When Opendoor makes an offer on a home, they don't know everything the seller knows. The seller has lived there for years. They know about the foundation crack behind the drywall, the neighbor who parks illegally every weekend, the basement that floods every March. Opendoor just has an AVM estimate and a few comps.
This information gap has a name in economics: adverse selection. And it creates a deeply counterintuitive problem — the very fact that a seller accepts your offer is evidence that you probably overpaid.
The Setup
Let F be the AVM's fair market value estimate, and V be the true value — which only the seller knows. The true value sits somewhere in a band around the estimate:
The parameter a is how wrong the AVM could be. For a 30-year-old home in a mixed neighborhood, that band might be 12% of the home's value. For new construction with builder warranties, maybe 3%.
The seller accepts when — when the offer exceeds what they privately know the home is worth.
The Winner's Curse
Here's where it gets painful. Given that the seller accepted, the expected true value of the home is always below the offer price. The Information Asymmetry Premium — what you're overpaying on every accepted deal — works out to:
At FMV (), you're still overpaying by on every accepted deal. For a $400K home with $40K of uncertainty, that's $20,000 lost per transaction just from adverse selection.
The key operational insight: the overpayment is directly proportional to your acceptance rate. High acceptance rate = high adverse selection exposure. One metric to watch.
The Optimal Offer
iBuyers capture a service margin on resale (speed, convenience, certainty). Accounting for both adverse selection and this margin, the profit-maximizing offer price is:
Bid below FMV by exactly the gap between your uncertainty and your service premium. The resulting maximum profit per deal:
Two things jump out. Profit scales quadratically with margin — doubling quadruples profit. But it scales inversely with uncertainty — every dollar of AVM improvement is worth more than a dollar of margin expansion. Better data beats better pricing power.
All of these results — the IAP formula, the optimal offer, the profit formula, and their edge-case properties — are formally verified in Lean 4. No off-by-one errors, no sign flips, no silent bugs in the discount logic.
Learning the Uncertainty from the Market
The uncertainty parameter isn't fixed — it varies by property type, age, location, and condition. The Bayesian layer learns the right for each market segment from acceptance and rejection data.
| Segment | Typical uncertainty (a/F) |
|---|---|
| New construction | 2–5% |
| Recently renovated | 5–10% |
| Older homes (30+ yr) | 8–15% |
| Distressed / as-is | 15–25% |
The critical insight: rejections are information too. A rejected offer at price tells you the true value was above , tightening the posterior from above. Most pricing systems throw away rejections. This one learns from them.
For exploration-exploitation — learning while simultaneously maximizing profit — the system uses Thompson Sampling. Sample from the current posterior on , compute the optimal offer, observe accept/reject, update. When uncertainty is high, offers are more variable and the algorithm explores. As data accumulates, it converges. No manual tuning needed.
Why This Matters
At scale — Opendoor was buying 17,000+ homes per quarter at peak — even a 0.5% improvement in average IAP discount translates to tens of millions of dollars in margin recovery.
The formally verified result: reducing information asymmetry by half doubles maximum profit per deal. Better data beats better pricing power, every time.