# If a decision tree already has very low entropy, do we still need a random forest

I need some help understanding the concept of random forests. As I understand, when I make a decision tree, I carefully select each node so as to maximize the information gain and minimize the entropy, i.e each node should result in a higher information gain than its parent node.

If that is true, then the decision tree is already the best possible learner. Why do I need to combine it with other trees that may not be as good and then take a vote?

If I created the tree to maximize the information gain, then this is already the 'best' model.

I would understand the need for a random forest if I created 10 decision trees by randomly selecting the nodes to split on.

• The gist of it is that you bootstrap your data for each tree and then build a decision tree only using $m$ randomly-selected features at a time, where $m$ is a training parameter. Then select a new bootstrap sample for your next tree and so on. (This is discussed at length in ESL.) – Sycorax Sep 24 '15 at 19:00