Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

When should you stop looking? The 37% rule for choosing the best

AA HLAA SLAI HL Ambitious Also in: Pure maths, Games & puzzles, Voting & game theory

Research question

In the secretary problem, why is rejecting the first n/e candidates the optimal strategy, and how well does the rule work in a realistic version such as house hunting with a limited number of viewings?

Make it yours, then agree it with your teacher.

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Why it makes a good exploration

Whether choosing a flat, a university or a parking space, you must decide without knowing what comes next. The optimal stopping rule is surprising and elegant, and testing it on a realistic scenario gives excellent Reflection.

The mathematics you'll need

Conditional probability and summation
Approximating a sum by an integral to get 1/e
Maximising a function of the cut-off
Simulation for finite n and variants

Where the data comes from

No data needed for the core; simulate variants in a spreadsheet or short program.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

A possible outline

State the problem and assumptions.
Derive P(success) for a cut-off r.
Find the optimal r for small n exactly, then the limit n/e.
Simulate variants (recall allowed, aiming for top 3).
Reflect on real decisions that break the assumptions.

Pitfalls that cost marks

Quoting 37% without derivation.
Not checking small cases by hand.
Ignoring that the rule maximises the chance of the best, not the average quality.

Showing personal engagement

Apply it to a real decision you face.
Run the experiment on classmates with shuffled cards.
Design a version that optimises expected rank instead.

See Criterion C: personal engagement for what examiners look for.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Fits — ambitious at SL	Conditional probability and summation; Approximating a sum by an integral to get 1/e
AA HL	Good fit	Conditional probability and summation; Approximating a sum by an integral to get 1/e
AI SL	Not a natural fit	The mathematics is mainly AA or HL (calculus or proof beyond AI SL); an AI SL version would need a data-driven, technology-based approach.
AI HL	Good fit	Conditional probability and summation; Approximating a sum by an integral to get 1/e

Level: Ambitious. Suits confident students; expect to learn some mathematics on your own. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: quoting 37% without derivation; and not checking small cases by hand. Say how each one affects your answer.

Use of mathematics (E)

SL: conditional probability and summation; approximating a sum by an integral to get 1/e; maximising a function of the cut-off; simulation for finite n and variants, each explained in your own words and carried out correctly.

How probability explorations reach the top bands in general: Probability & chance IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

HL: derive the result with the integral approximation carefully and investigate the “full information” version where values are known.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL probability exploration adds.

See a complete IA, marked

How long does a game of Snakes and Ladders last on my grandmother's board? (AI HL) is a complete probability exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AA HL, AA SL and AI HL. We rate it Ambitious: it suits confident students, who should expect to learn some mathematics on their own.

What mathematics does this IA use?

Conditional probability and summation, approximating a sum by an integral to get 1/e, maximising a function of the cut-off and simulation for finite n and variants.

Where can I get data for this IA?

No data needed for the core; simulate variants in a spreadsheet or short program. Checked sources and tools: Desmos graphing calculator.

Turn this idea into your IA

The planner opens with “When should you stop looking? The 37% rule for choosing the best” filled in: the question, the maths and the data sources.

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