Pairing strategy

It is based on dividing the positions on the game-board into disjoint pairs.

A pairing-strategy for Maker requires a set of element-pairs such that:[1]: 119 Whenever Breaker picks an element of a pair, Maker picks the other element of the same pair.

As an example, consider a game-board containing all vertices in a perfect binary tree except the root.

A pairing-strategy for Breaker requires a set of element-pairs such that: Whenever Maker picks an element of a pair, Breaker picks the other element of the same pair.

Another simple case when Breaker has a pairing-strategy is when all winning-sets are pairwise-disjoint and their size is at least 2.