# Chess And Physics

## Introduction

Me, Joao Neto and Claude Chaunier joined together to play a game of giveaway chess for an email tournament last year.

One day, in the middle of that game, Claude asked me to say a word and then try to invent a game with that word in mind. I said "inertia". We then started talking about what could mean inertia on a chess board. After some trials, we got a set of rules and called that Inertia Chess, a game full of pieces with lots of problems to stop in the middle of their way :-) We played some games and found out that it was a pleasant game to play. You will find some examples below.

Then I got another idea from the word Magnetic, and suddenly Magnetic Chess appeared. A great and fast game, full of danger and missile pawns! With magnetic came Gravity Chess. And with iteration, Chaos Chess appeared, a game where you cannot know all the consequences of your fair acts, despite the fact that all the rules are deterministic!

After a while, and with some new games in the way, we noticed that many of these variants have physics terms as their inspiration. We decided to present all of them in one file for you to read, play and above all enjoy.

btw, there are at least 19689 new chess variants in here :-), but don't panic, if we cut out the generalizations, we get six different variants.

Here are the variants covered in this document:

## Inertia Chess

1. The FIDE rules apply, except in the following, with the spirit that the last pieces moved continue to move the same way in the next turns.
2. There is no notion of check, checkmate or stalemate. The winner is the player who captures the opponent's king.
3. If you moved a piece without making a capture in your last move, you are forced to play the same piece in the same direction without making a capture. If you can't, you are free to play whatever you want following Rules 1-2.
4. If you made a capture in your last move, you are forced to play the same piece in the same direction and make another capture with it. If you can't, you're free to play whatever you want following rules 1-2.
5. Checking or mating the opponent according to the FIDE rules in the middle of the moves are not valid reasons to stop moving/taking.
6. 'Direction' is meant in the oriented sense, so that there are 16 different directions possible in all, including the knight moves.
7. A king is not allowed to castle if he escapes an immediate capture or if the intermediate square he would cross is under immediate attack - like in FIDE rules but with Inertia rules of moves.
8. After castling, player's next move is free: the castling king and rook stay on their new position without having to continue their course.
```-------------
Inertia 1: Joao - Claude
1. Nf3 a5 2. Ne5 a4 3. Nxf7 a3 4. Nxd8 h5 5. b4 h4 6. b5 h3  7. b6 cxb6
8. gxh3 Ra4 9. Nc3 d6 10. Nd5 Bxh3 11. Nxb7 Rh4 12. Nc7+ Kf7 13. Rg1 Kg6
14. Rxg6++ 1-0
```
```   Inertia 2: Claude - Joao
1. c4  Nf6 2. c5  Ne4  3. c6  e5 4. Qa4 Qh4 (* 4. cxd7 Bxd7? 5. h3 Bxh3
6. gxh3 *) 5. Nf3 Qxf2 6. Kd1 Qb6  7. cxd7 Nxd7 (* 7... Bxd7 h3 Bxh3
Qxe8++ *) 8. Qxe4 Qa5  9. a4  Kd8 10. Ng5 Nb6 (* 10... h5 Nh7 h4 Nxf8
