Deer get real nervous when something acts sneaky. If you walk at a steady pace looking ahead rather than looking all around, many deer will stand motionless and watch you walk by. I believe this is especially true with mature deer. I have walked 5 to 10 minutes ahead of my wife while hunting and had her see deer coming out of cover to sniff my trail. Both she and I have walked up on deer when we were crossing open fields in the dark. The last time I did this, the deer huffed at me so close that I tripped backing up and landed sitting down. My wife was with me and seemed to think this was very funny.
....exactly "they watch you walk by " or you get to see the flag as the wave bye bye ..i'd rather take my time and spot them first that way i at least get a crack at one !