### Retrochess - A chess variant challenge

You can make a chess variant (CV) by changing the FIDE rules in one or more ways, like the shape of the board, the movement of the pieces or the number of players. What we (Joao Neto and Ralph Betza) propose here is to make a game where the change happens in an unexpected point, the arrow of time!

The idea of retrochess would be to make a CV where you start with an empty board (an impossible FIDE position) or with just both kings (a FIDE draw) and start playing backwards. That is, the possible retraction moves of retrochess would be untakes, unmoves, uncastles and so on... (if you don't want to read the discussion, check the final rules for Progressive RetroChess)

In other words, you would play a game where every move was a retraction of a previous legal move, using the principle of retroanalysis. Until now, retroanalysis has been used in problems, but never to try to play a game!

The basic rules of Retrochess are:

1. Every position in the game must be a legal chess position that could be reached by a series of legal moves starting from the initial position of FIDE Chess. An exception is made for the first move, when the board is empty and the players must place their Kings.
2. A move is made by retracting a move: you must look at the current position and imagine the previous position and the move that was made to create the current position. The move, the current position, and the previous position must all be legal.
3. You retract the move you have chosen and now it is the other player's turn to unplay a move.

Here are a few examples of situations that may arise:

a) legal back moves

. . . . . . . .             . . . . . . . .
. . . . . . . .             . . . . . . . .
. . k . . . . .             . . Q . . . . .
. . . . . . . .             . k . . . . . .
. . . . . K . .     =>      . . . . . K . .
. . . . . . . .   Kb5:Qc6   . . . . . . . .
. . . . . . . .             . . . . . . . .
. . . . . . . .             . . . . . . . .

so in this position, black forces white to make some move with the queen

b) illegal back moves

. . . . . . q .             . . . . . . q .
. . . . . . . .             . . . . . . . .
. . . . . . . .             . . . . . . . .
. . . . . . . .             . . . . . . . .
. . . . . k . .     =>      . . . . . k . .
. . . . . . . .   Qg3-g1    . . . . . . Q .
. . . . . K . .             . . . . . K . .
. . . . . . Q .             . . . . . . . .

white cannot unmove his queen to g3, because it creates a illegal FIDE position (black is in check, but it is White's move).

Notice that when Black is choosing an unmove, the current position is "White to play", and vice versa!

c) impossible positions

. . . . . . . .             . . . . . . . .
. . . . . . . .             . . . . b . . .
. . . . . . . .             . . . . . . . .
. . . . . . . .             . . . . . . . .
. . . . . k . .     =>      . . . . . k . .
b . . . . . . .   Be7:a3    O . . . . . . .
O O . . . K . .             O O . . . K . .
. . . . . . . .             . . . . . . . .

there could not be a pawn in a3 in this position

There are some ideas that we have (but feel free to not use them)

 A player who has no legal retraction has lost the game. A player reaching the initial FIDE position of his army wins. Until all the pieces are on the board, every unmove must, if possible, be the retraction of a capture. Otherwise, it would be a very loooong game! (If you don't put any enemy pieces back onto the board, the other player can't win by getting back to the initial position.) This  rule is probably necessary. A player who makes a move that reaches an impossible position loses; but making an incorrect claim of "impossible position" also loses! (Once in a while, you might be able to create a clever retroanalysis problem on the board.)

We each had this idea independently when talking to other people, but we could not manage to find the perfect set of rules to make a good game out of it. Perhaps you can!

After the announce in Hans Bodlaender pages, we get some comments:

I saw your writeup of Retrochess on Hans's CV web site.  I was intrigued because I had been thinking of the same idea myself.  I would be interested in playing Retro by e-mail, once a set of cohesive rules is established. In the meantime, here are some random thoughts I had about the rules.  Let me know what you think!
- Mike Smolowitz (penguin2@ma.ultranet.com)

[Mike]You could say that you can't win until your opponent has all of his/her pieces on the board.  But that probably wouldn't work so well.  Doing all the untakes at the beginning would make for a very unlikely bloodbath, if you looked at the game going forwards; but at least it would be legal.

[Ralph] Right, so maybe if you had to make one uncapture every 2 moves, or something similar?

[Joao] I like it! Perhaps that should be agreed by the players, and the rules could give a default value. That value could even be used as a compensation in stronger vs weaker player games (not usual in chess, but typical in go)

[Mike] Sure, why not.  If it were more than every 3 moves, for instance, then the game would be very long - at least 60 moves each (15 uncaptures x 4 moves per uncapture).  A cycle of 2 or 3 should be enough.  And doing all the uncaptures at the beginning of the game might be interesting too.

