AND and OR rules

AND and OR are deduction rules that help build virtual connections and semi-connections. It allows to know how well two distant groups are connected.

AND

The AND rule states that for a given player (say Red), two of their pieces can be connected if it is their turn. In the example below, if Red is to play then she can connect the two pieces. The pieces are said to be connected weakly.

OR

The OR rule states that whoever turn it is, the pieces can be connected. Hence using the OR rule is a way to create virtual connections. The bridge is the most famous pattern involving the OR rule. In the example, even if it is Blue's turn, Red can maintain the connection because Blue cannot occupy both starred cells in one move.

Relations

Two not intersecting AND-connections make one OR-connection like in the bridge above. This is due to th fact that the opponent cannot counter both connection.

Two consecutive OR-connections make one AND-connection. If Red plays the star hexa then she has connected strongly the two extreme hexas.

External link

• Jack van Rijswijck.Search and evaluation in Hex. See paragraph 2.1.
• Anshelevich, Vadim V. A hierarichical approach to computer Hex. See paragraph 3.