h3 Nxd7 *) 11. Na3 Qd5 12. Nc4 a5 13. Qh4 c5 14. Ra3 Kc7 15. e4  Qd8
16. Qf4 Bd6 (* exf4 g3 fxg3 Ne6 gxh2 Nxc7++ *) 17. Nxd6 Kxd6 18. Nxf7 Kc6
19. Nxe5! Qd3 (* 19... Kc7 Nc4 Kc6 Nxa5 1-0 *) 20. Nxd3 Nc4 21. Nb4 1-0
(* 21... axb4 Rc3 bxc3 Qh6 cxd2 Qxc6++ *)

r . b . . . . r
. p . . . . p p
. . k . . . . .
p . p . . . . .
O N n . O Q . .
R . . . . . . .
. O . O . . O O
. . B K . B . R

Inertia 3: Joao - Claude
1. e4  e5 2. Nf3 Nf6 3. Ng5 g6 4. g4  Qe7 5. Nc3?! Qe6 6. Nd5 Qxg4
7. Ne7 Qxg5 8. Nxc8 Na6 9. Bxa6 bxa6 10. Nxa7 Ng4 (* 10... Rxa7 11. Rf1 *)
11. Qf3 Rxa7 12. Qh3 Qf5 13. f4  exf4 14. Rf1 Ne3 15. Qf3 Qf6 (* 15. Qxe3
fxe3 Rxf5 exd2 Rxf7 dxc1=Q+ Rxf8+ Qxf1++ *) 16. Rf2 Ba3 17. dxe3?? Qc3+
18. exf4 Qxe1++ 0-1

. . . . k . . r
r . p p . p . p
p . . . . . p .
. . . . . . . .
. . . . O O . .
b . . . . Q . .
O O O . . R . O
R . B . q . . .

Inertia 4: Claude - Joao
1. e4 Nf6  2. e5 Ne4  3. e6 dxe6  4. Nh3 e5  5. Na3 Nxd2
6. Qh5 Bxh3  7. gxh3  e6  8. Nb5 Na6 (* Black threatens Nb4 Nxc2+ 0-1 *)
9. Bxd2  h6 10. Bxh6  gxh6 11. Bc4 Nb4 12. Bb3 Rg1 13. Ba4 Nxc2+ (* Nc6
14. Rd1 forces Black's Q to be exchanged with R *) 14. Bxc2 Bg7
15. Rd1 Bf6 16. Rxd8+ Rxd8 17. Bh7 Rh8 18. Rxh6  Ke7 19. Qc1 Bh4
20. Bb1 Rh5 21. Qxc7+ Kg8 22. b4  Be7 23. Nxa7  Ke8 24. Qxb7  Bf8
25. Qb5+  Ke7 26. Nc6+  e4! 26. Ne5 e3 27. Ng4 e2 28. Qxe2  Rh4
29. Qf3 Ke8 30. Qf6 Bxb4+ 31. a3  Bxa3 32. Qxh4  1-0

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

Inertia 5: Joao - Claude

1. d4 e5  2. d5 e4  3. d6 e3  4. Nh3 Qh4 (* 4. dxc7 Qh4  cxb8=Q Qxf2++
4. Nh3 cxd6  Qd5 *)  5. Qd5 Nh6  6. Nc3 Ng4  7. Qf3 exg2+ 8. Nxg2 cxd6
9. Nb5 Na6 10. b4 g5 11. Rb1 h5 12. Rb3 Kd8  13. Re3 Be7  14. Bd2 Bf6
15. Bc3 b6  16. Nc7 b5  17. Nxa8 Bb7  18. Qxb7 Nxf2  (* 18... Qxf2+ Kd2
Qxe3+ Nb6! Qxb6 *) 19. Kd2 Bd4?  (* 19. Qxa6?? Nd3+  Kd2 Bxd3+ 0-1 *)
20. Ba1! Bb2 (* 20... Bc3+?? Rd8+ Bb2 1-0 *)  21. Qxa6 Qc4  22. Qxa7 Qxc2+
23. Ke1  Nd3+  24. exd3 Ba3 (* 24. Rxd3 Ba3 Rxa3 Qc1 0-1  24... Qb1+ Ke2
Qc2+ d4! 1-0 *) 25. Qb8+ Qc8 26. Qxc8+ Kxc8 27. Bxh8 Kb8 28. Ke2 Bxb4
29. h4  gxh4 30. Rh3 resign 1-0

N k . . . . . B
. . . p . p . .
. . . p . . . .
. p . . . . . p
. b . . . . . p
. . . O R . . R
O . . . K . O .
. . . . . B . .

Inertia 6 : Claude - Joao

1. Nh3  Na6  2. Na3  Nh6  3. Nb5  Ng4  4. b4   g5  5. Rb1  Bh6
6. Rb3  0-0  7. Ra3  b6  8. Nc3  b5  9. Ne4  Rb8 10. e2   Nxf2
11. Nxf2 Rb6 12. Bb2  Bb7 13. Qa1  Rg6 14. Nd3  Bg7 15. Ne5  Bxe4??
16. Bc4  Bxg2 17. Bxf7+ Bxh1 18. Bxg8  1-0

. . . q . r B .
p . p p p . b p
n . . . . . r .
. p . . N . p .
. O . . . . . .
R . . . O . . .
O B O O . . . O
Q . . . K . . b
```

## Entropy Chess

(with the help of Benjamin Good's sugestions)

1. All FIDE rules apply except in the following:
2. After each move, the player can make an optional "brownian move", i.e., pick an enemy piece (except the king and the last moved piece) and put it on a empty square not attacked by the player's pieces. Bishops, if moved, must be placed in squares of the same color.
3. A player cannot move the piece that was used in the last brownian move made by the adversary.
4. A player must release the king from a check within the normal move. If that is not possible, the player loses the game.

