The pie rule, sometimes referred to as the swap rule, is a meta-rule used to balance abstract strategy board games. Its use has been first reported in 1909 for a game from the Mancala

Mancala

Mancala is a family of board games played around the world, sometimes called "sowing" games, or "count-and-capture" games, which describes the game-play. Mancala games play a role in many African and some Asian societies comparable to that of chess in the West, or the game of Go in Eastern Asia...

 family. Among recent games, Hex uses this rule. Twixt

TwixT

TwixT is a two-player abstract strategy game invented by Alex Randolph. It is a member of the connection game family, along with games such as Hex, Havannah, Y, PÜNCT and *Star...

 in tournament play uses a swap rule.

The rule can be stated as follows:

• After the first move is made, the second player has the option of either:
  • Letting the move stand, in which case he or she remains the second player and moves immediately, or
  • Switching places, in which case he or she is now the first player, and the "new" second player now makes his or her "first" move. Effectively, the second player becomes the first player; the game proceeds from that opening move with the newly reversed roles.

The rule gets its name from the divide and choose

Divide and choose

In problems of fair division, divide and choose is a two-party proportional envy-free allocation protocol. The protocol also works for dividing an undesirable, as in chore division....

 method of ensuring fairness in the division of pie between two people; one person cuts a pie in half, then the other person chooses which half to eat. The person cutting the pie, knowing the other person will choose the larger half for themselves, will make as fair a division as possible.

This rule acts as a normalisation 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 the first move advantage is worth it.

Use for determining Komi in Go

In Go

Go (board game)

Go , is an ancient board game for two players that originated in China more than 2,000 years ago...

, one player can choose the amount of Komi

Komidashi

in the game of Go are points added to the score of the player with the white stones as compensation for playing second. Black's first move advantage is generally considered to equal somewhere between 5 and 7 points by the end of the game. Standard komi is 6.5 points under the Japanese and Korean...

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.