| Player 1 plays first move as White | ||
| Player 1 < | -- "chess diagram" has hard-coded 0.5em bottom margin -->Player 2 | |
|---|---|---|
| ↙ | ↘ | |
| Player 2 lets move stand | Player 2 switches places | |
| Player 1 Player 2 | Player 1 Player 2 | |
| Player 2 to play as Black, as before | Player 1 to play again, now as Black | |
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 must select one of two options:
Depending on the game, there may be two ways to implement switching places.
The use of pie rule 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] In Meridians, the first player places 2 stones on the board before the second player chooses the color. The rule can be applied to other games which are otherwise solved for one player, such as Gomoku or Tablut.[4]
The rule gets its name from the divide and choose method of ensuring fairness in when dividing a pie between two people: one person cuts the pie in half, then the other person chooses which half to eat. The person cutting the pie, knowing that 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 games that 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.
In Go, one player can choose the amount of komi. (These are the points given to the second player as compensation for not going first.) The other player then decides whether to accept that or switch colors with the other player. 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.[5]