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 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 interest 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; 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.