Good strategy is concentrate on the center early on. Just try to move all the corner marbles closer to center and make sure nothing is stranded.
When you're down to 10, 11, or 12 marbles, then stop and think. Mentally visualize and work out all remaining possible combinations. If you've worked to move things closer to center odds are great at least one combination that gets it down to 1 peg will now exist, though it isn't absolute.