To simplify things, there are actually a couple of V1 options available - Balanced and Optimized V1.
Balanced V1 is when accelerate stop equals accelerate go. This is based on the assumption that the clearway and stopway are of equal usuable distances. In reality this may not always be the case. However, this is the speed that we will obtain from the AA charts or FMC.
So if a balanced V1 is used, the aircraft's take off performance cannot be optimized for the given day's condition. Therefore an Optimized V1 should be utilized if available.
Optimized V1 takes into account the the actual lengths of the clearway and stopway should they be of unequal distances. The V1 is thus 'unbalanced' in this sense. As FE Hoppy has pointed out if there is a stopway with no clearway, the stopping distance is greater hence V1 can be increased.
Vice versa if there is a clearway with no stopway, the V1 can be unbalanced to provide a lower V1.
On the 777, the V1 provided by the EFB is an Optimized V1. At least thats how the EFB was configured for the operator I'm working with.