Pie rule

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The pie rule, sometimes referred to as the swap rule, is a meta-rule commonly used in abstract strategy board games like Hex and Havannah. It 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; since Hex has a proof for a first-player win, the pie rule technically gives the second player a win (depending on their choice of switching or not), 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.

The game of Orbit uses a "refined" pie rule, which technically has the "real" pie rule as a subset; like Hex being a subset of Y, however, the "refined" pie rule complicates matters considerably. The first player makes a set number of moves (3 in this case), but since Orbit allows passing, the first player could just play 1 move instead, as in the simplest pie rule. See also Renju rules.

[edit] Use for determining Komi in Go

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.