[...] I have also thought about retro-strategy.  I would tend to do my untakes in my back rows, so that the new enemy pieces have a long way to travel home (especially the pawns).  I might untake many pawns in the a (or h) column, so that my opponent would be forced to bring the pawns home by a series of untakes to get them in different columns.  The king would be a powerful piece in Retro:  you can walk into check, and force your opponent to undo the check.  Done properly, you could advance your king toward his home square while forcing your opponent to waste moves undoing checks.

One other bit of strategy I thought of might have to be prohibited by a special rule.  Under the rules mentioned so far, it's OK to leave a piece on an opponent's home square, preventing him/her from reaching the complete initial position.  It's not like the opponent can take the piece that's in the way. This is legal in backgammon, but the difference is that it's possible for the opponent to hit a single blot.  How would we prevent this approach?  We can't ban pieces from the 7th and 8th rows.  What about a variation of check: if a piece can reach its initial square, and an enemy piece is on it, that enemy piece must move right away.  That's off the top of my head as I write this; I don't know what the ramifications would be. We need some kind of rule to prevent both sides lounging around in their 7th and 8th ranks, just as we need a mandatory untaking rule.

Other oddities:  after uncastling, the king and the rook are frozen!  You can't move them, because that would invalidate the castle that's already happened.  The castling restrictions regarding check are still the same.

[Ralph] Since you demonstrate that uncastling may be undesirable, I am tempted to make it forced.

[Mike] How about "un passant"?  For instance, a black pawn moves from a3 to b4, leaving a white pawn at a4.  This forces white to immediately move the new pawn from a4 to a2!

Other obligations might arise.  If white moves pawns back to b2 and d2, and there is a dark-square white bishop already on the board, then it can't reach c1.  So it must be un-underpromoted (underdemoted?), or else black has to untake the bishop on c1.  And black might choose not to cooperate.

[Ralph] Wow! That's a three-exclamation-point winning tactic. Black must cooperate because of the requirement to make a legal uncapture, and must do so without delay or else his piece from c1 might have a long journey home. However, is it a winning tactic? The promoted Bishop must become a Pawn on the 7th rank, so White also has some disadvantage, which might well be larger. If nothing else, this is a way to make a position more complicated and difficult. If you have several of these situations and some tripled Pawns, finding a legal unmove could be very hard; and deciding whether your opponent's unmove was legal could be equally hard.

[Joao] About unpromotion: should it be a good strategy to untake 10 knights? or 10 bishops?

[Mike] Yes and no, IMO.  It would force your opponent to unpromote all the extra
pieces, but he/she could easily retaliate by doing the same to you.  So if your opponent uses this approach as much as you do, then all it does is slow down the game without giving either side an advantage.  Maybe we should only allow uncaptures that don't create extra pieces (or two bishops on the same color square).

[Joao]We should try the game with the least possible move restrictions!

[Mike] I agree!  It wouldn't be as much fun to play if you had to constantly check
a long list of restrictions before each move.  I'd like to allow at least some dirty tricks. :)  Making things difficult for the opponent is a natural part of the strategy - especially if you can't remove the opponent's pieces!

Progressive ideas

[Ralph] There should also be a shorter way to win, I think. Of course, if a game takes too many moves, people can play Progressive!

[Joao] That's a good idea! But in this case, Progressive Orthodox moves (both players move the opponent pieces)

[Mike] Well, I'd be content to try basic Retro first.  We could always have basic Retro and Progressive Retro as separate games.

[Joao] I had another different idea for progressive retrochess, here it goes:

1. White puts the white king on the board
2. Black puts the black king in a legal position on the board
3. White makes a legal FIDE unmove, then Black makes two unmoves (one black and one white), then White makes 3 unmoves (b,w,b), then Black makes 4 (w,b,w,b), and so on (like in Progressive Orthodox Chess)
4. The winner is the one who obtains the initial FIDE setup, and that means all pieces (black and white)
5. A player looses if he puts the board into an impossible position

So now, both players are interested in unmoving all pieces, not just their own. It's kind of a race, a progressive retro-race, where you run and run just to get at the start line of a usual FIDE game (I wonder why this reminds me of Alice?...)

