The Allies knew that reports on the buying up of Pas de Calais maps in Switzerland would reach Hitler, and this would have its own realistic logic. As for the Montgomery sightings in Gibraltar, little did the German agents know they were seeing a look-alike, a man trained to act like the general. In the end the picture the Allies painted was so real to Hitler that well into July he believed in it, long after D-Day had actually happened. Through such subtle deceptions they had compelled him to keep his forces dispersed—perhaps the decisive factor in the success of the invasion.