Parity Chess

Parity Chess

 A V MURALI

Introduction

In chess, as defined by FIDE rules (also referred to as standard chess in this article), players take turns with white starting the game. In standard chess, it is generally considered that white starts the game with a small advantage as he gets the first move. Parity chess that is described here is a variant of chess created by the author. It was created with the objective of eliminating this first mover advantage for white and placing both the players at par in terms of advantage right from the beginning of the game. In addition to that, parity chess offers several new variations to the game that are not available in standard chess. 

In parity chess two players start with the same set of pieces as in the standard chess, but they make their moves simultaneously, independent of each other. The board and initial setup are same as in the standard chess (see fig. 1). Pieces move as in the standard chess. A player can move only one piece per move and the null move is not allowed. Almost all the rules of the standard chess apply, with a few exceptions. A few additional rules apply to take care of situations peculiar to this variant. 

The rules of parity chess are simple and easy to learn and play. Because of its departure from turn-based play like a game of chess, it may appear little difficult at first sight. With little practice you would find it really easy and fun. Further, the absence of an opening theory, at present, makes it a fertile ground for exploration and offers a level-playing field for amateurs.

When the players make simultaneous moves, their pieces may land on the same square. When this happens, the two enemy pieces are allowed to occupy the same square. This would necessitate a slightly larger board or smaller pieces. Game rules for parity chess and their implications are described in the following paragraphs.

Though not mandatory, it would be better for the players to place some small visible object at the square where they place their piece in the last move. After every move, they should be shifted to another square where they place their respective pieces next. This would show the players which piece on the board has been moved last and so cannot be moved out in the immediate move.

New Terms
Terminology used by FIDE is followed as far as possible. Following 4 terms are introduced to denote new situations that arise due to simultaneous moves.

 immediate check, delayed check, failed check, failed capture.

Game rules for Parity Chess are listed here. At the end of this article, game rules for a related variant (Parity Chess with Single Occupation) that was created by the author, are listed.

Game rules:-

Parity chess is governed by the 7 rules listed below. The pieces move according to their types as in chess. The capture move, castling, en passant, pawn promotion and draw by 3-fold repetition are same as in chess. A player can move only one piece at a time and a null move is not allowed as in chess. 

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1.  Players make a note of their moves on a sheet of paper and commit to it. Once both of them commit, they move their respective pieces independently. In a game with timer control, the player would hit the timer once he has finalized his move by writing it down. If implemented as a software, a player’s move would be made known by the software to his opponent only after both of them have played their moves.

2. A piece that has been just moved to a square should remain in that square in the next move. It may be moved out of that square in a later move. This rule applies to all the pieces. A player would lose the game if he does not have a move without violating this rule. If it happens to both the players the game is declared drawn.
   This rule may seem unusual, but it is exactly same as what we do in chess. In chess when a player moves a piece, his opponent gets a chance to capture that piece in his turn if he has a piece attacking it. In this variant, without this rule in place, a player would be able to move the same piece successively, leaving no chance for his opponent to capture that piece.    

3. When players place their pieces simultaneously on the same square, the two enemy pieces are allowed to occupy the same square. 
  This is the only situation when two enemy pieces are allowed to occupy the same square. Simultaneous occupation of a square by 2 enemy pieces is allowed only by a coincidence like this when the players move their pieces to the same square. At any point of time during the course of a game there can be more than one instance of such simultaneous occupation of square.

4. Two friendly pieces are not allowed to occupy the same square. So, as in chess, a player is not allowed to place a piece in a square which is already occupied by another piece belonging to him. 

5. When two enemy pieces occupy the same square, they can remain there as long as players want it. A piece placed there cannot be captured by the opponent as that would result in two friendly pieces occupying the same square after capture, which violates rule (4).

6. Stalemate is treated at par with checkmate. This rule however can be modified based on consensus. If both the players got checkmated or stalemated simultaneously, the game is declared drawn. 

7. En passant is allowed in parity chess; it can happen in the next move. En passant is not allowed to happen when the concerned enemy pawns are moved simultaneously. This is because a player would not know whether his opponent is going to move his pawn by 2 squares or 1 square in a simultaneous move. This again is similar to chess though it may seem different at first.
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     Further description:-

Description of the above rules and their implications are covered here. They are a direct consequence of the 7 rules given above. Please note that some of the points listed above are repeated in this section for the sake of clarity. The description below might be bit lengthy but should not be difficult to understand; once you have read it, the rules can be easily applied.

