A private loses to every officer, so it is tempting to treat it as expendable. That reading misses its special job: a private defeats a spy. Six privates create moving pockets of uncertainty that spies must respect.
Make the threat travel
Do not ask each private to survive. Ask whether its movement makes an adjacent enemy harder to classify. A private behind an officer can follow the officer's challenge and punish a spy that revealed itself. A private on a quiet file can also make an enemy officer hesitate, because the same hidden back might conceal a spy.
Challenge for information
A lost private can still narrow the field. If it falls to an enemy, you know that piece was not a spy at that moment. Use that fact carefully: the piece may be strong, but moving another private beside it still controls where an unseen spy can pass.
Keep one reserve
Early private trades can open lanes, yet spending all six leaves enemy spies with few natural predators. Preserve at least one private near the route to your flag. Its value rises as the board thins and hidden pieces become easier to track.