Probability
Decision Tree Expected Value Calculator
Calculate conditional and weighted branch values, gross and net tree expected value, branch-probability reconciliation, better-branch value, mixing loss, and break-even decision cost.
Conditional expected value of Branch A-
Conditional expected value of Branch B-
Probability-weighted Branch A value-
Probability-weighted Branch B value-
Gross tree expected value-
Net tree expected value after cost-
Entered branch probability total-
Absolute gap from 100%-
Higher conditional branch value-
Value gap versus always selecting better branch-
Maximum break-even decision cost-
Decision view
Two-stage decision tree with payoff leaves
Two-stage decision tree with payoff leavesThe root splits into Branch A and B, each branch splits again into success and failure leaves, and every edge carries its current probability before values reconcile to gross and net expected value.
Exact scenario comparisonProbability of Branch A (%) changes while all other entered assumptions remain constant.
| Probability of Branch A (%) | Conditional expected value of Branch A | Conditional expected value of Branch B | Probability-weighted Branch A value | Probability-weighted Branch B value | Gross tree expected value | Net tree expected value after cost | Entered branch probability total | Absolute gap from 100% | Higher conditional branch value | Value gap versus always selecting better branch | Maximum break-even decision cost |
|---|
How to use Decision Tree Expected Value Calculator
- Enter top-level Branch A and B probabilities.
- Enter conditional success probabilities and leaf values within each branch.
- Enter the shared decision cost and inspect probability reconciliation.
Calculator guide
Understanding Decision Tree Expected Value Calculator
A decision tree has two probability levels: the chance of entering a branch and the success/failure chance inside that branch. Calculating inside each branch first prevents conditional probabilities from being applied to the wrong base.
Detailed calculation process
Detailed two-stage expected-value calculation
The default tree has two top-level branches and two conditional payoff leaves within each branch.
General formula: EV_A=s_A V_AS+(1-s_A)V_AFEV_B=s_B V_BS+(1-s_B)V_BFEV_g=p_A EV_A+p_B EV_BEV_n=EV_g-C Leaf values are averaged conditionally first, then branch expected values are weighted at the root.
What each symbol means
Worked substitution with the default inputs
The two weighted branches sum to $67,425, and deducting the single $15,000 cost reproduces the $52,425 net tree value.
Worked situations
Practical examples
- Branch A combines a 70% chance of $120,000 with a 30% chance of -$35,000 before its 55% top-level weight is applied.
- A $15,000 shared cost is deducted once from the gross tree value, not once per leaf.
Better inputs
Useful tips
- Keep conditional and top-level probabilities distinct.
- Enter losses as negative leaf values.
- Investigate probability totals that do not equal 100% before using the result.
Before relying on the result
Limitations and common mistakes
- Expected value ignores risk preference, timing, financing, and tail concentration.
- Branches are modeled as mutually exclusive and collectively complete.
- Strategic flexibility and later decisions are not represented.
Reference
Key terms
- Conditional probability
- Probability of an outcome given that its parent branch occurred.
- Leaf value
- Payoff or loss at a terminal tree outcome.
- Expected value
- Probability-weighted average across mutually exclusive outcomes.
Important note
Resolve nonzero probability reconciliation gaps before treating net expected value as complete.
Frequently asked questions
Why can Branch B have a higher success payoff but lower conditional EV?
Its success probability and failure value may offset the larger payoff.
What if branch probabilities total 90%?
Ten percent of the decision space is missing, so the displayed gross value is incomplete.
Does the highest expected value always define the best decision?
Not when risk tolerance, timing, constraints, or irreversible consequences matter.