Check: 

     When king comes in the line of attack of a piece of opponent, it can be in one of the following situations:-

     Delayed check, where a piece that has just moved attacks the opponent’s king. In this case, the king can remain where it is for one move, as the attacking piece has just moved in and so cannot be moved again immediately (as per rule 2) to capture the king. In this case, the player can respond to the check by blocking the line of attack to his king in the very next move. Alternatively, he can move his king out of that square either in the next move or next to next move.
 Delayed check is not a check. The king does not have to be moved out of the line of attack. It is just a warning sign of impending danger for king. It becomes a 'check' as in standard chess only in the next move.

Immediate check, where the attacking piece got its line of attack on the king cleared by a movement of another piece, as in discovered check. Immediate check is equivalent to 'check' in standard chess. Immediate check needs to be answered by moving the king immediately out of that square as otherwise the king will be captured in the very next move. Note that blocking the king in the next move is of no help, as the attacking piece of opponent would have captured the king by a simultaneous move. 

If the king that has moved out of a square gets into immediate check due to a simultaneous move of opponent that opens up line of attack of a stationary piece, the king will be captured in the next move by that attacking piece and the player would lose the game. This is an important point to remember when moving the king. 

As in chess, the king should not be  moved to a square that is currently under attack by a stationary piece belonging to the opponent. This is because that piece can capture the king in the next move. It can however move to a square that comes into attack from a enemy piece moved last, because that piece cannot be moved immediately to capture the king.

A situation can arise where the players move their kings to adjacent squares resulting in mutual check to each other. In this case they have to be moved out of their respective squares in the next to next move, as it is a case of delayed check for both. If for some reason they cannot be moved out, the game would be declared drawn. On the other hand, one of the players loses if he cannot do so while his opponent can move his king out of check without getting into another immediate check. 

Two enemy kings shall not land on the same square. This is because in doing so, a player is trying to give a check to opponent’s king using his own king. Player may lose the game as this amounts to moving to a position that can lead to immediate check from the opponent's king, had the king remained stationary.

   

     Simultaneous occupation of a square: 

   Two friendly pieces are not allowed to occupy the same square. This means that a player is not allowed to capture a piece of opponent in a square that is being simultaneously occupied by his own piece, as that would result in two friendly pieces occupying the same square. It means that a piece that shares a square with a piece of opponent is indirectly protected from capture. 

If one of the pieces happens to be a king, it gets protection against checks from the enemy piece occupying the same square. Check will not apply to it from an enemy piece attacking it from anywhere on the board. But if the enemy piece occupying the same square vacates that square, then the attack from another piece of the opponent becomes an immediate check, as the attacking piece has not moved now. In this case, king is actually under attack from two pieces of opponent namely one that has vacated and another one attacking it already, though only one of them is of immediate concern. If a king in simultaneous occupation with an enemy piece is moved out of the square and comes under attack from the same piece (which has not moved) the player loses as the king can be captured.

    

     Capture and failed capture: 

    Capture is same as in standard chess if the attacked piece has not been simultaneously moved out of the square by the opponent.

    When a piece attempts to capture an opponent’s piece, and if the opponent has moved that piece to another square in the same move, then the capture would not happen. This situation is termed as failed capture. It can even arise simultaneously to both the players as when their respective pieces try to capture each other. In this case, both the pieces will be safe on the board; they are not removed.
    

     Failed check: 

    An attempted check can turn out to be failed check if the opponent has either moved his king out of the line of attack of that piece or has placed a piece in that line of attack in the simultaneous move, thereby protecting the king.

   

     Checkmate, stalemate and draw: 

    Checkmate or stalemate can happen to both the players simultaneously unlike standard chess. In this case the game is treated as drawn. One way stalemate can happen in the same way as in standard chess. Game may be declared drawn if players agree for a draw (1/2 – 1/2).

    

     Diagonal move of pawn: 

   When a player moves his pawn diagonally to capture his opponent’s piece while his opponent has moved that piece in the same turn, there will be no capture but pawn is allowed to stay in that destination square, although it has not actually captured any piece. This is another instance of failed capture. This is the only instance when a pawn is allowed to move diagonally forward without actually capturing a piece. This kind of a move gives better mobility to pawn when compared to standard chess. 

