I only now made the connection that Sauron lost because he fell prey to the Typical Mind Fallacy (assuming that everyone’s mind works the way your own does). Gandalf in the book version of The Two Towers:
The Enemy, of course, has long known that the Ring is abroad, and that it is borne by a hobbit. He knows now the number of our Company that set out from Rivendell, and the kind of each of us. But he does not yet perceive our purpose clearly. He supposes that we were all going to Minas Tirith; for that is what he would himself have done in our place. And according to his wisdom it would have been a heavy stroke against his power.
Indeed he is in great fear, not knowing what mighty one may suddenly appear, wielding the Ring, and assailing him with war, seeking to cast him down and take his place. That we should wish to cast him down and have no one in his place is not a thought that occurs to his mind. That we should try to destroy the Ring itself has not yet entered into his darkest dream. In which no doubt you will see our good fortune and our hope. For imagining war he has let loose war, believing that he has no time to waste; for he that strikes the first blow, if he strikes it hard enough, may need to strike no more. So the forces that he has long been preparing he is now setting in motion, sooner than he intended. Wise fool. For if he had used all his power to guard Mordor, so that none could enter, and bent all his guile to the hunting of the Ring, then indeed hope would have faded: neither Ring nor Bearer could long have eluded him.
I only now made the connection that Sauron lost because he fell prey to the Typical Mind Fallacy (assuming that everyone’s mind works the way your own does). Gandalf in the book version of The Two Towers: