Decision Analysis — Oceanview Property Purchase

Discussion prompt

Before we open Decision Analysis — Oceanview Property Purchase: without looking back, what was the main idea of Monte Carlo Simulation — Four Corners Case, and what could you do by the end of it that you could not do before?

Hint: One sentence for the idea, one for the skill. If the second one is blank, that is the part to revisit.

Comparison matrix

From The situation Glenn faces: refill the Event column from what you know. The rest of the table is as it appeared.

Comparison matrix

From Every number the case gives you: every row here is a choice with a cost. Fill the Symbol column, then say which row you would actually pick and what you give up for it.

Match the pairs

From Four questions, four analytical moves — match each one to what it actually does. The descriptions have been shuffled.

• c1. Draw the tree
• c2. Decide without research
• c3. Strategy with research
• c4. Value the survey

• b1. The logical sequence of decisions and chances.
• b2. Fold back the tree → bid or not.
• b3. Bayes-revise, then a conditional plan.
• b4. EVSI vs. its $15,000 price; EVPI.

Why: Draw the tree, Decide without research, Strategy with research, Value the survey are easy to tell apart while they are sitting next to their descriptions and much harder afterwards, which is what this checks.

Discussion prompt

Once a bid is submitted, exactly three endpoints are possible. Work out the profit for each explicitly — these are the numbers that sit at the tips of the tree.

That is stated as though it always holds. Do one of two things: produce a case where it fails, or say precisely what rules such a case out. "It just does" is not on the menu.

Hint: Hunt at the extremes first — zero, one, negative, empty, equal. If every extreme survives, the reason they survive is the proof.

Put in order

Put the moves of The three payoffs, in dollars into the order they have to happen.

1. Build: Revenue − Property − Construction = $15M − $5M − $8M = +$2,000,000
2. Walk away: forfeit only the 10% deposit = −0.10 × $5,000,000 = −$500,000
3. Lose the bid: $0. Not bidding at all: $0.

Why: These are the moves of the worked example in the order it makes them, and each one is set up by the one before it. Won the bid and zoning approved, so all three cash flows land: sell for $15M, pay $5M for the land and $8M to build.

Draw it

Draw what The three payoffs, in dollars just did — the shape of it, not the line-by-line working. One picture, labels only where you need them. Then check it against the steps: anything you could not draw is a step you followed rather than understood.

Predict first

A student writes this, and it looks reasonable:

Assume that if zoning fails, Oceanview is stuck with the land it bid on.

It is wrong. Say what breaks — and say it before you turn the page.

Correct: Treats the purchase as completed — as if the $5M were already spent and unrecoverable.

Read the case: if zoning is rejected, Glenn simply does not complete the purchase.

Why: Treats the purchase as completed — as if the $5M were already spent and unrecoverable.

Discussion prompt

Read the picture before the words. What is this showing, and what is the one thing it is built to make obvious? Commit to an answer, then read on.

Hint: Name the parts, then say what changes between them — and if nothing changes, say what is being held still.

Discussion prompt

Explain The decision tree by analogy to something with no Business Analytics in it at all — a queue, a recipe, a map, a bank balance, whatever fits. Then say where your analogy breaks.

Hint: An analogy that never breaks is not an analogy, it is the same idea wearing a hat. Find the seam — that is the part that is actually new.

Discussion prompt

Explain What "folding back" means to a student a year behind you. No notation, no jargon they have not met — and it still has to be true.

Hint: If your explanation needs a symbol they have never seen, you are describing the notation rather than the idea.

Discussion prompt

Fold it back with no survey — before any calculation: what is the plan? Name the moves in order, in plain English, without doing the arithmetic.

Hint: It starts with: Referendum node: EV = 0.30(+$2,000,000) + 0.70(−$500,000) = 600,000 −…

Discussion prompt

Work backwards. The example finished here:

Decision node: compare EV(bid) = $50,000 vs. EV(don't bid) = $0 → BID

What was it asked to do, and what must it have been given? Reconstruct the problem from its answer.

Hint: Every quantity in the result had to enter somewhere. Account for each one.

Predict first

A student writes this, and it looks reasonable:

See the referendum node's $250,000 and call that the value of bidding.

It is wrong. Say what breaks — and say it before you turn the page.

Correct: Silently assumes the bid is certain to win — it skips the 0.2 win-probability chance node entirely.

Push the $250,000 through the win/lose node before comparing anything.

Why: Silently assumes the bid is certain to win — it skips the 0.2 win-probability chance node entirely.

Discussion prompt

Run The fold-back recipe with this step confiscated:

Work right to left, one node at a time.

Is it still possible? If it is, say what takes its place and what it costs you. If it is not, say exactly what that step was providing that nothing else does.