    

     Pawn promotion: 

    Pawn promotion is same as in standard chess. When a pawn promotes and the opponent tries to occupy that square in the same move, the two enemy pieces would occupy the same square, as we saw earlier. When a pawn promotes, it cannot be moved in the next turn, as the resulting piece (of higher strength) that has come into existence is still treated as a continuation of the pawn.
  

     Castling: 

    Rules for castling are same as in standard chess. King shall not be under immediate check irrespective of which side the castling is done. For king side castling, none of the intermediate squares between the rook and the king can be under immediate attack whereas for queen side castling only the squares b1 or b8 can be under attack. On castling, neither the rook nor the king would come under simultaneous occupation with an opponent’s piece, as these squares shall not be under attack for castling to be legal.

Some interesting characteristics of Parity Chess:

1. More variations: Possibility of pieces of opponents landing on the same square gives rise to more variations that are not encountered in standard chess. Simultaneous moves of the opponents are valid even if the moves cross each other or overlap each other. For example, white’s pawn moving from g2 to g4 and black’s queen moving from g7 to g3 (or to g2) simultaneously, is legal.

2. Capture move: A capture move is guaranteed to be successful when the to-be captured piece of opponent has no vacant square to move to simultaneously. Even otherwise, if the opponent has not simultaneously moved that piece or if the piece has just moved into that square in the previous move then its capture would be successful.

3. Controlled movement: The additional condition that a piece which has just moved shall wait in the square for one turn, before it can move again, ensures that pieces do not move across the board without any control. In a way it is very similar to chess. In chess once a player makes a move and leaves it to opponent, his opponent gets a chance to capture that piece that was moved just now. In this variant, the capture of a piece that was moved just now would not have been possible if the players are allowed to move the same piece in the successive moves.

4. Status of check: A check that is about to be given may not actually result in check because the opponent’s simultaneous move could block the line or the king might have moved out of the square, thereby avoiding it. You would come to know the status of the check only after the opponent’s simultaneous move has also been made. On the other hand, a normal move may result in check if the king gets exposed unintentionally, because of opponent’s simultaneous move.

5. Simultaneous occupation: We have seen that the enemy pieces can occupy the same square after landing on it in a simultaneous move. Pieces are allowed to remain there unlike some previous variants where the pieces are taken out of the board. This prevents us from losing pieces by chance which would result in the game coming quickly to a draw. It gives better mobility to pieces and more choices to players as extra precaution need not be taken to avoid squares where an enemy piece may land simultaneously. Additionally, it gives the players a chance to create new variations by mobilizing these pieces differently in subsequent moves.

6. Leaving a common square: After two pieces land on the same square, they have to stay there for one move. Subsequently, if a player moves his piece out of that square, it would automatically attack his opponent’s piece that stays there. But it cannot capture that piece immediately, because it has to stay in its square for one move. On the other hand, if the opponent’s piece that has stayed there has the same move type, it would be able to immediately capture the piece that has moved out.

7. Mobility of pawns: The diagonal movement of pawns due to failed capture gives greater mobility to pawns than in standard chess. When two enemy pawns along the same file land on the same square, they are allowed to move forward from there after one move. This again gives greater mobility to pawns unlike standard chess. A player can take advantage of this feature to create weakness in the opponent's pawn structure and eliminate doubled pawns for himself. 
However, as in standard chess, the enemy pawns along the same file may end up blocking each other if they land on successive ranks.

Examples of simultaneous occupation

E.g. 1: Here the g-file pawns of both the players were moved to ‘g4’. The initial and the final positions are shown in fig. 2 and fig. 3, respectively.

E.g. 2: In this case, the white’s knight and the black’s bishop landed on the same square ‘b4’. See fig. 4 and fig. 5 for the initial and the final positions.

Case of both the kings coming under check (Mutual check):- Here, fig. 6 and fig. 7 show the initial and the final positions.

The black gives a check to the white using his bishop while the white gives a check to the black using his knight. Both of them are delayed check. Players need not move their kings out immediately as the attacking piece cannot be moved immediately to capture the king. They have to wait for one move.

A sample game:

A sample game is shown below, giving a glimpse of parity chess. It is not a very smart game. It’s only meant to show some of the unique features of parity chess. The moves are denoted as in standard chess. But these moves are made simultaneously by white and black. Some of them may look incorrect if you think of it from the perspective of standard chess. As mentioned earlier, it may be better for the players to place some small object at the square where a piece is placed in the last move. After every move, it should be shifted to another square where they place their pieces next.

