In Uncertainty, all of the pieces start out as pawns. They acquire their distinct identities during the course of the game. Uncertainty can be played on many different boards, using different sets of pieces. Here are my suggestions for how it might be played on a normal board, on a 10x12 torus, on my three-dimensional Five Up board, and on a 6x6x6 hypertorus.
Unlike normal pawns, the pawns in Uncertainty exhibit no directional bias. On a two-dimensional board, they can make non-capturing moves of exactly one square vertically or horizontally in any direction, and they capture by moving one square diagonally in any direction. There is no pawn promotion in the usual sense, and no initial double move. On a 3D board, pawns can make non-capturing moves of exactly one cell in any of the orthogonal directions, and they capture by moving exactly one cell on 2D diagonals within any plane, but not on 3D diagonals.
Each player begins the game with a full complement of non-pawn pieces in reserve. Each time a pawn is moved, it can (optionally, at the player's discretion) be replaced after the move with one of the pieces remaining in the reserve. Pawns replaced in this manner are retired from play, and take no further part in the game. In a sense, the pawn is like a quantum probability cloud that has now collapsed into an actual particle -- hence the name of the game. Once a pawn takes on the identity of a non-pawn piece, it retains that identity until the end of the game (or until it is captured). Pieces that are captured are removed from play in the normal manner; they don't return to the player's stash of not-yet-assigned pieces.
A pawn is not required to be transformed the first, second, or nth time it is moved, nor is it required to be transformed when it reaches any particular square. Transformations can occur after either capturing or non-capturing moves. Transformations can be performed throughout the game, until the player's entire complement of reserve pieces has been placed in play (or until the player runs out of pawns or is checkmated). If a player loses all of his or her pawns before placing all of the pieces in play, those which have not yet been placed in play are simply lost. A pawn can only be transformed immediately after it is moved, and on the square to which it is moved; it cannot be transformed in place, nor can it transform and then move (using its new movement power as a piece) in the same turn.
If a board is being used on which the white and black squares define distinct diagonal grids, once a player has created a bishop on a white square, the other bishop must be put in play on a black square (or vice-versa).
The goal of play is to checkmate the enemy king. So why would you convert any of your pawns to a king at all, if you can't lose until you do so? Because you can't capture enemy pieces until you have a king, that's why. I would expect that gameplay would proceed through two phases. In the first phase, neither player has a king, and both are free to jockey for position without worrying about imminent capture. When one player puts his or her king in play, however, the other will find it necessary to do the same immediately; failure to do so would lead to a catastrophic loss of material. This begins the second phase of the game.
At the point when the players have kings, they may still have pieces that have not yet been put in play. Pawns continue to be converted to these pieces in the same manner as before.
My guess is that the question of when to put your king in play will be a delicate one. Once the position of your king is known, your opponent can transform pawns into pieces in such a way as to build up the strongest possible attack against it, so waiting has some value. On the other hand, there's an advantage in being the first to place your king in play, because on the next move you'll be able to make the first capture of the game.
On a standard chessboard, each player begins the game with 16 pawns, in the setup shown in Figure 1, and the usual complement of non-pawn pieces.
Figure 1. The opening setup for Uncertainty on a standard chessboard. Some of the pawns in the second row are advanced to allow pawns in the rear row to move (and then be transformed) without the necessity of clearing the way for them. To make the ASCII diagram easier to understand, I've abbreviated all of the black pawns with a lower-case 'q'.
_ _ _ _ _ _ _ _ |q|q|q|q|q|q|q|q| |q|_|q|_|q|_|q|_| |_|q|_|q|_|q|_|q| |_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_| |_|P|_|P|_|P|_|P| |P|_|P|_|P|_|P|_| |P|P|P|P|P|P|P|P|
On a Torus
The inspiration for Uncertainty lay in the fact that having weak, undefined pieces that can't initially be captured makes it easier to create an opening setup for pieces on a torus of reasonable size. On a toroidal board, the top and bottom edges wrap around to one another, as do the left and right sides. There are, in effect, no corners and no edges. Figure 2 shows one possible opening setup. Each player begins with 24 pawns, which would logically transform into 12 pieces and 12 pawns. I'd suggest that this variant be played with a king, queen, marshall and cardinal (familiar from many chess variants -- the marshall moves like either a rook or knight, the cardinal like either a bishop or knight), two rooks, and three each of knights and bishops.
Figure 2. A 10x12 toroidal board set up for a game of Uncertainty. Here again, interior spaces have been left to allow pawns to be transformed without being exposed to attack.
