ba/bd	-	Wazbaba	Prince	Fazbaba
	bb/bc	Pasha	Fearful	Alibaba	Waffle
	ca/cd	-	Dybbuk	Wazbaba	Vicbaba
	cb/cc	Khan	Duke	Vinnock	Wazzock
	da/dd	-	Baron	Fearful	Wilful
	db/dc	Imam	Elk	Vinnock	Fezzock
Is this correct? If so, these images work for me.

To George Duke: I judge by who takes up my variants for implementation. It looks like Redistribution 3d Chess is a success by that measure.

Joe Joyce wrote on Mon, Jun 7, 2010 03:24 AM UTC:
I think we're in agreement, or close enough. I will have to put a complete chart together to make sure we are playing with the same pieces, or more accurately, to make sure I know what pieces we're playing with. I don't need it to re-do the preset, but it's getting toward midnight here, so I'll save that part for a later time. I've had enough trouble from working on this thing sleepy. :)

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