You can also win if there are 3, 4, 5, 6, or 7 pearls. Most of those are unlikely to happen.

You have to make sure that you end up with one row with one pearl and one row with any number of pearls.

The main endgames seem to be 0-0-1-2, 0-0-2-2 and 0-1-2-3. The problem, though, is that you've lost way before you get to those points.

Lemme work some more.