After some time, I did manage to play one game with Ted Hwa (in Feb. 2000)

[Progressive RetroChess]

1st Player: Theodore Hwa (hwatheod@Stanford.EDU)
2nd Player: Joao Pedro Neto (vascog@uol.com.br)

1.   Ke3     * Kd7       11. * Rf8:Bc8   Qa1:Ne1
2. * Kd4:Qe3   Qe1:Re3   12.   Qa3-c5     Kf6:e6
3.   Re2-e3    Ke6:Nd7   13.   Nf7:e5+    Ke7:f6
4. * Ke4:Bd4 * Bg7:d4    14.   f6+        f6:e5
5. * c3:d4   * c5:Bd4    15. * Ra2-e2  * c7:b6
6.   Ne5:d7    b6:Rc5    16. * a4-a5   * Qc1-a1
7.   Ra5:c5    b7-b6     17. * b5-b6   * Qd2:Bc1
8.   Ra7:a5  * d6:Qc5    18. * c2-c3   * Qg5-d2
9. * Ra8:a7  * b6:a5
10. * Rc8:Ra8 * Bh8:g7                 1-0

Winning Claim by Ted (accepted by Joao): This is an impossible position.  White is missing only one piece, which is the bishop moving on light squares.  But a Black capture (which must have captured this missing piece) has happened on d6, a dark square.

Final Position

===============
r . b . . R . b
p p p p k N O .
. . . p O p . .
. O . . O O q .
O . . B K . . .
Q . . . . . . .
R . O . . . . .
. . B . N . . .
===============

 Hints so far:

[jpn] Uncapture two Bishops in the same color, means that one of them must be unpromoted first

[ted] Configurations like black pawns on b7, d7 force an uncapture of the light squared black bishop on its original square (c8).  Any other light
squared black bishop must be promoted.

[jpn] What will be the critical turn? Possibly this is a game with 80-100 moves, so decomposing it to progressive, 1+2+3+4+5+6+7+8+9+10+11+12 = 78 moves Then, possibly the first 12 moves would be "safe"...

[ted] For the first few moves of the game, both sides were in a hurry uncapturing pieces.   However, once there are pawn captures on the board, one must be careful of uncapturing too many pieces with other non-pawn moves, leaving too few missing pieces to account for pawn captures. And uncapturing the wrong pieces may lead to impossible promotions or pawn structures.

 Some Final Remarks

[ted] There should probably be some rule "requiring" uncaptures near the beginning of the game, to speed things up.  Otherwise the players could just move the kings around forever.  Of course, theoretically, this is not necessary since if both players just move kings around, eventually one of the players will have enough moves to go all the way back to the starting position in one turn, but that would take a long time in practice.

[jpn] I believe that players will not uncapture. What's the point of just moving the King? Anyway, there is the 50-move rule that does not permit such kind of behaviour!

[ted]  Another point is that repetition of position should be disallowed, for the same reason.

[jpn] The FIDE 3-repetition rule will cover it nicely, I think, since the game would end in a undraw, something impossible.

[ted] I and a friend wrote some retro software a few years ago.  You can use it to try out some of these variants.  The software (for Windows) is at: http://www.stanford.edu/~hwatheod/Retractor. It lets you set up a position and take back moves, and checks for illegal positions.   It does not detect every illegal position, but all common illegalities are detected.  It also won't incorrectly declare a position illegal.

Hmmm... maybe we could add code to allow network play of one of these retro variants ?!?!  (Or even some how modify it to be used with one of the chess servers...)   Then we could try these games out.  Unfortunately I have no time for that currently...

[jpn] I received this text from the itaprob mailing list:

This is left the devout record of the short one that it finishes with single the two King on the chessboard. The previous result (old of 100 years) was of Sam Loyd: 17 movements, with two various examples. Giuseppe Ponzetto (brother of the director of the Scacco review), than cica a year fa' I had goaded goaded with the result of Loyd, has introduced us from the pages of the newspaper one solution (sara the only one? si/ci the same Ponzetto) with 16,5 movements asks... "

Giuseppe Ponzetto - Italy,  T&C/Scacco! 1/1, 2000

+-a-b-c-d-e-f-g-h-+
8 . . . . . . . . 8
7 . . . .-K . . . 7
6 . . . . . . . . 6
5 . . . . . . . . 5
4 . . . . . . . . 4
3 . . . . . . . . 3
2 . . . . . K . . 2
1 . . . . . . . . 1
+-a-b-c-d-e-f-g-h-+

SPG 33 1+1

This the short resolutive line, with reversal of the movements that generate 866 varying...

