## Introduction

A decision tree helps you evaluate decisions in the face of uncertainty. Decision trees are relatively simple to design and communicate and can offer value even when many inputs are uncertain.

Read below for a couple of brief examples or go to Essy Tree to quickly and easily build and analyze decision trees online.

## A simple example

Imagine you can pick between two boxes, Box A and Box B. You get to keep whatever you find inside the box you choose. You know that Box A contains \$100 and Box B contains \$50. The decision tree would look like this: In decision trees, a square represents a decision and a triangle represents an outcome or payoff. In this case the decision is obvious. Box A contains more than Box B, so choose Box A. The blue line shows that Box A is the optimal decision. The strike marks show that Box B is not the optimal decision. The numbers in the gray boxes show the values at each node based on that decision.

## A more complex example

Now imagine that you don't know for certain what Box A contains: there's a 40% chance it contains \$100 and a 60% chance it contains nothing. Here the circle represents a chance or event node, showing the uncertainty in the outcomes that follow. The probabilities of events occurring (0.4 and 0.6) are labeled below the branches.

To solve this new tree, we need to calculate the expected value at the chance node. The expected value is the sum of the probabilities mutliplied by the payoffs:

Expected value = (0.4)(100) + (0.6)(0) = 40 + 0 = \$40. In this case your best bet is to choose Box B, since on average you'll get \$50 compared to an expected \$40 from Box A.

The above screen shots and calculations were created with Essy Tree software.