The pie rule, sometimes referred to as the swap rule, is a metarule (or "game mutator") commonly used in many abstract strategy board games. It can be stated as follows:
After the first player makes their first move, the second player has the option of either:
- Letting the move stand, in which case they are the second player and move immediately, or
- Switching places, in which case they are now the first player, and the "new" second player now makes their "first" move. Effectively, the second player becomes the first player, and it is as if that move was theirs; the game proceeds from that opening move with the newly reversed roles.
The rule gets its name from the solution to the age-old problem of cutting a pie into slices. If you have someone you distrust (say, your younger sibling) cutting pieces of pie, how do you ensure that you get a piece that will satisfy you? The answer is similar to the one above: Let them cut two pieces which they feel are equal, and you get to pick which one you like. If they "cheat" and make one slice much larger than the other, you will obviously pick that one; it is in their best interests to cut two slices which are very close to the same size.
This rule acts as a normalisation factor in games where there may be a first-move advantage; if a game 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 Pie Rule in Mancala Games
It is also a standard rule in 55Stones, which is a modern game.
The pie rule can be applied to any mancala game which
- has a strong first-move advantage
- is played without simultaneous decision-making
if there is a first move which doesn't give any player a clear advantage.
Kalah is usually considered a children's game because the first move can be very strong. If, however, Kalah is combined with the pie rule, the game becomes well-balanced. Other mancala games may also be saved for serious play by this meta-rule.
There are several other ways to balance a mancala game:
- Simultaneous opening move: In some Indonesian and Filipino games (e.g. Congkak and Sungka) both players perform their first move simultaneously. This rule can only be applied to multi-lap games with a shared distribution cycle.
- Fixed komi: As in the Japanese game of Go the disadvantaged player receives a number of points called komi before the game actually starts. Of course, giving komi only works in games with point-scoring. The rule has been suggested in Afrika.
- Auction komi: Instead of prescribing a fixed komi, a tournament may instead use a system of bidding to determine the komi for each game. There are a number of ways in which this can be done. In one system, one player is given the right to choose the komi, and the other player then chooses whether to play first or second. In another system, the players bid against each other in a standard auction, the player who bids the most points chooses sides and gives that number of komi to his opponent.
A modified pie rule can also be used in Space Walk to prevent a move stealing strategy.
The Pie Rule in Other Games
The pie rule is best known in connection games such as Hex, TwixT and Havannah. 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 the game 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.
- Browne, C.
- Hex Strategy: Making the Right Connections. A K Peters, Ltd., Natick MA, USA 2000.
- Schmittberger, R. W.
- New Rules for Classic Games. Wiley, New York NY, USA 1992.