Decision Trees

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name: decision-trees description: Decision tree analysis for complex decision-making across all domains. Use when user needs to evaluate multiple options with uncertain outcomes, assess risk/reward scenarios, or structure choices systematically. Applicable to business, investment, personal decisions, operations, career choices, product strategy, and any situation requiring structured evaluation. Triggers include decision tree, should I, what if, evaluate options, compare alternatives, risk analysis.

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Decision Trees — Structured Decision-Making

Decision tree analysis: a visual tool for making decisions with probabilities and expected value.

When to Use

✅ Good for:

Business decisions (investments, hiring, product launches)

Personal choices (career, relocation, purchases)

Trading & investing (position sizing, entry/exit)

Operational decisions (expansion, outsourcing)

Any situation with measurable consequences

❌ Not suitable for:

Decisions with true uncertainty (black swans)

Fast tactical choices

Purely emotional/ethical questions

Method

Decision tree = tree-like structure where:

Decision nodes (squares) — your actions

Chance nodes (circles) — random events

End nodes (triangles) — final outcomes

Process: 1. Define options — all possible actions 2. Define outcomes — what can happen after each action 3. Estimate probabilities — how likely is each outcome (0-100%) 4. Estimate values — utility/reward for each outcome (money, points, utility units) 5. Calculate EV — expected value = Σ (probability × value) 6. Choose — option with highest EV

Formula

EV = Σ (probability_i × value_i)

Example:

Outcome A: 70% probability, +$100 → 0.7 × 100 = $70

Outcome B: 30% probability, -$50 → 0.3 × (-50) = -$15

EV = $70 + (-$15) = $55

Classic Example (from Wikipedia)

Decision: Go to party or stay home?

Estimates:

Party: +9 utility (fun)

Home: +3 utility (comfort)

Carrying jacket unnecessarily: -2 utility

Being cold: -10 utility

Probability cold: 70%

Probability warm: 30%

Tree:

Decision
├─ Go to party
│  ├─ Take jacket
│  │  ├─ Cold (70%) → 9 utility (party)
│  │  └─ Warm (30%) → 9 - 2 = 7 utility (carried unnecessarily)
│  │  EV = 0.7 × 9 + 0.3 × 7 = 8.4
│  └─ Don't take jacket
│     ├─ Cold (70%) → 9 - 10 = -1 utility (froze)
│     └─ Warm (30%) → 9 utility (perfect)
│     EV = 0.7 × (-1) + 0.3 × 9 = 2.0
└─ Stay home
   └─ EV = 3.0 (always)

Conclusion: Go and take jacket (EV = 8.4) > stay home (EV = 3.0) > go without jacket (EV = 2.0)

Business Example

Decision: Launch new product?

Estimates:

Success probability: 40%

Failure probability: 60%

Profit if success: $500K

Loss if failure: $200K

Don't launch: $0

Tree:

Launch product
├─ Success (40%) → +$500K
└─ Failure (60%) → -$200K
EV = (0.4 × 500K) + (0.6 × -200K) = 200K - 120K = +$80K
Don't launch
└─ EV = $0

Conclusion: Launch (EV = +$80K) is better than not launching ($0).

Trading Example

Decision: Enter position or wait?

Estimates:

Probability of rise: 60%

Probability of fall: 40%

Position size: $1000

Target: +10% ($100 profit)

Stop-loss: -5% ($50 loss)

Tree:

Enter position
├─ Rise (60%) → +$100
└─ Fall (40%) → -$50
EV = (0.6 × 100) + (0.4 × -50) = 60 - 20 = +$40
Wait
└─ No position → $0
EV = $0

Conclusion: Entering position has positive EV (+$40), better than waiting ($0).

Method Limitations

⚠️ Critical points:

1. Subjective estimates — probabilities often "finger in the air" 2. Doesn't account for risk appetite — ignores psychology (loss aversion) 3. Simplified model — reality is more complex 4. Unstable — small data changes can drastically alter the tree 5. May be inaccurate — other methods exist that are more precise (random forests)

But: The method is valuable for structuring thinking, even if numbers are approximate.

User Workflow

1. Structuring

Ask:

What are the action options?

What are possible outcomes?

What are values/utility for each outcome?

