Pie rule

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Player 1 plays first move as white
Player 2
Chessboard480.svg
a8 black rook
b8 black knight
c8 black bishop
d8 black queen
e8 black king
f8 black bishop
g8 black knight
h8 black rook
a7 black pawn
b7 black pawn
c7 black pawn
d7 black pawn
e7 black pawn
f7 black pawn
g7 black pawn
h7 black pawn
c3 white knight
a2 white pawn
b2 white pawn
c2 white pawn
d2 white pawn
e2 white pawn
f2 white pawn
g2 white pawn
h2 white pawn
a1 white rook
c1 white bishop
d1 white queen
e1 white king
f1 white bishop
g1 white knight
h1 white rook
Player 1
Player 2 lets move stand Player 2 switches places
Player 2
Chessboard480.svg
a8 black rook
b8 black knight
c8 black bishop
d8 black queen
e8 black king
f8 black bishop
g8 black knight
h8 black rook
a7 black pawn
b7 black pawn
c7 black pawn
d7 black pawn
e7 black pawn
f7 black pawn
g7 black pawn
h7 black pawn
c3 white knight
a2 white pawn
b2 white pawn
c2 white pawn
d2 white pawn
e2 white pawn
f2 white pawn
g2 white pawn
h2 white pawn
a1 white rook
c1 white bishop
d1 white queen
e1 white king
f1 white bishop
g1 white knight
h1 white rook
Player 1
Player 2
Chessboard480.svg
h1 white rook
g1 white knight
f1 white bishop
e1 white king
d1 white queen
c1 white bishop
a1 white rook
h2 white pawn
g2 white pawn
f2 white pawn
e2 white pawn
d2 white pawn
c2 white pawn
b2 white pawn
a2 white pawn
c3 white knight
h7 black pawn
g7 black pawn
f7 black pawn
e7 black pawn
d7 black pawn
c7 black pawn
b7 black pawn
a7 black pawn
h8 black rook
g8 black knight
f8 black bishop
e8 black king
d8 black queen
c8 black bishop
b8 black knight
a8 black rook
Player 1
Player 2 to play
as black, as before
Player 1 to play again,
now as black
A chess game using the pie rule, Player 2's options in bold

The pie rule, sometimes referred to as the swap rule, is a rule used to balance abstract strategy games where a first-move advantage has been demonstrated. After the first move is made in a game that uses the pie rule, the second player has one of two options:

  1. Letting the move stand, in which case the second player remains the second player and moves immediately, or
  2. Switching places, in which case the second player becomes the first-moving player, and the "new" second player then makes their "first" move. (I.e., the game proceeds from the opening move already made, but with roles reversed.)

The pie rule's use was first reported in 1909 for a game in the Mancala family.[1] Among modern games, Hex uses this rule.[2] Twixt in tournament play uses a swap rule.[3] The rule can be applied to other games which are otherwise solved for one player, such as Tablut.[4]

The rule gets its name from the divide and choose method of ensuring fairness in the division of a pie between two people; one person cuts the pie in half, then the other person chooses which half to select to eat. The person cutting the pie, knowing the other person will choose the larger piece, will make as equal a division as possible.

This rule acts as a normalization factor in games where there may be a first-move advantage. In a game which cannot end in a draw, such as Hex, the pie rule theoretically gives the second player a win (since one of the players must have a winning strategy after the first move, and the second player can choose to be this player), but the practical result is that the first player will choose a move neither too strong nor too weak, and the second player will have to decide whether switching places is worth the first-move advantage.

Use for determining komi in Go[edit]

In Go, one player can choose the amount of komi and the other player decides whether to accept that or switch colors with the other player. In the long run, this leads players to choose fair komi amounts because if they choose a Komi that is too advantageous, the other player can just choose to play White and take advantage of that high komi.

References[edit]

  1. ^ Parker, Henry (1909). Ancient Ceylon: An Account of the Aborigines and of Part of the Early Civilisation. London: Luzac & Co. pp. 601–02. LCCN 81-909073. 
  2. ^ Browne, Cameron. Hex Strategy: Making the Right Connections. ISBN 1-56881-117-9
  3. ^ Mind Sports Olympiad Twixt page http://www.boardability.com/game.php?id=twixt
  4. ^ Schmittberger, R. Wayne (1992). New Rules for Classic Games. John Wiley & Sons Inc. ISBN 978-0471536215.