Hint: A step you can drop for free was never load-bearing. If you cannot drop it, name the thing that goes wrong the moment it is gone.

Discussion prompt

The fold-back recipe works on the cases you have just seen. Push it to the edge: what is the most degenerate input it still handles — empty, zero, one item, everything equal — and what is the first case where it stops being true? Name the case, not just "it breaks".

Hint: Try the smallest legal input, then the largest, then the one where two things collide. Methods are specified at their edges; the middle takes care of itself.

Eliminate the wrong options

What is EV(bid) with no survey, and what should Oceanview do?

3 of these 4 are wrong. Strike them one at a time, and say what rules each one out before you strike the next. The survivor is the answer.

• A. $50,000 — submit the bid
• B. $250,000 — submit the bid
• C. $50,000 — do not bid
• D. $75,000 — submit the bid

Survives elimination: A

Why: EV(bid) = 0.20 × $250,000 + 0.80 × $0 = $50,000. Since $50,000 beats the $0 of not bidding, submit the bid. This $50,000 is the no-information benchmark every later value is measured against.

Check your understanding

What is EV(bid) with no survey, and what should Oceanview do?

• A. $50,000 — submit the bid (correct)
• B. $250,000 — submit the bid
• C. $50,000 — do not bid
• D. $75,000 — submit the bid

Answer: A

Why: EV(bid) = 0.20 × $250,000 + 0.80 × $0 = $50,000. Since $50,000 beats the $0 of not bidding, submit the bid. This $50,000 is the no-information benchmark every later value is measured against.

Why B tempts people

Reported the referendum node's $250,000 as the bid's value — skipping the 0.20 win-probability node. That number assumes the bid is certain to win.

Why C tempts people

Right EV, wrong call: any expected value above the $0 of not bidding favors bidding. A small positive EV still beats zero.

Why D tempts people

Used the referendum probabilities (0.30 / 0.70) at the win/lose node instead of 0.20 / 0.80: 0.30 × 250,000 = $75,000. The two chance nodes have different probabilities — don't swap them.

Comparison matrix

From The survey and its track record: refill the P(predicts N) column from what you know. The rest of the table is as it appeared.

Discussion prompt

Explain Why we must flip the probabilities by analogy to something with no Business Analytics in it at all — a queue, a recipe, a map, a bank balance, whatever fits. Then say where your analogy breaks.

Hint: An analogy that never breaks is not an analogy, it is the same idea wearing a hat. Find the seam — that is the part that is actually new.

Predict first

Three mechanical steps. First, multiply each prior by each conditional to get joint probabilities P(prediction and state).

Commit before you compute: what does Bayes: joint table → marginals → posteriors come out to? A rough magnitude and the right form is enough — the point is to have something concrete to be wrong about.

Correct: Posteriors: divide each joint by its column total

Why: A prediction you can defend turns the computation into a check rather than a leap of faith — and an answer that contradicts it is caught on the spot. P(s₁|A)=0.27/0.41=0.6585, P(s₂|A)=0.3415, P(s₁|N)=0.03/0.59=0.0508, P(s₂|N)=0.9492.

Annotate

From Bayes: joint table → marginals → posteriors — read this one piece at a time. What is each part doing?

On: \( P(s_1 \mid A) = \dfrac{P(A \mid s_1)\,P(s_1)}{P(A)} = \dfrac{0.9 \times 0.30}{0.41} = 0.6585 \)

• Sum each column — these are the probabilities the survey says 'approve' or 'reject' at all, the branch probabilities in the tree.
• P(s₁|A)=0.27/0.41=0.6585, P(s₂|A)=0.3415, P(s₁|N)=0.03/0.59=0.0508, P(s₂|N)=0.9492.

Predict first

A student writes this, and it looks reasonable:

The survey says 'approve' and it's 90% accurate when approval will happen — so approval is now 90% likely.

It is wrong. Say what breaks — and say it before you turn the page.

Correct: Grabs P(A | s₁) = 0.9 and uses it as P(s₁ | A).

Flip it with Bayes — divide the joint probability by the marginal.

Why: Grabs P(A | s₁) = 0.9 and uses it as P(s₁ | A). This is the classic inversion — confusing P(prediction | state) with P(state | prediction).

Discussion prompt

The rule this trap just fixed:

The joint 0.27 shares the 'approve' branch with the 0.14 false-alarm from s₂; dividing by P(A)=0.41 accounts for both.

Now break it on purpose. Build a case that violates it and follow the consequences until something visibly fails. Where does the failure first show up — and would you have noticed it if you had not been looking?

Hint: The dangerous rules are the ones whose violation still produces an answer. If yours fails loudly, try to find one that fails quietly.

