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Escher Staircase

The board and pieces are exactly the same in Escher Staircase as in normal chess, and all of the usual rules apply. The board, however, is not a static playing surface. It contains eight "staircases," each six squares in length. In certain circumstances the staircases move, rather like escalators or conveyor belts, carrying the pieces on them to new locations. The board is illustrated in Figure 1. The movement is not an optional aspect of play: It can't be prevented, and is intrinsic to the playing surface. It turns Escher Staircase into rather a tactical tangle. The game-play is a little like Magnetic Chess, in that it's difficult to plan an attack even two moves ahead, because you don't know where the pieces you're attacking will be, nor exactly what resources you'll have available for the attack. Pouncing on your opponent's weakness the moment it appears is likely to be a winning strategy. If you don't like improvising, you may not like this game.

Figure 1a. A schematic representation of the board in Escher Staircase. The direction in which each staircase moves is indicated by the direction of the arrows. Note that eight of the squares are on two different staircases. Note also that none of the staircases extends entirely across the board. The ends of the vertical staircases are indicated in the ASCII diagram as '==='. (As the ASCII character set lacks a double vertical line, I haven't indicated the ends of the horizontal staircases in this way, but you should have no trouble seeing where they end.) In this sea of constant motion, certain squares are islands of stability -- the four in the center, and a five-square 'L' extending inward from each edge.

   +---+---+---+---+---+---+---+---+
 8 |  >|  >| v>|  >|  >|  >|   | v |
   +---+---+---+---+---+---+---+---+
 7 |   |   | v |   |   |   |   | v | 
   +===+---+---+---+---+===+---+---+
 6 | ^ |   |< v|<  |<  |<^ |<  |< v|
   +---+---+---+---+---+---+---+---+
 5 | ^ |   | v |   |   | ^ |   | v |
   +---+---+---+---+---+---+---+---+
 4 | ^ |   | v |   |   | ^ |   | v |
   +---+---+---+---+---+---+---+---+
 3 | ^>|  >|v >|  >|  >| ^>|   | v |
   +---+---+===+---+---+---+---+===+
 2 | ^ |   |   |   |   | ^ |   |   |
   +---+---+---+---+---+---+---+---+
 1 | ^ |   |<  |<  |<  |<^ |<  |<  |
   +---+---+---+---+---+---+---+---+
     a   b   c   d   e   f   g   h

Figure 1b. The two diagrams below may be easier to grasp visually. The first shows only the horizontal staircases, the second only the vertical ones.

   _ _ _ _ _ _ _ _    _ _ _ _ _ _ _ _
8 |>|>|>|>|>|>|_|_|  |_|_|v|_|_|_|_|v|
7 |_|_|_|_|_|_|_|_|  |_|_|v|_|_|_|_|v|
6 |_|_|<|<|<|<|<|<|  |^|_|v|_|_|^|_|v|
5 |_|_|_|_|_|_|_|_|  |^|_|v|_|_|^|_|v|
4 |_|_|_|_|_|_|_|_|  |^|_|v|_|_|^|_|v|
3 |>|>|>|>|>|>|_|_|  |^|_|v|_|_|^|_|v|
2 |_|_|_|_|_|_|_|_|  |^|_|_|_|_|^|_|_|
1 |_|_|<|<|<|<|<|<|  |^|_|_|_|_|^|_|_|
   a b c d e f g h    a b c d e f g h

When a staircase moves (I'll explain shortly what triggers the movement), all of the pieces on it are carried along. Also, the staircases "wrap around" like an endless conveyor belt. If a piece is situated on f3, for instance, when row 3 moves the piece will be conveyed around to a3. The same thing happens on the vertical staircases: If a piece is situated on a6, when the a column moves the piece will relocate to a1 (not a7, because a7 isn't part of the staircase).

Each time a staircase moves, it moves by exactly one square. Its movement is triggered by the "takeoff energy" or "departure energy" of a piece making a move that starts on one of the squares on the staircase. Each time a piece leaves a staircase, or moves from one square on the staircase to another square on the same staircase, the staircase moves in its designated direction by exactly one square. When the staircase advances, all of the pieces on it change position.

