Rollback

Rollback the Tree

Rollback folds a tree from payoff leaves to the root, one visible step at a time.

highlighted = computed this step

Work from leaves

Rollback works from the payoff leaves back toward the root. Motivation: no choice can be compared until the future branches have values.

leaves→root\text{leaves}\rightarrow\text{root}
RollbackFold chance nodes first, then fold the decision node.rollback resultHigh p=1/2Low p=1/2High p=1/2Low p=1/2Build chosenSmallPayoff$120Payoff$-20ChanceEV $50Payoff$40Payoff$30ChanceEV $35DecisionEV $50

Chance first

Each chance node becomes one expected value. The visual keeps the role label Chance next to that computed value.

chance node→EV\text{chance node}\rightarrow EV
RollbackFold chance nodes first, then fold the decision node.rollback resultHigh p=1/2Low p=1/2High p=1/2Low p=1/2Build chosenSmallPayoff$120Payoff$-20ChanceEV $50Payoff$40Payoff$30ChanceEV $35DecisionEV $50

Decision second

The decision node keeps Build, because its folded-back value is largest.

chosen branch=Build\text{chosen branch}=\text{Build}
RollbackFold chance nodes first, then fold the decision node.rollback resultHigh p=1/2Low p=1/2High p=1/2Low p=1/2Build chosenSmallPayoff$120Payoff$-20ChanceEV $50Payoff$40Payoff$30ChanceEV $35DecisionEV $50

Root value

The tree value at the root is $50. Interpretation: this is the expected value before demand is known.

tree value=$50\text{tree value}=\$50
RollbackFold chance nodes first, then fold the decision node.rollback resultHigh p=1/2Low p=1/2High p=1/2Low p=1/2Build chosenSmallPayoff$120Payoff$-20ChanceEV $50Payoff$40Payoff$30ChanceEV $35DecisionEV $50