Each time we pick a decision variable (by some branching heuristic), we also need to choose its polarity. This page is about some efficient strategies of doing it.
A simple strategy is to always pick True value of a variable (or always False).
However, on practice this strategy is not as effective as advanced ones.
Another more effective approach is to pick polarity randomly. It's a kind of random, but this method can be rather effective in practice.
The idea of this heuristic is to store last assigned polarity for each variable in a
corresponding array called polarity. And when we need to choose it,
we just take value from the array.
More about phase saving can be found here
(in the 5-th section)