How do we measure value? (money, utility units, happiness points)

2. Probability Estimation

Help estimate through:

Historical data (if available)

Comparable situations

Expert judgment (user experience)

Subjective assessment (if no data)

3. Visualization

Draw tree in markdown:

Decision
├─ Option A
│  ├─ Outcome A1 (X%) → Value Y
│  └─ Outcome A2 (Z%) → Value W
└─ Option B
   └─ Outcome B1 (100%) → Value V

4. EV Calculation

For each option:

EV_A = (X% × Y) + (Z% × W)
EV_B = V

5. Recommendation

Option with highest EV = best choice (rationally).

But add context:

Risk tolerance (can user handle worst case)

Time horizon (when is result needed)

Other factors (reputational risk, emotions, ethics)

Application Examples by Domain

Trading & Investing

Position Sizing:

Options: 5%, 10%, 20% of capital

Outcomes: Profit/loss with different probabilities

Value: Absolute profit in $

Entry Timing:

Options: Enter now, wait for -5%, wait for -10%

Outcomes: Price goes up/down

Value: Opportunity cost vs better entry price

Business Strategy

Product Launch:

Options: Launch / don't launch

Outcomes: Success / failure

Value: Revenue, market share, costs

Hiring Decision:

Options: Hire candidate A / candidate B / don't hire

Outcomes: Successful onboarding / quit after X months

Value: Productivity, costs, opportunity cost

Personal Decisions

Career Change:

Options: Stay / change job / start business

Outcomes: Success / failure in new role

Value: Salary, satisfaction, growth, risk

Real Estate:

Options: Buy house A / house B / continue renting

Outcomes: Price increase / decrease / personal situation changes

Value: Net worth, monthly costs, quality of life

Operations

Capacity Planning:

Options: Expand production / outsource / status quo

Outcomes: Demand increases / decreases

Value: Profit, utilization, fixed costs

Vendor Selection:

Options: Vendor A / Vendor B / in-house

Outcomes: Quality, reliability, failures

Value: Total cost of ownership

Calculator Script

Use scripts/decision_tree.py for automated EV calculations:

python3 scripts/decision_tree.py --interactive

Or via JSON:

python3 scripts/decision_tree.py --json tree.json

JSON format:

{
  "decision": "Launch product?",
  "options": [
    {
      "name": "Launch",
      "outcomes": [
        {"name": "Success", "probability": 0.4, "value": 500000},
        {"name": "Failure", "probability": 0.6, "value": -200000}
      ]
    },
    {
      "name": "Don't launch",
      "outcomes": [
        {"name": "Status quo", "probability": 1.0, "value": 0}
      ]
    }
  ]
}

Output:

📊 Decision Tree Analysis
Decision: Launch product?
Option 1: Launch
  └─ EV = $80,000.00
     ├─ Success (40.0%) → +$500,000.00
     └─ Failure (60.0%) → -$200,000.00
Option 2: Don't launch
  └─ EV = $0.00
     └─ Status quo (100.0%) → $0.00
✅ Recommendation: Launch (EV: $80,000.00)

Final Checklist

Before giving recommendation, ensure:

✅ All options covered

✅ Probabilities sum to 100% for each branch

✅ Values are realistic (not fantasies)

✅ Worst case scenario is clear to user

✅ Risk/reward ratio is explicit

✅ Method limitations mentioned

✅ Qualitative context added (not just EV)

Method Advantages

✅ Simple — people understand trees intuitively ✅ Visual — clear structure ✅ Works with little data — can use expert estimates ✅ White box — transparent logic ✅ Worst/best case — extreme scenarios visible ✅ Multiple decision-makers — can account for different interests

Method Disadvantages

❌ Unstable — small data changes → large tree changes ❌ Inaccurate — often more precise methods exist ❌ Subjective — probability estimates "from the head" ❌ Complex — becomes unwieldy with many outcomes ❌ Doesn't account for risk preference — assumes risk neutrality

Important

The method is valuable for structuring thinking, but numbers are often taken from thin air.

What matters more is the process — forcing yourself to think through all branches and explicitly evaluate consequences.

Don't sell the decision as "scientifically proven" — it's just a framework for conscious choice.

Further Reading

Decision trees in operations research

Influence diagrams (more compact for complex decisions)

Utility functions (accounting for risk aversion)

Monte Carlo simulation (for greater accuracy)

Real options analysis (for strategic decisions)