Comments/Ratings for a Single Item

If the players are cooperating, why do you need two of them?

Rather than competing against each other, the players are mutually
participating in problem-solving.  And each might either help or hinder
the solution.

This should be a friendly conversational game, with strong players
challenging each other to create and duplicate extremely complex positions
with the minimum number of moves.

This also should be a nice exercise game to aid players in their ability
to extrapolate positions in other games.

Another variation would be that the player, who reaches initial position
first, wins. The game can start e.g. with white King on a1 and black one
on h8 (or other postions to deversify the game). Then black starts with
undoing the last move. As 'uncapturing' of pieces is disadvantageous and
would never made otherwise, then it should be obligatory to 'uncapture',
if possible. So the game could start (black moves are shown before white
also in notation):

-1. kg8 (*Qh8) // black uncaptures white queen, undoing the last move
kg8xh8.
-1. ... Qf6 (*nh8) // white undoes Qf6xh8
-2. nf7 (*Rh8) Rh1 (*bh8)
-3. bg7 (*Rh8) Rh2 (*rh8)
. . . etc.

I need to think something more about uncapturing of pawns, but may be no
restriction should be made here, so that if e.g. white leaved with doubled
pawn and all black pieces already on the board, then white can't win
anymore. If black in the same situation, then it is a draw. 

There should be probably a rule for uncapture of bishops to forbid that
two bishops e.g. on light squares are produced.

Un-capturing Pawns would create an interesting dynamic.  For instance,
forcing the opponent to make a reversed two-step move by performing a
reversed en passant.

Might not a player move a power piece to the far rank and demote it to a
Pawn?

And by putting their King in check, they could force the opponent to
remove the threat.  Obviously, there must be the possibility of removing
such a threat.

I'm beginning to really like this variant.

I am liking a lot Andrea´s variant, but it is the need of a good analysis
to see if the game has ever 'solution'. If not, it is the need of a set
of rules for guaranteeing it. The game, at first view, looks extremely
interesting, but some refinements must be made. We all can think on it.

I am afraid that Pawns management is not trivial. You can 'create' enemy
Pawns in theoretically impossible positions, and it should not be so
evident, or construct a position in which it is impossible for both bands
going back to the past. Rules for Pawns management are necessary, although
I think it is not so easy!. Can be constructed a playable game with the
initial ideas?. If so, it would be great!.

The game dynamics can be extremely bizarre, this was the reason I thought
in a co-operative game. Following with Andrea´s variant, I have not a good
idea on how can it work, because I have not played an experimental test
yet. I have doubts about the playability, unless a good set of rules can
be performed. Difficult task, Andreas, you have entered a very difficult
problem in Games Design...

How's this for a rule:

No Pawn may be un-captured on its player's first rank.

Does anyone have others?

No restriction on pawn uncaptures (except that it can't be done on first
or last rank) could probably lead to a too drawish game. A player just
needs to delay pawn uncaptures until all other pieces are uncaptured and
than try to uncapture all opponent's pawns on the same file. 

So, I would suggest the following rules:
* Pawn uncapture is not allowed on the file where there is already pawn of
the same color. For example, black can't uncapture white pawn on g-file if
the file already contains another white pawn.
* Uncapture is also not allowed if it produces a pawn, which is behind
player's pawn. For example, black can't uncapture white pawn on g7 if
there is already black pawn on g2. 
* A player can't uncapture more pieces then present in usual chess setup
(light and dark-colored bishops are considered as different pieces).
However if a player unpromotes one of his pieces, that piece becomes
available for uncapture again. 

The game finished when:
* A player reaches starting postion with his pieces (this player wins).  
* A player can't make a legal unmove (this player loses).

There is already a ZRF file for this game without any restriction on
uncaptures: 'Unplay Chess' by  Karl Scherer (can be downloaded from
Zillions of Games pages:
 
http://www.zillions-of-games.com/cgi-bin/zilligames/submissions.cgi/26414?do=show;id=966

I slightly modified it to place white king on a1 and black on h8 in
initial position. Here is my first game against Zillions (I played
black):

-1. kg8 (*Rh8) // black uncaptures white rook: kg8xh8
-1. . . . Pg7 (*rh8) ?? // white unpromotes the rook and uncaptures the
black rook, undoing the move P g7xh8 R. This move loses the game.
-2. rh7 (*Qh8)! // undoing rh7xh8. Black wins as white doesn't have any
unmoves which wouldn't leave black king in check by queen on h8.

Another short game against Zillions:
-1. kg7 (*Qh8) Qh4 (*rh8) ??
-2. rh7 (*Bh8)!

White loses, as it can't remove check by bishop h8 to king on g7. I first
thought that -1. kg7 (*Qh8) quarantees win for black, but then found the
only defense: -1...Qh4(*bh8)!.

One more game. I played it against myself, trying to find a forced win for
black. As surprise, white won!

1. kg7 (*Bh8) Ph7 // white unpromotes bishop, there were no uncaptures
possible, so a regular unmove is allowed
2. kh8 (*Pg7)?? Pf6 (*pg7)!

White wins as black doesn't have any legal unmove now.

In actuality, placing a King in a check position which the opponent cannot
 remove in the next move would be a loss for the player moving the King. 
 Consider that in a normal flow of events, the checking player would not
 previously have the opposing King under threat or it would have already
 been a won game.

So in this game, checkmate would still be a loss.  There just would be
 little restriction to placing a King in a checked position.

The King would become a piece which the opponent needs to avoid, the
 player could use the King to influence the opponent's moves.  Removing
 the check of an opposing King would be mandatory.  But the player must
 consider that the opponent must have the ability to remove this check.

So placing a King in threat against a Pawn on its initial position would
 be illegal since that piece would not have the option to remove the
 threat.   Placing the other pieces into initial positions which limit
 their mobility would take up most of the tactics in this game.  For
 example: the Rooks in their initial position would not be forced to move
 if their Pawns are also in position.

Rather than controlling the center of the field, players might attempt to
 control the outer cells.