Figure 2a. The position before a move. The black rook on h8 is about to move to f8. h8 is on the h staircase, so the h staircase will be affected by the move. The rook will land on the row 8 staircase; this staircase is not affected by the move.

    _ _ v _ _ _ _ v
8 >|_|_|_|_|_|_|_|r|
7  |_|_|_|_|_|_|_|p|
6  |_|_|_|_|_|_|_|_|<
5  |_|_|_|_|_|_|_|_|
4  |_|_|_|_|_|_|_|N|
3 >|_|_|_|_|_|_|_|B|
2  |_|_|_|_|_|_|_|_|
1  |_|_|_|_|_|_|_|_|<
    ^         ^
    a b c d e f g h

Figure 2b. After the rook move, the position in Figure 2a is altered to this:

    _ _ v _ _ _ _ v
8 >|_|_|_|_|_|r|_|B|
7  |_|_|_|_|_|_|_|_|
6  |_|_|_|_|_|_|_|p|<
5  |_|_|_|_|_|_|_|_|
4  |_|_|_|_|_|_|_|_|
3 >|_|_|_|_|_|_|_|N|
2  |_|_|_|_|_|_|_|_|
1  |_|_|_|_|_|_|_|_|<
    ^         ^
    a b c d e f g h

If a piece makes a one-square move in the "backwards" direction on a staircase, the motion of the staircase will return it to where it started. All of the other pieces on the staircase will change position, however. If there are no other pieces on the staircase, the player can, in effect, pass his or her turn by making such a move. Conversely, a piece that moves by a single square in the forward direction of a staircase will be carried onward, effectively moving two squares.

The alert reader may be wondering: What happens when a piece leaves a square that is on two staircases? In this situation, both staircases move. Ah, but this raises a problem. Consider this position:

    _ _ v _ _ _ _ v
8 >|_|_|_|_|_|_|_|_|
7  |_|_|n|_|_|_|_|_|
6  |_|_|q|p|_|_|_|_|<
5  |_|_|_|_|_|_|_|_|
4  |_|_|_|_|_|_|_|_|
3 >|_|_|_|_|_|_|_|_|
2  |_|_|_|_|_|_|_|_|
1  |_|_|_|_|_|_|_|_|<
    ^         ^
    a b c d e f g h

When the queen leaves c6, both the c7 knight and the d6 pawn will need to move onto c6. In this situation, there will be a loud grinding noise, smoke will pour out from the underside of the board, and ... no, okay, what actually happens is that in this position it's illegal to move the queen. The queen is stuck there until either the knight or the pawn is moved, or until one of the belts is shifted by the movement of some other piece. A move that would result in two pieces occupying the same square is always illegal.

It's also illegal to make a move that would cause your king to be put in check by the operation of a staircase. Other than that, there's no restriction on what can happen when a staircase moves.

There is no castling in Escher Staircase, because it's not possible to clear out the space between the king and rook without moving one or both of them.

Pawns can always advance by one or two squares when positioned in their first or second row, even if moved previously. (This prevents a certain amount of confusion that might otherwise arise over whether a move is legal.) A pawn that is whisked around to the enemy's home row by a moving staircase is promoted instantly; if this happens as a result of a move by the opponent, the promoted pawn can immediately move using its new identity. This type of situation, which is shown in Figure 3, is important to watch out for.

Figure 3. White had better not move the a2 pawn, because the upward-moving staircase (which ends, remember, on a6) will whisk the a6 pawn around to a1, resulting in a promotion.

    _ _ v _ _ _ _ v
8 >|_|_|_|_|_|_|_|_|
7  |_|_|_|_|_|_|_|_|
6  |p|_|_|_|_|_|_|_|<
5  |_|_|_|_|_|_|_|_|
4  |_|_|_|_|_|_|_|_|
3 >|_|_|_|_|_|_|_|_|
2  |P|_|_|_|_|_|_|_|
1  |_|_|_|_|_|_|_|_|<
    ^         ^
    a b c d e f g h

A Sample Opening

Just for fun, let's take a look at a possible opening in Escher Staircase. (The black pawns in the diagrams below are shown as 'o' rather than 'p' because it's hard to see the difference between capital 'P' and lower-case 'p'.) You'll note that the opening positions of the black king and queen are reversed in the opening lineup of Escher Staircase. This is so the positions are identical with respect to the staircases.

