Contents:

RANDOMIZED INITIAL POSITIONS IN CHESS
FISCHER RANDOM
RANDOMIZED INITIAL POSITIONS WITHOUT A COMPUTER


RANDOMIZED INITIAL POSITIONS IN CHESS

Zork supports randomized initial positions as well as the familiar RNBQKBNR starting position.  It also supports a variant of randomization proposed by Former World Champion Robert J. Fischer.  In RJF's variant, Zork allows you to drop the King on a Rook to indicate castling, since dropping it on the to-square can be ambiguous.

When the initial position is randomized, the men all begin on the usual ranks, but the placement of the back-rank pieces is selected at random.  The randomization algorithm is described below under "Random Initial Positions without a Computer".  The Bishops are always on opposite colors, of course.  The King's Leap is available instead of Castling.

The King's Leap is, in essence, Castling without the Rook.  Once in a game, the King may move two squares to either side.  As with Castling, the King cannot leap if he if he has already made a move, if he is in Check or would move across Check, or if the square to which he is leaping is already occupied.  But note this difference:  if one of his own pieces occupies the adjacent square, the King can jump over it.  Thus a Rook trapped away from the center can be released by moving it next to the King, and then leaping.

The Leap gives the King an additional method for getting out of trouble.  Castling originated as a variant of the King's Leap some five centuries ago, when RNBQKBNR was the only initial position.  Castling serves two additional purposes: moving the King away from the center, and getting the Rook past the King and into the center.  When the King and Rooks may begin on any back-rank square, it is impractical for the Rook to participate in the King's Leap.  It is also not very important, since the two additional purposes served by Castling frequently do not occur.

The variety of opening positions gives randomized chess its distinctive quality.  Opening theory becomes obsolete.  The players must rely on their own wits from the first move.  It is a big shock at first, but then you begin to enjoy the liberation from the massive accretions of opening theory, the freedom to use your imagination, to create your own gambits and opening strategies from the beginning in every game.


FISCHER RANDOM

Former World Champion Robert J. Fischer proposed a variant of randomization that limited the possible positions to the ones in which the King is nearer the center and the Rooks are more likely to be blocked from the center by the King.  The essence of his proposal is a goofy new castling rule with the following characteristics:

1) The King might move all the way from b1 to g1.  This is a move suitable for Fairy Chess, but not for real chess.
2) The King might end up nearer to the center than before castling, and the Rook might move farther from the center.
3) There are no magic squares in chess; RJF's castling defines c1 and g1 as magic squares.  Castling is a move by the King, two squares in either direction, not a move to a magic square.

For this, RJF threw away most of the possible positions and thus most of the variety of randomized chess.  Zork thinks he was distracted by the notion of defining a Castling rule so that Castling could continue to work "the same" -- although he did not succeed in this.  In any case, Castling was tailored for a specific non-randomized initial position.  When there are 5760 possible initial positions, it is silly to warp the rules with one initial position in mind.  The simple and obvious (and traditional) King's Leap remains the best.

Despite her preference for Classical Random, Zork has participated in the IECC Fischer Random event and recommends it to all chessplayers.

The randomization procedure for Fischer Random is not the same as the one given below.  Special handling is needed to arrange the King and Rooks properly, and four pebbles are needed for the Rooks.  Zork incorporated the algorithm for Fischer Random with the help of the Chess Variant Pages,

  http://www.cs.ruu.nl/~hansb/d.chessvar/Gindex.html

Under the heading "Chess Variants with Unusual Equipment", select "Different opening setups".  This will take you to a page with several Fischer Random links.


RANDOMIZED INITIAL POSITIONS WITHOUT A COMPUTER

There are millions of chess sets out there, and few of them have dice in the box.  Randomization is accomplished without adding any pieces to the standard chess set.  Whether you are at home, in Yosemite National Park, or on Padre Island, you can select an initial position with materials readily at hand.  All you need is a reasonably flat two-sided object.  The kind of flat rock you might pick up to skip across a pond, a sand dollar found on the beach, a car key, a piece of wood or plastic... even a coin would do.

After randomizing the pieces, place a pebble next to the Kings, to avoid disputes over where they started out.  The first time a King moves, toss away the pebble.

The randomization procedure is accomplished by placing each piece on the board in succession.  Bishops are placed first because they have the additional requirement of opposite colors.  A final coin toss determines whether the two sides will be a mirror image of each other, or whether they will be placed in opposite order.

Each piece in succession is placed on the first unoccupied square nearest the a-file.  Then the "coin" is flipped:

  once, if only one square remains unoccupied
  twice, if two or three squares remain unoccupied
  three times, if four or five squares remain unoccupied

With each coin toss, if the result is "heads", the piece is moved towards the h-file:

  two unoccupied squares
    if there is another coin toss for this piece
  one unoccupied square
    if this is the last or only coin toss for this piece

On the last coin toss for a piece, it may be that there are no more unoccupied squares nearer the h-file.  In this case, the piece moves one unoccupied square back towards the a-file.

To clear up any ambiguities in this description, here is the procedure in detail:

 Place a Bishop at a1
   heads on first toss:
     move two black squares toward h1
   heads on second toss:
     move one black square toward h1
 Place a Bishop at b1
   heads on first toss:
     move two white squares toward h1
   heads on second toss:
     move one white square toward h1
 Place a Knight on the unoccupied square nearest a1
   heads on first toss:
     move two unoccupied squares toward h1
   heads on second toss:
     move two unoccupied squares toward h1
   heads on third toss:
     move one unoccupied square toward h1
 Place a Knight on the unoccupied square nearest a1
   heads on first toss:
     move two unoccupied squares toward h1
   heads on second toss:
     move two unoccupied squares toward h1
   heads on third toss:
     move one unoccupied square,
       toward a1 if necessary
 Place a Rook on the unoccupied square nearest a1
   heads on first toss:
     move two unoccupied squares toward h1
   heads on second toss:
     move one unoccupied square toward h1
 Place a Rook on the unoccupied square nearest a1
   heads on first toss:
     move two unoccupied squares toward h1
   heads on second toss:
     move one unoccupied square,
       toward a1 if necessary
 Place the Queen on the unoccupied square nearest a1
   heads on only toss:
     move to the other unoccupied square
   the King now takes the last unoccupied square
 
 Final toss to set up the Black pieces:
   heads:  mirror image of the White pieces
   tails:  reverse order to the White pieces

This procedure is based on the requirement mentioned earlier, the use of an object of convenience; and to maximize simplicity.  A uniform distribution of probabilities is not a requirement; some initial positions have a higher probability than others.  For example, the second Knight is less likely to end up on the corner square h1.  The position can occur, but will not occur as often.
