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Decision Tree Maker

Branch a decision into chance and choice nodes, attach values and probabilities, and let the tree roll back the expected value for each path.

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Start from a real example

Pick one and change it to fit. Everything stays on this device. Nothing is uploaded.

Expected value: $0

Drag a node onto another to move that branch

Select a node to edit it, or to add a branch after it.

Worth fixing

  • Nothing to calculate yet. Add the first choice after the root.

Frequently asked questions

The questions people actually ask about this document.

What is a decision tree?
A map of a choice and everything that could follow it, with a number at the end of each path. Squares are choices you make, circles are things that happen to you, and the arithmetic rolls value back from the far end to tell you what each option is worth before you commit to it.
What is the difference between a square and a circle?
A square is a decision: you pick, so it is worth the best branch available from it. A circle is a chance event: the world picks, so it is worth the probability-weighted average of its branches. Getting these the wrong way round is the most common mistake in a tree, and it inflates the answer: averaging what you would have chosen, or choosing what you can only average.
Where do the probabilities come from?
Usually from judgement, and that is fine as long as it is written down. A number you can argue about beats a feeling you cannot. If you have base rates (past projects that overran, historical win rates), start there. If you do not, put in your honest guess and then use the tree backwards: ask how far the guess would have to move before the recommendation changes.
Is expected value always the right thing to maximise?
No, and this is the honest limit of the method. Expected value assumes you can run the decision many times and average out. For a one-off bet that could end the company, the option with the higher expected value can still be the wrong one, because you do not get a second go. Use the tree to see the spread, not only the average, and refuse ruin regardless of what the number says.
Why put costs on the branches rather than in the outcomes?
Because a cost you pay to take an option is paid whatever happens afterwards. Putting it on the branch charges it once, on every path that runs through it. Folding it into each outcome instead means repeating it in several places, and it stops being obvious when one option is expensive simply to attempt.
How big should a decision tree be?
Smaller than you expect. Two or three decisions deep is usually the limit of what anyone will read, and precision past that is false: the probabilities four layers down are guesses multiplied by guesses. If the tree will not fit on a screen, the question is probably two decisions that should be drawn separately.
When should I use this instead of a decision matrix?
Use a tree when the options lead to uncertain outcomes and the question is what each is worth. Use a weighted decision matrix when the options are known quantities and the question is which best fits your criteria. Choosing a vendor from a shortlist is a matrix. Deciding whether to build, buy or wait is a tree.
How do I tell whether the answer is fragile?
Change one number and watch the recommendation. If a five-point move in one probability flips the choice, the tree is telling you the options are close and the extra work belongs in sharpening that estimate. If you can swing the numbers a long way without the answer moving, you can stop analysing and decide.

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