1.e2-e4 d7-d5 2.e4xd5 Qd8xd5 3.Bf1-d3 Qd5xa2 4.Bd3xh7 Qa2xb1 5.Bh7xg8 Qb1xc2 6.Bg8xf7+ Ke8xf7 7.Ra1xa7 Qc2xc1 8.Ra7xb7 Rh8xh2 9.Rb7xb8 Rh2xg2 10.Qd1xc1 Rg2xg1+ 11.Rh1xg1 Ra8xb8 12.Qc1xc7 Rb8xb2 13.Qc7xc8 Rb2xd2 14.Qc8xf8+ Kf7xf8 15.Rg1xg7 Rd2xf2 16.Rg7xe7 Kf8xe7 17.Ke1xf2 diagr

[jpn] This means the shortest progressive retrochess must have 8 prog. moves (1+2+...+8=36>33 moves). It is impossible to have less (7 prog. moves means just 28 moves and there are 30 pieces to untake).

After the end of the 1st game, we got some comments from Alfred Pfeiffer:

[apf] Why you will start only from positions where the white king did the last move?   Let the player which will unmoves first decide whether white or black did the last move.

[ted] I like the rule about have the first retractor select who unmoves first. In stalemate positions these rules seem to require that the stalemating side make the first retraction, even though from a pure positional point of view, either side might have made the last move (ignoring the stalemate). Of course this does not apply to checkmates, in which the last player to move is determined.

[apf] An extension for the rules above could be to start from any position, which is in FIDE chess a final condition (mate, stalemate, draw because insufficent mating material), and positions that theoretical could not more reduced (simplified) by further captures.

The idea for this proposal is that for each game that could occur in regular FIDE chess (forward playing) its final position also could be the starting point for a (progressive) retroplay game.

[ted] I don't understand that last condition.  Do you mean some position where, say, pawns are all blocked and no captures could be made by any pieces on the board?   I will refer to such a position as a 'blocked' position below. Also, there's really no reason to insist we play from a 'final' position, e.g., any middle game position will do.  We could have players make several 'dropping' moves before starting the retractions.  A drop is legal if the resulting position could be completed to a legal position in some way, even if the position itself is not necessarily legal. One way to implement such a rule would be to allow either player to end the dropping process at his turn and start the retractions, provided the position at that point is legal.  Or we could have some minimum number of required drops.

[jpn] Something like that would need a 3rd party to give the initial end position. But it can be fun to undo a tied middle game, things would be even faster!

That idea can be transformed into a puzzle: "given an end game, find the minimum unmoves to reach initial FIDE board position"

If some initial positions were played a lot , it could appear a kind of opening theory to handle those notorious cases... And every retrochess tournament should have an award for the most elegant retrochess game seen backwards (ie, a FIDE game) ok, I know I'm dreaming... :-)

[apf] A further condition should be, that the first unmove should a such retracting move that the new position does not belong to the class  of final positions. When starting with two alone kings (like above)  therefore it should recapture at least a pawn or a piece with mating capabilities.

[jpn] Using the previous sugestions, I can remake the rules of Progressive RetroChess as follows:

Progressive RetroChess

1. White puts the white king on the board (see note)
2. Black puts the black king in a legal position on the board
3. White makes a legal FIDE unmove (with the white or black King), then Black makes two unmoves (alternating colors), then White makes 3 unmoves (alternating colors), then Black makes 4 and so on (like in Progressive Orthodox Chess)
1. The first unmove should produce a position that does not belong to the class of final positions. A final position is a mate, stalemate, draw because insufficent mating material or a blocked position.
4. The winner is the one who obtains the initial FIDE setup, and that means all pieces (black and white)
5. A player looses if he puts the board into an impossible position

note: rules 1 and 2 can be replaced with any position agreed by both players. This position can be proposed by one player (or a 3rd party) or made after several 'dropping' moves just before starting the retractions. A drop is legal if the resulting position could be completed to a legal position in some way, even if the position itself is not necessarily legal. One way to implement such a rule would be to allow either player to end the dropping process at his turn (there can be a minimum number of drops) and start the retractions, provided the position at that point is legal.

[jpn] Some people has pointed out that RetroChess seems rather pointless in the 1st moves (what should a player do in the first 30 piece moves?). In order to give more tactical interest, I propose the following:

RetroChess Race: A match is made of two prog. retrochess games (check rules above). In each board, one player tries to delay the ending (i.e., avoid reaching the initial FIDE position) and the other tries to achieve it! The player that finished first in his board, wins!