#### Entropy 1: Sample Game

```    1. d4   (fd6)  e6    (ed3)  2. h4     (Nge7) Nc6? (Rhd2)
3. Qh5+ (gf6)  Ng6?? (cd1)  4. Qxg6++ (he7)  1-0
```

## Magnetic Chess

1. The FIDE rules apply, except in the following.
2. There is no notion of check, checkmate or stalemate. The player capturing the opponent's king wins.
3. Every piece has a charge generating a magnetic field, except the two kings which have a neutral charge. White pieces are positive, and Black are negative (or vice versa, of course :)
4. When a piece is moved to a specific square, their closest neighbours at the same rank and column (not diagonal) are repelled if they have the same charge (hence the same colour), and attracted if they have an opposite charge (hence have different colours). A king isn't repelled or attracted, doesn't repel or attract and has a blocking effect on the magnetic field lines (in the example, the bishop Bd8 is not attracted by the queen because of Kd6).
5. ```   Eg,

8 . . . b . . . .       . . . b . . . .
7 . . . . . . . .       . . . . . . . .
6 . . . K . . . .  Qd5  . . . K . . . .
5 q . R . . r P .   =>  q R . Q r . P .
4 . . . Q . . . .       . . . b . . . .
3 . . . . . . . .       . . . . . . . .
2 . . . b . . . .       . . . . . . . .
1 . . . . . . . .       . . . . . . . .
a b c d e f g h       a b c d e f g h
```
6. There is no en-passant rule.
7. In castling, the changes are made by the rook movement.
8. A white pawn in the 1st or 2nd rank, or a black pawn in the 7th or 8th rank, can move 2 squares ahead, even if it has already been played before.

To be precise: pawns are also considered to be pieces, and the effects apply to pawns as to the other types of pieces.

```-------------
Magnetic 1: Joao - Claude
1. d4  Nf6 2. Bg5 Ne4 3. g4  Bxg4 4. Qxg4 f5! 5. Qf3 Nxh1 6. Qxh1 Nc6
7. Nf3 Qa5+ (* 7. Bxf4? then 7. ...Qd7! promoting pawn at d1 *)
8. Nd2 Nxd4+ 9. Rb1 Nxf3+ 10. Qh3 Qxa2 11. Rc1 Qxb2 12. cxd8=Q+ Kxd8
13. Rd1+ Qxe5 14. Rd3 Rg8=Q+ 15. Bg6 Rxg6+ 0-1

r . p k p b . .
p p . O . . . p
. . . . . . r O
. . . . q . . .
. . . . N . . p
O . . R n . . Q
. . . . . . . .
. . . . K . q .

Magnetic 2: Claude - Joao
1. Nf3  Nf6 2. Nc3  e5 3. Bxc4 Ng4 4. Qxg4 h5 5. exf5 gxh4 6. Qg6+ Ke7
7. Qf7+ Kd6 8. Nb5+ Kc6 9. Qd5+ Kd7 10. Qe6+ Kc6 11. Bd5+ Kxb5 12. a4+ Ka6
13. g2  Qe7 14. Bc4+ Ka7 15. Qxe7+ Bxe7 16. Rg1=Q exd=Q+ 17. Kxd1 Rxg8
18. Bxg8 Bh4 (better than 18.Rxe7+Nd7 Rxd7+d5 Rxd5Rg1+ Ke2Re8+ Kf2Rxc1 ?)
19. Rg4  Bg3 (* After the next moves, White position becomes desperate *)
20. Rg7+ Kb8 (* Then 21. fxg6?? f5=Q++! and 21. Rxg6? b5! *)
21. c3  Bxf5=Q++ (* What could have played White anyway? *) 0-1
```

```
Magnetic 3: Joao - Claude
1. e4 Nf6 2. Nc3 Na6 3. h4 Ng3 (* 3. Bxc4?Bxg1 Rxg1Qh4 Kf1Be7=Q Kg2Qg3
Kh1Qgg1 Nxg1Qxd1 -+ *) 4. Ng5 Qe7 5. Qxe2 Qxe2 6. Bxe2 gxf4
7. Bxg4 hxg6 8. d3Q+ Kf7 9. Qf6+ Ke8 10. Bd2Q+ Nd4 11. Qdd8++ 1-0

r . b Q k b p r
p p p n . . . .
. . . . . Q p .
. . . . O p . .
p . . . O . . .
. . . B . . . .
. O O . . . . O
R . B . K . N R

