Now, suppose your friend offered you the opportunity to play the game presented in the previous section or simply accept $40 cash. What should you do?
Playing the game is worth $50, which is more valuable than $40, so you should play the game. This decision can be illustrated as follows:
This diagram contains two new nodes: Root and Accept Cash.
Note that Root is presented slightly differently from Play Game. Root is followed by a square, rather than a circle, and there are no outcome probabilities on the branches leading from Root. Furthermore, the value of the node Root is not a weighted average of option values, but is exactly equal to the value of only one of the options.
Root is called a decision node. Play Game is called an event node. All other nodes are called end nodes. At a decision node, you get to pick which path you want to take. Being a rational decision-maker, you would choose the path with the highest value. Therefore, the value of a decision node is equal to the value of the best option branching from the node. In the example above, the best option is to play the game, which has a value of $50, so the value of the decision node is also $50. The branch labeled Accept Cash is marked with a double slash to indicate that you would not choose this option; it has been pruned from the tree.
The diagram above is called a decision tree. Decision trees map all options and potential consequences in a manner that makes it easy to understand and communicate the situation you face. As you move from left to right in the tree, you generally move forward in time. The root node is where you are now and immediately branches off into all options from which you can choose. What might happen as a result of choosing each option is illustrated as additional branches.
Note that this tree has five nodes, not two. Because the tree is displayed without node boxes, it is a common mistake to refer to the junction points (square or circle) as nodes. In fact, these are just symbols that are appended to the back of each node. Keep in mind that Win, Lose, and Accept Cash are also nodes. They are end nodes and include a triangle symbol.