_ _ _ _ _ _ _ _ _ _ |_|_|_|_|_|_|_|_|_|_| |_|q|q|q|_|_|_|_|_|_| |q|q|q|q|q|_|_|_|_|_| |q|q|_|q|q|_|_|_|_|_| |q|q|_|q|q|_|_|_|_|_| |q|q|q|q|q|_|_|_|_|_| |_|q|q|q|_|_|P|P|P|_| |_|_|_|_|_|P|P|P|P|P| |_|_|_|_|_|P|P|_|P|P| |_|_|_|_|_|P|P|_|P|P| |_|_|_|_|_|P|P|P|P|P| |_|_|_|_|_|_|P|P|P|_|
Five Up Board
Uncertainty can be played using the board and pieces of Five Up. The opening setup is shown in Figure 3.
Figure 3. The opening setup for Uncertainty on a Five Up board consists of 20 pawns in each army. The pieces are exactly the same as those in Five Up.
_ _ _ _ _ |q|q|q|q|q| |_|q|_|q|_| |q|_|q|_|q| |_|_|_|_|_| |_|_|_|_|_| _ _ _ _ _ |q|_|q|_|q| |q|q|q|q|q| |_|q|_|q|_| |_|_|_|_|_| |_|_|_|_|_| _ _ _ _ _ |_|_|_|_|_| |_|_|_|_|_| |_|_|_|_|_| |_|_|_|_|_| |_|_|_|_|_| _ _ _ _ _ |_|_|_|_|_| |_|_|_|_|_| |_|p|_|p|_| |P|P|P|P|P| |P|_|P|_|P| _ _ _ _ _ |_|_|_|_|_| |_|_|_|_|_| |P|_|P|_|P| |_|P|_|P|_| |P|P|P|P|P|
On a Hypertorus
A 6x6x6 hypertorus, it seems to me, is probably the smallest hypertorus on which a game of chess can reasonably be played. On the board shown in Figure 4, the upper and lower edges of each layer wrap around, as do the left and right edges. In addition, the top and bottom layers are touching at every point, so that a piece can travel up from the top layer and arrive on the bottom layer.
Each player starts the game with 26 pawns. I'd suggest that 15 of these be converted into pieces during the game. Borrowing from and expanding slightly on the set of pieces used in Five Up, I'd suggest that each player have a king, a queen, two guards, two wizards, and three each of rooks, bishops, and knights.
Figure 4. On a 6x6x6 hypertorus, Uncertainty pawns can be set up this way. Because the top layer wraps around to the bottom, the white pawns (p) and black pawns (q) are in symmetrical positions with respect to one another.
_ _ _ _ _ _ |_|_|_|_|_|_| |_|_|_|_|_|_| |_|_|_|_|_|_| |_|_|_|q|q|q| |_|_|_|q|_|q| |_|_|_|q|q|q| _ _ _ _ _ _ |_|_|_|_|_|_| |_|_|_|_|_|_| |_|_|_|_|_|_| |_|_|_|q|q|q| |_|_|_|q|_|q| |_|_|_|q|q|q| _ _ _ _ _ _ |_|p|_|_|_|_| |p|p|p|_|_|_| |_|p|_|_|_|_| |_|_|_|_|q|_| |_|_|_|q|q|q| |_|_|_|_|q|_| _ _ _ _ _ _ |p|p|p|_|_|_| |p|_|p|_|_|_| |p|p|p|_|_|_| |_|_|_|_|_|_| |_|_|_|_|_|_| |_|_|_|_|_|_| _ _ _ _ _ _ |p|p|p|_|_|_| |p|_|p|_|_|_| |p|p|p|_|_|_| |_|_|_|_|_|_| |_|_|_|_|_|_| |_|_|_|_|_|_| _ _ _ _ _ _ |_|p|_|_|_|_| |p|p|p|_|_|_| |_|p|_|_|_|_| |_|_|_|_|q|_| |_|_|_|q|q|q| |_|_|_|_|q|_|
A Possible Sub-Variant
Uncertainty could be played with a rule that until the kings are placed in play, the players can transform any piece already on the board into any piece not yet on the board, in the same manner in which a pawn is transformed into a piece -- on the square to which the piece is moved, immediately after it is moved. A piece transformed in this way returns to the reserve set, and can be returned to the board later in another transformation. Once a player's king is on the board, however, the player can only transform pawns into pieces. Transforming pieces into other pieces is no longer allowed. The advantage of this idea is that it increases mobility during the first phase of the game, making it easier to achieve a desired setup or adjust to the opponent's evolving setup.
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