By convention, the root of the decision tree is in the middle of the left hand side of the space available. The tree branches to the right so the leaves are in a single column along the right hand side. If a particular tree does not fit nicely into this model it may be modified to fit the available space. By convention, the nodes (including the root but excluding the leaves) are rectangular for decisions and circles if the branches are probabilistic. The leaves (called goals) are triangular. The advantage of the tree approach is that an entire complex system can be encoded but a particular path displays only those decisions that are needed for a particular task.
Decision trees have been used to diagnose mechanical failures in a variety of machines. Each node represents a test that the mechanic performs to know which exit branch to take. The leaf or goal represents the diagnostic of what is wrong. Similar decision trees are used in medicine. Decision trees have also been used by investors to decide how to invest money. In these trees, circles represent "high risk" and "low risk" options. The advantage of these decision trees is that all possible failures are addressed, but the failure for a particular system only involves the small set of symptoms that are relevant for the system at hand.
One of the major advantages of decision trees is that they are intuitive and easy to understand. An expert can code up a series of questions and observations that a novice can work through and get the same results that the expert would. For the expert, decision trees can give an overall picture of a complex topic built up by looking at one aspect at a time. A very real advantage of decision trees is the flexibility of application for this simple model.
Complex statistical and probabilistic situations can be analyzed using decision trees. Each node represents different possible results given what has happened on previous nodes in the path. Simple calculations give the probability of each node. If two goals are identical--for example, there are two ways to make a seven with two dice: four and three, or one and six--the probabilities are added. As with most decision trees, one advantage is that the trees are easy to code up for the expert--one branch at a time. For the user, the chief advantage is that only one path through the tree--that corresponds to a particular problem--needs to be considered.