Use a rubber band between the screw and screwdriver bit. Most of the time it will give you enough grip to pull out the screw or at the very least get it loosened. Use a screwdriver bit one size up from the actual head of the screw when using this technique. Don’t be shy in applying force on the screw while you slowly turn to the left.
How does this work you may ask? The rubber band fills in the backs of the screw head. So don't use a super thick rubber band but don’t use one that’s almost invisible either.