Magnetic 4: Claude - Joao
1. Nf3  h5 2. Nd4  e5 3. dxe3 Nf6 4. c3  Rg8 5. Qa4+ Ke7
(* 5... Kf7 Qd7+ *) 6. Bd2  gxf2+! 7. Kxf2 Bxd7 8. Qb3  Be6
(* 8. Qc2=Q e3+ *) 9. fxe4 dxe3+ 10. Qxe3 Bg3+ 11. Qe3  Bd5
12. Bb4+! Ke8 13. Bxb5+ 0-1

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

Magnetic 5: Joao - Claude
1. e4 Qf6 2. Nf3 Ba3?! 3. bxa3 Ne7 4. c3 Nxf5 5. 0-0 Ne3 6. dxe3 Qxa1
7. Qd6 Nc6 8. Nd2 Qxa2 9. Nc4 Qxb3 10. Ne5 Qc3 11. Qxd5 gxh2+
12. Kh1 Qxh3?? 13. Qxf7+ Bf5 14. Qf7++  1-0

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

## Gravity Chess

1. The Magnetic Chess rules apply, except in the following.
2. The friendly pieces are attracted like the enemy pieces.
```-------------
Gravity 1: Joao - Claude
1. d4 Nf6 2. Nf3 Ng4 3. Qd2 Na6 4. fg5 e5 5. Nh4 Nxf2 6. Qxf2 Bb4+
7. Bd2 Qxg5 8. Nxf3 Qxd5+! 9. Nd2 Rxh1+ 10. Ng1 fxg3+ 11. Qf1 Qxg2
12. e3 0-1

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

## Anti-gravity Chess

1. The Magnetic Chess rules apply, except in the following.
2. The enemy pieces are repelled like the friend pieces.
3. KO rule: No position can be repeated.
```-------------
Anti-Gravity 1: Joao - Claude

1. h4 Nh6  2. Nc3 c5  3. h4 Nc6  4. e4 Qc7  5. d4 Bxg4  6. g3 Qa5
7. Qd2  Nxc2+ (c8=Q)  8. Kd1 Qe1+  9. Kxc2 Rxc8+  10. Kd3 Qd1+  0-1

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

## Anti-magnetic Chess

1. The Magnetic Chess rules apply, except in the following.
2. The friend pieces are attracted while the enemy pieces are repelled.
```-------------
Anti-Magnetic 1: Joao - Claude

1. c4 d5  2. cxd5  Qxd5  3. f4    Bh3  4. Nxh3  Qxg2  5. Rg1  Qh4+
6. Nf2 Qh2  7. Bxf7+ Ke7  8. Nxg8+ Rxg8  9. Bf6+  Bh6 10. Rf1  Rxg2
11. Bxb7 cxb6 12. Bxa8  Bxa8 13. Qb3   Rxf2 14. Qb4+  Kd8 15. 0-0-0 Rf4
(* Rf2Qh1+ Rf1Qf1 Kf1h1=Q+ Kf2Qa1 Na1h1=Q seems -+ *) 16. Nd4 a5
17. Qg8+ Kc7 18. Nf3   b4+ 19. Qxc4+ bxc4 20. Nxh2  bxa3 21. Kc2 Bb7
22. Re8  h6 23. Rg8  1-0

n . . . . . R .
. b k p . . O .
. . . . . . . p
. . . . . . . .
p . p . . . . .
p . . . . . . O
. . K . . . . N
O . . R . . . .
```

## Generalization Of Mag, Grav, Anti-grav And Anti-mag

Let's introduce the following notation:

xOy
( x,y belongs to {b,w} and O belongs to {R,A,N} ) means a piece of colour x (b=black, w=white) operates (R=repels, A=attracts or N=don't interfere) with piece of colour y at the same row or column where it moves to (like in the above games)

eg, bRb means a black piece repels a black piece (like in Magnetic)

We can define these 4 games in the following way:

Magnetic:
wRw wAb bAw bRb, or shortly, RAAR
Anti-Mag:
ARRA
Gravity:
AAAA
Anti-Grav:
RRRR
Normal Chess:
NNNN, ...

