Pie Rule

The pie rule, sometimes referred to as the swap rule, is a rule used to balance abstract strategy board games in which a first-move advantage has been demonstrated. Its use has been first reported in 1909 for a game from the Mancala family. Among recent games, Hex uses this rule. Twixt 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 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.