1. e4        e5
2. Bc4(1,f)  c5(c)

    _ _ v _ _ _ _ v
8 >|r|n|_|k|q|b|n|r|
7  |o|o|b|o|_|o|o|o|
6  |_|_|_|_|_|_|_|_|<
5  |_|_|_|_|o|_|_|_|
4  |_|_|o|_|P|_|_|_|
3 >|_|_|B|_|_|P|_|_|
2  |P|P|P|P|_|_|P|P|
1  |R|N|Q|K|_|N|R|B|<
    ^         ^
    a b c d e f g h

Already the position is dramatically different from anything that would arise in ordinary chess. Both white's and black's second moves have triggered the movement of staircases. In fact, Bc4 moves both the row 1 staircase and the column f staircase. The former carries the bishop on c1 around to h1, and the latter advances the f pawn. 2. ... c5 brings the black bishop into play, and gives the c pawn a three-square advance. At the same time it drives the white bishop backward. If white doesn't move this bishop, the next time this staircase moves the bishop will be carried around to c8, where it will be threatened by the black king.

3. Ba5+(c,3)  b6

    _ _ v _ _ _ _ v
8 >|r|n|_|k|q|b|n|r|
7  |o|_|_|o|_|o|o|o|
6  |_|o|b|_|_|_|_|_|<
5  |B|_|_|_|o|_|_|_|
4  |_|_|_|_|P|_|_|_|
3 >|P|_|o|_|_|_|_|_|
2  |P|P|P|P|_|_|P|P|
1  |R|N|Q|K|_|N|R|B|<
    ^         ^
    a b c d e f g h

The movement of the c staircase has dragged the c7 bishop forward to c6, leaving the king exposed. White's move also rotates the 3 staircase, which moves the f3 pawn to a3.

4. Bxc3(a)    Bxa4(c)

    _ _ v _ _ _ _ v
8 >|r|n|B|k|q|b|n|r|
7  |o|_|_|o|_|o|o|o|
6  |_|o|_|_|_|_|_|_|<
5  |_|_|_|_|o|_|_|_|
4  |b|_|_|_|P|_|_|_|
3 >|P|_|_|_|_|_|_|_|
2  |R|P|P|P|_|_|P|P|
1  |_|N|Q|K|_|N|R|B|<
    ^         ^
    a b c d e f g h

White captures the wandering black pawn with the bishop, but when black returns the favor, the white bishop finds itself in dire straits. Fortunately, white has a response.

5. Ba6(c,8)    Nf6

    _ _ v _ _ _ _ v
8 >|b|r|n|_|k|q|_|r|
7  |o|_|_|o|_|o|o|o|
6  |B|o|_|_|_|n|_|_|<
5  |_|_|_|_|o|_|_|_|
4  |b|_|_|_|P|_|_|_|
3 >|P|_|_|_|_|_|_|_|
2  |R|P|P|P|_|_|P|P|
1  |_|N|Q|K|_|N|R|B|<
    ^         ^
    a b c d e f g h

Ba6 moves black's rear row. Black would like to take the unprotected pawn at e4 with the a8 bishop -- but alas, that would bring the b8 rook to c8, where it would fall to the white bishop. Instead, black develops a knight. White follows suit. Black might like to play Bb7, but first the other bishop needs to be moved to safety:

6. Nc3      Bc6(a)

    _ _ v _ _ _ _ v
8 >|b|r|n|_|k|q|_|r|
7  |o|_|_|o|_|o|o|o|
6  |_|o|b|_|_|n|_|_|<
5  |_|_|_|_|o|_|_|_|
4  |P|_|_|_|P|_|_|_|
3 >|R|_|N|_|_|_|_|_|
2  |_|P|P|P|_|_|P|P|
1  |B|_|Q|K|_|N|R|B|<
    ^         ^
    a b c d e f g h

White's rook is now freed for action, but the bishop is not doing much good at a1. White's e4 pawn, meanwhile, is in some trouble. Next, white might try g3 or d3.

There may be any number of flaws in this opening; I don't claim to be a great chess player. But it should serve to illustrate the kinds of positions that arise in Escher Staircase.