Teach decision analysis with the rollback shown
Textbook EMV trees with the rollback written out step by step. Free for students, no accounts needed.
The problem
Drawing the tree eats the lesson
Half the tutorial goes on boxes and arrows in a slide tool. Here the tree is a few lines of indented text and the picture draws itself.
Students see the answer, not the method
A spreadsheet gives a number. The rollback panel lists every chance node's weighted average and every decision node's best branch, in the order a student should work them.
Every problem needs a variant
Change one probability and the whole solution recomputes, so the same problem becomes a homework set, a quiz and a what-if discussion.
Drill or sell the lease?
The classic problem from Raiffa's Decision Analysis: drill now, sell the lease, or pay for a seismic test whose result changes the odds of striking oil. Payoffs are the gross revenue from the well; drilling costs 70,000 whatever it finds.
The rollback, step by step
- 1Drill now is a chance node. Its value is the probability-weighted average of its branches: 50% × 0 + 30% × 120,000 + 20% × 270,000 = 90,000.
- 2Drill is a chance node. Its value is the probability-weighted average of its branches: 73% × 0 + 22% × 120,000 + 5% × 270,000 = 39,900.
- 3No structure is a decision. You would pick the best branch: Drill = −30,100 (39,900 − 70,000 cost); Sell = 45,000. Best: Sell at 45,000.
- 4Drill is a chance node. Its value is the probability-weighted average of its branches: 43% × 0 + 34% × 120,000 + 23% × 270,000 = 102,900.
- 5Open structure is a decision. You would pick the best branch: Drill = 32,900 (102,900 − 70,000 cost); Sell = 45,000. Best: Sell at 45,000.
- 6Drill is a chance node. Its value is the probability-weighted average of its branches: 21% × 0 + 25% × 120,000 + 54% × 270,000 = 175,800.
- 7Closed structure is a decision. You would pick the best branch: Drill = 105,800 (175,800 − 70,000 cost); Sell = 45,000. Best: Drill at 105,800.
- 8Seismic test first is a chance node. Its value is the probability-weighted average of its branches: 41% × 45,000 + 35% × 45,000 + 24% × 105,800 = 59,592.
- 9Drill or sell the lease? is a decision. You would pick the best branch: Drill now = 20,000 (90,000 − 70,000 cost); Sell the lease = 45,000; Seismic test first = 49,592 (59,592 − 10,000 cost). Best: Seismic test first at 49,592.
- ✓So the whole decision is worth 49,592, and the recommendation is Seismic test first followed by Sell if No structure, Sell if Open structure, Drill if Closed structure.
Value of the test. With the test the decision is worth 59,592 before paying for it, against 45,000 for the best option without it. So the test is worth up to 14,592, and it costs 10,000.
Chance of a loss: 5%
Work the rollback from the leaves as the steps below do, then ask the class why the test is worth paying for when the well itself is not worth drilling blind. The answer, that information has value only if it can change the decision, is the whole course in one tree.
The outline behind this example
# Analytical: the classic oil lease problem
Drill or sell the lease?
Drill now (cost 70000)
Dry (p 0.5): 0
Wet (p 0.3): 120000
Soaking (p 0.2): 270000
Sell the lease: 45000
Seismic test first (cost 10000)
No structure (p 0.41)
Drill (cost 70000)
Dry (p 0.73): 0
Wet (p 0.22): 120000
Soaking (p 0.05): 270000
Sell: 45000
Open structure (p 0.35)
Drill (cost 70000)
Dry (p 0.43): 0
Wet (p 0.34): 120000
Soaking (p 0.23): 270000
Sell: 45000
Closed structure (p 0.24)
Drill (cost 70000)
Dry (p 0.21): 0
Wet (p 0.25): 120000
Soaking (p 0.54): 270000
Sell: 45000What you get
Rollback shown step by step
Every node's arithmetic written out in post-order, the way the textbook solves it.
The tree from text
Students type an outline; the diagram and the maths follow. No drawing.
Sensitivity as a live slider
Sweep a probability and watch the switch point, the moment the recommendation changes.
Value of information
Expected value of perfect information per chance node, and problems like this one that price a test.
Share a problem by link
The tree lives in the URL. Send a link and every student opens the same problem, no accounts.
Templates as problem sets
Seven worked examples to copy and change, from launch decisions to lawsuits.
How people use it
- 01
Lecture
Open the problem on the projector with the analysis closed, ask the class to predict the answer, then open the rollback panel and go through the steps.
- 02
Homework
Share a link to the tree with one number changed. Students submit their outline text; you paste it in and the answer checks itself.
- 03
Exam review
Sweep the probability of a closed structure and ask at what point the test stops being worth it. The sensitivity panel shows the exact figure.
Templates for this work
- Launch a product
Launch nationally, pilot first, or hold? A decision tree with the expected value of each option, the recommended choice and the demand level where the answer flips.
- Litigate or settle
Accept the settlement or go to court? A decision tree with the expected value of trial versus settlement and the win probability where it flips.
- Bid on a tender
Is the bid worth the cost of bidding? A decision tree with the win probability, the bid cost and the expected value of a full bid versus a light one.
All templates · How to make a decision tree · Expected value and decision trees
Questions
- Do students need an account?
- No. The tree lives in the link. An account is only needed to save trees to a list or to make them public under a name.
- Does it follow the textbook conventions?
- Squares are decisions, circles are chance nodes, probabilities sit on the branches and costs are subtracted along the path. The rollback panel writes each step out with the arithmetic.
- Can I license it for a course?
- Yes. A course licence is $299 per course per year. Email hello@decisionbranch.com with the course name and the number of students.
Start with the example, or your own decision.
The editor is free and needs no account. Describe the decision in a sentence and the AI builder drafts the tree.