Predict first

After the survey predicts rejection, what is P(approved | N) = P(s₁ | N)?

Answer it in your own words, now, with nothing to choose from. The options are on the next slide — and picking the right one off a list is an easier skill than producing it.

Correct: ≈ 0.05

Why: P(s₁ | N) = joint / marginal = 0.03 / 0.59 ≈ 0.0508. A rejection prediction drives approval odds from 0.30 down to about 5% — the survey nearly rules approval out.

Check your understanding

After the survey predicts rejection, what is P(approved | N) = P(s₁ | N)?

• A. ≈ 0.05 (correct)
• B. 0.10
• C. 0.30
• D. 0.03

Answer: A

Why: P(s₁ | N) = joint / marginal = 0.03 / 0.59 ≈ 0.0508. A rejection prediction drives approval odds from 0.30 down to about 5% — the survey nearly rules approval out.

Why B tempts people

Used P(N | s₁) = 0.10 directly — the inversion again. That's how the survey behaves when approval is true, not the chance of approval given the prediction.

Why C tempts people

Kept the prior 0.30 and ignored the survey. The whole point of paying for the survey is to move off the prior.

Why D tempts people

Stopped at the joint probability 0.03 without dividing by P(N) = 0.59. A joint is not a conditional until you normalize by the marginal.

Put in order

Put the moves of Fold back each survey branch into the order they have to happen.

1. Survey says A → referendum node: 0.6585($2M) + 0.3415(−$500k) = 1,317,073 − 170,732 = $1,146,341
2. EV(bid | A) = 0.20 × $1,146,341 = $229,268 > 0 → BID
3. Survey says N → referendum node: 0.0508($2M) + 0.9492(−$500k) = 101,695 − 474,576 = −$372,881
4. EV(bid | N) = 0.20 × (−$372,881) = −$74,576 < 0 → DON'T BID

Why: These are the moves of the worked example in the order it makes them, and each one is set up by the one before it. Use the favorable posteriors 0.6585 / 0.3415 in place of the 0.30 / 0.70 priors.

Comparison matrix

From Fold back each survey branch: every row here is a choice with a cost. Fill the Action column, then say which row you would actually pick and what you give up for it.

Predict first

A student writes this, and it looks reasonable:

"Bidding was worth $50,000 before, and we already paid for the survey — so bid regardless."

It is wrong. Say what breaks — and say it before you turn the page.

Correct: Ignores that the survey rewrote the odds — approval just fell from 0.30 to 0.05.

Act on the revised odds — that's the entire reason you bought them.

Why: Ignores that the survey rewrote the odds — approval just fell from 0.30 to 0.05. The old number no longer applies.

Predict first

What is EV(bid | approval predicted), and what should Oceanview do?

Answer it in your own words, now, with nothing to choose from. The options are on the next slide — and picking the right one off a list is an easier skill than producing it.

Correct: $229,268 — submit the bid

Why: EV(bid | A) = 0.20 × $1,146,341 = $229,268. It's positive, so bid. The favorable survey roughly quadruples the bid's value versus the $50,000 no-survey case.

Check your understanding

What is EV(bid | approval predicted), and what should Oceanview do?

• A. $229,268 — submit the bid (correct)
• B. $1,146,341 — submit the bid
• C. $50,000 — submit the bid
• D. $229,268 — do not bid

Answer: A

Why: EV(bid | A) = 0.20 × $1,146,341 = $229,268. It's positive, so bid. The favorable survey roughly quadruples the bid's value versus the $50,000 no-survey case.

Why B tempts people

Reported the referendum node ($1,146,341) as the bid's value — the same skip-the-0.20-win-node error from Part 2, now inside the A branch.

Why C tempts people

Used the original priors (0.30 / 0.70) instead of the revised posteriors (0.6585 / 0.3415). That throws away the survey information you paid $15,000 for.

Why D tempts people

Correct EV, wrong call: +$229,268 clears the $0 of walking away, so bidding is the right action.

Discussion prompt

We already have the without-info value: $50,000 (Part 2). We need the with-info value: fold back the survey tree, letting Oceanview take the best action under each prediction.

That is stated as though it always holds. Do one of two things: produce a case where it fails, or say precisely what rules such a case out. "It just does" is not on the menu.

Hint: Hunt at the extremes first — zero, one, negative, empty, equal. If every extreme survives, the reason they survive is the proof.

Put in order

Put the moves of EVSI = $44,000 → hire the firm into the order they have to happen.

1. EV(with info) = P(A)·EV(bid | A) + P(N)·EV(no bid | N) = 0.41($229,268) + 0.59($0) = $94,000
2. EVSI = $94,000 − $50,000 = $44,000
3. Compare to the price: $44,000 worth vs. $15,000 cost → net gain $29,000

Why: These are the moves of the worked example in the order it makes them, and each one is set up by the one before it. Weight each prediction by how often it occurs (marginals 0.41 / 0.59) times the value of the best action then — bid on A, walk on N ($0).