1	e4	e6
2	d4	Be7
3	Nf3	c6
4	Nc3	d6
5	e5	e5	simultaneous occupation by pawns
6	Be2	f6
7	b3	d5
8	Bd2	Bb4
9	g4	e4
10	a3	Be6
11	Nh4	exN	failed capture by black's pawn
12	axB	Be7	failed capture by white's pawn
13	Bxf	f3xB	failed capture by both the players
14	Qxe	fxe
15	Nf5	B7xN	failed capture by black's bishop
16	g5	g5	simultaneous occupation by pawns
17	NxB	BxN	failed capture by black's bishop
18	Rg1	gxN
19	dxe	e4	failed capture by white's pawn
20	b5	Nd7
21	Bg4	Qc7
22	bxc	BxB
23	QxB	bxc
24	e6	Qxe	failed capture by black's queen
25	O-O-O	Nc5
26	h3	h3	simultaneous occupation by pawns
27	f3	Ne7
28	Ne2	h2	black's pawn has passed opponent's pawn on the same file
29	Rh1	Rg8
30	h4	O-O-O
31	c3	exf
32	Qxf	Nxe
33	Re1	Rde8
34	Qg3	Qd6
35	Rd1	Rd8
36	Rxh	Rgf8
37	Re1	Rde8
38	QxQ	Qc7	failed capture by white's queen
39	Nd4	Ng7
40	Qa3	QxQ	failed capture by black's queen
41	Kb2	Nef5
42	Ra1	Rf7
43	NxN	NxN	failed capture by both the knights
44	cxN	RxN
45	Qxa7	Re7
46	Ba5	R5f7
47	Qa6+	RxQ	failed capture by black's rook
48	Re2	Kd7
49	Qb6	Qc7
50	Bb4	Rb7
51	Qc5	Ne6
52	Rae1	Rb5
53	Qc3	Qd8
54	RxN	c5
55	Bxc	Qc7
56	Re7+	Kc6
57	Ba3+	RxR	discovered check by white
58	RxR	Kb6
59	QxQ+	Qh2+	failed capture by white's queen; simultaneous check for both the players
60	Kc1	Ka6
61	Qc6+	QxQ	failed capture by black's queen
62	RxQ	Ka5
63	Ra7+	Rb6
64	Qa4+
	White wins (1 - 0)

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Game design considerations

When designing this chess variant, several points were considered to arrive at the game rules. A brief discussion of these points follows:-

1. One of the most glaring differences between Chess and Parity chess is that 2 enemy pieces are allowed to occupy the same square when they are placed simultaneously. While this rule might appear less acceptable to chess lovers, it has some merits.

If we want to avoid simultaneous occupation of a square, alternatively the rule could be such that the pieces that land on the same square were taken back and a fresh move made by both the players. If the pieces are taken back and a fresh move made, the game will have less variations at any point of time because this can happen with several such pairs of moves through out the game and more so in the middle game.  This will not only reduce the game variations but can some times reduce the tempo.

Alternatively, if the pieces that land on the same square are removed from the board, a player who wants to move a major piece would tend to become more cautious and avoid several candidate moves if the opponent can move a minor piece to the same destination square. This again would reduce the game variations drastically. Instead, if we have a rule that compares the piece values and removes the piece which is less in value (like a pawn against a bishop) or remove both pieces if they have same value or transform the piece that stays on the board to a piece having lower value (like bishop against pawn resulting in knight), it would make the game very complicated and difficult to calculate and think ahead.

As another alternative, if we force the players to move their respective pieces out of that square immediately in the next move, the game can become very sharp and come to abrupt endings very soon, as we are allowing movement of the same piece in successive moves which includes captures. To mitigate this, if we impose a restriction that the piece moved out from simultaneous occupation should not capture an enemy piece when it is moved out, it would make the calculations little more complicated, as the ability to capture becomes conditional. It may be noted that the resulting moves of players may again lead to a simultaneous occupation. In this case, the players will be required to move their pieces again immediately. However, this rule seems to be better than most other alternatives that we have considered. When pieces in simultaneous occupation at a square are moved out, they are allowed to land on the square they had occupied previously.

Allowing the enemy pieces to occupy the same square avoids such complications in game calculations. Moreover, it gives rise to many more game variations than standard chess.

2. As per Rule 2, a piece is not allowed to move successively. As explained earlier, this would help in avoiding an unrestricted movement of a piece and abrupt game endings within few moves.

