Pie rule

From Wikimanqala

The pie rule, sometimes referred to as the swap rule, is a metarule 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

The pie rule is a fixed rule in 55Stones, but 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, although a good computer program will beat you anyway. If kalah is combined with the pie rule, however, the game becomes well-balanced. Other mancala games may also be saved for serious play by this metarule.

There are several other ways to balance a mancala game:

• In Indonesia and the Philippines, there are several games, e.g. congkak and sungka, in which both players perform their first move simultaneously. This rule can only work in multi-lap games with a shared distribution cycle.
• As in the Japanese game of go the disadvantaged player can receive a number of points beforehand to make the game fair (called komi). This is only possible in Mancala games which have point-scoring.