This leads to other games, in fact, to 3x3x3x3=81 different variants.

Other features may be needed to make these games more playable (like the KO rule in Anti-Grav).

Several variants can be created using this notation:

• For each move, the player decides what rule he will apply
• For each move, the player decides what rule the opponent will apply
• The type of rule is cyclic for each pair of moves. Eg, AAAA -> ARRA -> RRRR -> RAAR -> AAAA -> ... (Hmmm... How many different cicles are possible?)
• The rule is decided for each pair of moves in a random way (Ups! A non perfect information game!)

We can extend the notation, giving effect to the square that was left by the piece. So now, a game is defined by 8 values, eg, Magnetic = NNNN/ARRA ARRA/RAAR is a game that is anti-magnetic in the destiny square and it is magnetic in the origin square.

There is also the need to introduce a rule to define where the pieces that are affected by both squares go (eg, player choice).

We can also let the charge of the interacting pieces change in some way. Eg, RAAR if the next left piece has the same color, ARRA otherwise...

## Chaos Chess

Another way to generalize is to iterate the process and make the changes of the moved pieces, again and again, until the board reaches a fixed point or a cycle! Of course this type of game can only be programmed in a computer because the number of iterations can be very large (but certainly finite).

This type of game brings a sort of chaos idea, everything determined by fixed rules, but the sensitivity to the initial conditions brings uncertainty to simple moves! Because of this, we suffix the specific game with the 'chaos' word (eg, Magnetic Chaos).

Yet another way, is to use the chaos idea, not applying all combinations, but just one chosen by the player, until it reaches a fixed cycle. With this idea in mind, we invented the following game:

## Anti-magnetic Chain Chess

1. All FIDE rules apply except in the following.
2. There is no notion of check, checkmate and stalemate. The winner is the player who captures the opponent's king.
3. A moved piece must interact in an anti-magnetic way with another piece. That piece must then interact with another and so on until the player reaches his own king (a piece cannot interact twice in the same move).
4. ```Eg,
r n b q k . b r       r n b q k . b r       r n b . k . b r
p p p p p p n p       p p p p p p n p       p p p . p p n p
. . . . . . p .       . . . . . . p .       . . . q p . . .
. . . . . . . .  g4   . . . . . . . .  d5   . . . p . . . .
. . . . . . . .  =>   . . . . . . O .  =>   . . . . . . O .
. . . . . . . N       . . . . . . B N       . . . . . . B N
O O O O O O O O       O O O . O O O O       O . O O O O O O
R N B Q K . B R       R N B Q K . . R       R N B Q K . . R

