You want to move along a route that is slightly different than normal, but also gives you a view of your normal route. This allows you to look for the person looking for you. Very few people play FPS games hunting, but some do, and if you play a game with people like that, it is far more intense. You are playing a chess match with one person, while chaos is going on around you.
The hunter will usually have an advantage, so to win more engagements, try to establish yourself as the hunter. Getting to a strong point first, and setting up your active ambush works, or going to a good hiding spot, and just waiting for the other player to pass in front of your sights keeps them off guard. Animals hunt in many different ways, you want to watch how different animals hunt, and use some of those patterns. Even watching a housecat go after a mouse is watching hunter and hunted.