3. Two friendly pieces are not allowed to occupy the same square. One of the reasons for this rule is to keep this variant as close as possible to Chess.

We get into this situation if we allow a friendly piece to capture an enemy piece that occupies a square with another friendly piece. When 2 friendly pieces occupying a square are under attack from an enemy piece, the opponent should then be allowed to choose the piece that they want to remove from the board. Alternatively, we can allow both the pieces to be captured. Rules like these have both merits and demerits. While they give rise to some interesting variations, they make the game calculations complicated and the game difficult to play. Secondly, such rules make the game lot more different from chess and divert us from our objective of finding a variant that is almost similar to chess while avoiding the first-mover advantage.

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An Alternative Variant : Parity Chess with Single Occupation:

We have examined a few alternative game rules and we conclude that the rules listed under Parity Chess are better compared to others discussed above. The only good alternative, as mentioned above, seems to be that whenever 2 enemy pieces occupy the same square simultaneously, the players should move their respective pieces to another square immediately, but they are not allowed to capture a piece in that move. (from the perspective of ease of calculation of the moves, it might be better to allow this piece to capture a piece of the opponent in the very next move. But since it violates the primary condition of this variant that a piece cannot be moved in two successive moves (this was devised to prevent uncontrolled movement of pieces), it has been decided to disallow the capture of a piece while vacating that square, as a compromise solution between the two extremes. Moreover, it helps in achieving greater mobility; if a capture were to be allowed in the very next move, then the players would probably avoid making such moves for the fear of losing their own piece in that move; this would reduce move possibilities). 
In this situation, if a player's king is under immediate check, he loses because he has to move the king, but at the same time he should move his piece in simultaneous occupation with a piece of opponent. Let us refer this alternative variant as Parity Chess with Single Occupation. The game rules for this alternative variant are listed below.

Game Rules for Parity Chess with Single Occupation:

1.  Players make a note of their moves on a sheet of paper and commit to it. Once both of them commit, they move their respective pieces independently. In a game with timer control, the player would hit the timer once he has finalized his move by writing it down. If implemented as a software, a player’s move would be made known by the software to his opponent only after both of them have played their moves.

2. A piece that has been just moved to a square should remain in that square in the next move. It may be moved out of that square in a later move. This rule applies to all the pieces. Only exemption to this rule is when the enemy pieces occupy the same square as a result of simultaneous moves and are required to move out of that square immediately (see rule 3). A player would lose the game if he does not have a move without violating this rule. If it happens to both the players the game is declared drawn.

3. When the players place their pieces simultaneously on the same square, the two enemy pieces will have to be moved out of that square immediately. The pieces moved out of that square are not allowed to capture an enemy piece in that move. The destination square of a piece in this situation can even be the square it was previously placed. If a player does not have a move as when it is his pawn to be moved forward but the square in the next rank is occupied, then he loses the game. Likewise, he loses if the piece to be moved happens to be his king and the king cannot be moved anywhere without getting into check or when the move of his piece results in discovered check to his king placed elsewhere on the board.

4. Two friendly pieces are not allowed to occupy the same square.  

5. Stalemate is treated at par with checkmate. This rule however can be modified based on consensus. If both the players got checkmated or stalemated simultaneously, the game is declared drawn. 

6. En passant is allowed in parity chess with single occupation; it can happen in the next move. En passant is not allowed to happen when the concerned enemy pawns are moved simultaneously. This is because a player would not know whether his opponent is going to move his pawn by 2 squares or 1 square in a simultaneous move. This again is similar to chess though it may seem different at first.  

Conclusion:

Both the variants, namely Parity chess and Parity Chess with Single Occupation offer many new possibilities. They place black and white on the same footing and offer many new exciting game variations. While "Parity chess" treats simultaneous occupation in a simpler way, "Parity chess with Single Occupation" makes the board look more like chess, because whenever 2 enemy pieces land on the same square, the players will have to move their pieces out of that square in the next move itself. In parity chess there can be more than one instance of 2 enemy pieces occupying a square; this might make the board visually too different from chess. In parity chess with single occupation, the simultaneous occupation of a square is instantly removed by requiring the players to move their pieces out of that square immediately. While it gives the players a chance to move the same piece in the next move in order to remove the simultaneous occupation, it does not allow them to capture a piece of the opponent in that move, thereby reducing its impact. 

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