Edge template IV2n
Red can connect both red stones to the bottom (i.e., Red does not have to choose which stone to connect). The proof of this property is relatively lengthy.
Note: edge template IV2l also has the property that Red can simultaneously connect both stones:
However, the following, which is "between" these two templates, does not have this property:
Here, with Blue to move first, Red can choose to connect either the left or the right stone, but cannot connect both. In fact, the following move by Blue forces Red to choose one side or the other.