Compare Two Choices - Decision Trees: Expected Value, Step by Step

A decision node chooses the branch with the best folded-back expected value.

highlighted = computed this step

Small EV

The Small branch folds back to $35. Motivation: compute every branch before choosing.

EV(\text{Small})=\$35

Compare values

Build has $50 and Small has $35. The decision is based on values, not on the largest single payoff.

\$50>\$35

Decision gap

The exact gap is $15. Interpretation: that is the expected-value advantage of Build in this pinned tree.

\text{gap}=\$15

Choice honesty

The comparison is only as honest as the input probabilities and payoffs. The probabilities and dollar payoffs are assumed inputs. This book folds back a known decision tree; it does not learn probabilities or prove the payoffs will occur.

\text{assumed inputs, exact comparison}