Comparison matrix

From EVSI = $44,000 → hire the firm: refill the Expected value column from what you know. The rest of the table is as it appeared.

Predict first

EVPI — expected value of perfect information — is the ceiling: what a flawless crystal ball on the referendum would be worth. It bounds what any survey could ever earn.

Commit before you compute: what does EVPI and efficiency: how good is this survey? come out to? A rough magnitude and the right form is enough — the point is to have something concrete to be wrong about.

Correct: EVPI = $120,000 − $50,000 = $70,000

Why: A prediction you can defend turns the computation into a check rather than a leap of faith — and an answer that contradicts it is caught on the spot. Perfect foresight beats the no-info $50,000 by $70,000 — the most any information about the referendum could be worth.

Annotate

From EVPI and efficiency: how good is this survey? — read this one piece at a time. What is each part doing?

On: \( \text{Efficiency} = \dfrac{\text{EVSI}}{\text{EVPI}} = \dfrac{44{,}000}{70{,}000} \approx 0.629 \)

• You'd know the outcome before bidding — bid only in the 30% of cases zoning passes (still subject to the 0.20 win node), never otherwise.
• Perfect foresight beats the no-info $50,000 by $70,000 — the most any information about the referendum could be worth.

Predict first

A student writes this, and it looks reasonable:

"EVSI is the with-survey value minus what the survey costs."

It is wrong. Say what breaks — and say it before you turn the page.

Correct: Subtracts the $15,000 price. But that mixes the value question with the cost question — and ignores the $50,000 you could already make without any survey.

EVSI compares information to NO information — the fee is a separate, later comparison.

Why: Subtracts the $15,000 price. But that mixes the value question with the cost question — and ignores the $50,000 you could already make without any survey.

Sort into buckets

Some of these hold up and some are the exact mistakes this lesson is built to prevent. Sort them.

Holds up

Once a bid is submitted, exactly three endpoints are possible. Work out the profit for each explicitly — these are the numbers that sit at the tips of the tree.; The payoffs from Part 1 sit at the tips: +$2.0M, −$0.5M, and two $0 ends. Everything else is just weighting them by probability.; You can't evaluate the tree left to right — you don't know the payoff until you reach a tip. So you work right to left, collapsing one node at a time.

Breaks

Assume that if zoning fails, Oceanview is stuck with the land it bid on.; See the referendum node's $250,000 and call that the value of bidding.

sound

These are stated as this lesson states them — each one survives the edge cases Decision Analysis — Oceanview Property Purchase puts it through.

flawed

Each of these is lifted from a trap in this deck: reasonable-sounding, and wrong in a way that only shows up once you rely on it.

Eliminate the wrong options

What is the EVSI, and should Oceanview buy the $15,000 survey?

3 of these 4 are wrong. Strike them one at a time, and say what rules each one out before you strike the next. The survivor is the answer.

• A. $44,000 — yes, buy it
• B. $79,000 — yes, buy it
• C. $94,000 — yes, buy it
• D. $44,000 — no, don't buy it

Survives elimination: A

Why: EVSI = $94,000 − $50,000 = $44,000 — the gain over the best no-survey action. Since $44,000 far exceeds the $15,000 price (net +$29,000), buy the survey.

Check your understanding

What is the EVSI, and should Oceanview buy the $15,000 survey?

• A. $44,000 — yes, buy it (correct)
• B. $79,000 — yes, buy it
• C. $94,000 — yes, buy it
• D. $44,000 — no, don't buy it

Answer: A

Why: EVSI = $94,000 − $50,000 = $44,000 — the gain over the best no-survey action. Since $44,000 far exceeds the $15,000 price (net +$29,000), buy the survey.

Why B tempts people

Subtracted the $15,000 fee from the $94,000 instead of the $50,000 no-info baseline. $79,000 is the net study-branch value, not the EVSI.

Why C tempts people

Used the gross with-info value ($94,000) as the EVSI, forgetting that $50,000 was already attainable with no survey at all.

Why D tempts people

Right EVSI, wrong decision: $44,000 of value against a $15,000 cost is clearly worth buying — a net gain of $29,000.

Draw it

One page, no notation unless you need it: draw how these connect — Part 1 — Payoffs at Every Endpoint · Part 2 — The Tree & the No-Research Call · Part 3 — Revising the Odds with Bayes · Part 4 — The Strategy With Research · Part 5 — Is the $15,000 Study Worth It?. Put an arrow wherever one of them is what makes another possible, and label the arrow with why.