1. Nh3     | 21ge    meaning Nh3,h2,Rh1,Bf1->g1,Ke1
...  g6 | 7h8ge   meaning g6,Ng8->g7,h7,Rh8,Bf8->g8,Ke8
2. g4      | 3h2gfe1 meaning g4,Bg1->g3,Nh3,h2,f2->g2,e2->f2,d2->e2,Ke1
...  d5 | 6e2dc78e
and so on...
```

## Particle Collision Chess

1. The FIDE rules apply except in the following.
2. There is no notion of check, checkmate and stalemate. The winner is the player who captures the opponent's king.
3. Each piece has a mass: Pawns=1, kNight=Bishop=3, Rook=5, Queen=7. King mass is irrelevant :-).
4. Mass-Energy transformation - let c=1 in E=m.c^2
When a piece takes another, the removed piece mass is transformed into energy units (e.u.). This energy is accumulated on the orthogonal ends of the column/rank's free space squares. The distribution of this energy is 1 e.u. for each direction in N->E->W->S->N->E->... rotation for black and S->W->E->N->S->W->... for white.
5. When a piece takes another, the removed piece mass is transformed into as many energy units. This energy is ejected from the square in orthogonal directions and accumulates on squares right before it hits some other piece or some border. The first energy unit goes straight toward the player side. If there are some left, the two next energy units go Eastward and Westward. The two next go Nortward and Southward. The two next go Eastward and Westward again. The succession of energy directions are thus N,E,W,S,N,E,... for black's captures and S,W,E,N,S,W,... for white's. If the captured piece was beside some other piece or some border, some energy may accumulate on its square.
6. A piece can only move to a square if its mass and the - possibly new - energy on that square sum to a multiple of 3, 5 or 7. The piece is then transformed into a piece of that value, thus transforming some energy into mass and destroying any remaining energy. The player may have to choose between several possibilities, eg. between a kNight and a Bishop if the sum is a multiple of 3, or between a kNight, a Bishop and a Rook if it's 15... The king does not change his form and absorbs the square energy. The game starts with all squares having zero energy.
7. There is no promotion in the classical way. A pawn reaching the last rank is transformed into energy put on that specific square.
8. ```note: since the total amount of e.u. distributed is always odd in a
capture, it will always send as many energy Eastward as Westward:
Eg,

r n b q k b n r       r n b q k b n r       r n b q k b n r
p p p p . p p p       p p p p . p p p       p p p p . p p p
. . . . . . . .       . . . 1 . . . .       . . . 1 . . . .
. . . . p . . . exd4  . . . . . . . . Qxd4  . . . . . . . .
. . . O O . . .  =>   . . . p O . . .  =>   . . . Q O . . .
. . . . . . . .       . . . . . . . .       . . . . . . . .
O O O . . O O O       O O O . . O O O       O O O . . O O O
R N B Q K B N R       R N B Q K B N R       R N B 1 K B N R

1. e4 e5  2. d4 exd4
(* 1 energy unit (e.u) goes N, black cannot do d6 or Bd6 (rule 6) *)
3. Qxd4 (* white can move Kd1 absorving d1 energy *) Bc5
4. Bg5 ...

r n b q k b n r       r n b q k . n r       r n b R k b n r
p p p p . p p p       p p p p . p p p       p p p p . p p p
. . . 1 . . . .       . . . 3 . . . .       . . . 3 . . . .
. . b . . . B . Bxd4  . . . . . . B . Bxd8+ . . . . . . . .
. . . Q O . . .  =>   2 . . r O . . .  =>   2 . . r O . . .
. . . . . . . .       . . . . . . . .       . . . . . . . .
O O O . . O O O       O O O . . O O O       O O O . . O O O
R N . 1 K B N R       R N . 2 K B N R       R N . 3 K B N R

4... Bxd4 (* there are 7 e.u. to distribute, North is d6, East is
d4 (there is a pawn is e4), South is d1, West is a4. Since 2 e.u.
are placed in d4, they sum with the 3 e.u. of the bishop, 3+2=5,
so it is transformed into a rook *)
5. Bxd8 (* all 7 e.u's of d8 queen are placed in d8, plus 3 e.u
of the bishop, sums 10 e.u, a multiple of 5, so it turns into
a rook *) Kxd8 (* leaving 1 e.u. in e8 *)
```

Variants allowing more moves:

• A piece may walk into a charged square and redistribute the energy through the board when the sum of its mass and the energy isn't a multiple of 3, 5 or 7.
• A piece may be transformed into a pawn when the sum isn't a multiple of 3, 5 or 7 - as a multiple of 1.

## (Counter)Clockwise Rotation Chess

1. The FIDE rules apply except in the following.
2. Every two moves, the board rotates 90 degrees (counter)clockwise. The pieces moving direction doesn't rotate with the board.
3. ```   Eg,

r . b q k b n r      r p . . . . O R       R Q B K Q B N R
p p p p p p p p      . p . . . . O .       O . O O . O O O    \/
. . n . . . . .      b p n . . N O B       . . N . . . . .   black
. . . . . . . .      k p . . . . O K       . . . . O . . .
. . . O . . . .  =>  q p . . O . . Q   =>  . . . . . . . .
. . . . . . . .      b p n . . . O B       . . n . . n . .   white
O O O . O O O O      . p . . . . O N       p p p p p p . p    /\
R N B Q K B N R      r p . . . . O R       r . b k q b q r

1. d4 Nc6  2. Nc3 Nf6  3. g1=Q b1=Q ...
```

Note: Only pawns behave differently with respect to the board. All the other pieces are invariant to rotation. So a convenient way to play is to keep the board fixed and to show how the pawns move with the help of some rotating arrow.

## Play It!

Use Zillions of Games to play these games! If you have Zillions of Games installed, you can download these games and play them.

Thanks to: Benjamin Good, Bill Taylor, Modest Solans & Ralph Betza.
Written by Joao Neto. Edited by David Howe. Thanks to Michael Keller for some corrections and clarifications.
WWW page created: September 23, 1997. Last modified: June 28, 1999. ﻿