Manual Procedure for Generating Piece Placements

- Place all White Pawns on their usual squares.
- Throw a six-sided die and note the number of pips that turn up.
- Use this 'pip number' to determine piece placements according to the following table.
- Repeat for subsequent tables.
- Complete the array according to instructions following the last table.

Roll the die and place a white Bishop according to the following table:

PIPS | PIECE PLACEMENT |
---|---|

1 | White Bishop on a1 |

2 | White Bishop on c1 |

3 | White Bishop on e1 |

4 | White Bishop on g1 |

5 | Throw again using this table. |

6 | Throw again using this table. |

Roll the die and place the remaining white Bishop according to the following table:

PIPS | PIECE PLACEMENT |
---|---|

1 | White Bishop on b1 |

2 | White Bishop on d1 |

3 | White Bishop on f1 |

4 | White Bishop on h1 |

5 | Throw again using this table. |

6 | Throw again using this table. |

Roll the die and place the white Queen according to the following table:

PIPS | PIECE PLACEMENT |
---|---|

1 | White Queen on 1st empty square of 1st rank. |

2 | White Queen on 2nd empty square of 1st rank. |

3 | White Queen on 3rd empty square of 1st rank. |

4 | White Queen on 4th empty square of 1st rank. |

5 | White Queen on 5th empty square of 1st rank. |

6 | White Queen on 6th empty square of 1st rank. |

Roll the die and place a white Knight according to the following table:

PIPS | PIECE PLACEMENT |
---|---|

1 | White Knight on 1st empty square of 1st rank. |

2 | White Knight on 2nd empty square of 1st rank. |

3 | White Knight on 3rd empty square of 1st rank. |

4 | White Knight on 4th empty square of 1st rank. |

5 | White Knight on 5th empty square of 1st rank. |

6 | Throw again using this table. |

Roll the die and place the remaining white Knight according to the following table:

PIPS | PIECE PLACEMENT |
---|---|

1 | White Knight on 1st empty square of 1st rank. |

2 | White Knight on 2nd empty square of 1st rank. |

3 | White Knight on 3rd empty square of 1st rank. |

4 | White Knight on 4th empty square of 1st rank. |

5 | Throw again using this table. |

6 | Throw again using this table. |

Complete the array as follows:

- Place a White Rook on the 1st empty square of the 1st rank
- Place the White King on the 2nd empty square of the 1st rank
- Place the remaining White Rook on the 3rd empty square of the 1st rank.
- Place all black pieces equal-and-opposite the white pieces.

This procedure generates any of the 960 possible setups with equal chance; it is a good alternative to a computer-generated array. On the average, you will make 6.7 die rolls. (More complex tables which yield fewer die rolls are possible.) Another method is to use a Michael Staiff die, which is not strictly random, yet lessens the chance of a Knight being placed on a corner square.

I found a simpler procedure to set up Fischer Random Chess. It doesn't require computers, dice, or lookup tables:

- Put the eight white pieces in a bag. Draw them one by one and place them on squares a1, b1, ... h1.
- If the bishops are on the same color, look at the following pairs: a1-b1, c1-d1, and e1-f1. Swap the leftmost pair that contains a bishop.
- If the king is not between his rooks, swap the king with the closer rook.

This mention is indeed simpler than the one with dice. All 960 positions can be the result of this method. However, not all positions have the same probability to be generated. Mathematical analysis shows that positions with the bishops on a pair a1-b1, c1-d1, e1-f1, or g1-h1 actually have half the probability to be generated than the other positions.

Written by: Hans Bodlaender.

WWW page created: May 19, 2002. Last modified: November 7, 2002.