IA idea · Games & puzzles
How big is White's advantage in chess, and does it depend on skill?
Research question
In rated online games, is White's score significantly above 50%, and does the advantage grow with the players' rating?
Make it yours, then agree it with your teacher.
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Why it makes a good exploration
Moving first is an advantage, but how big? Millions of Lichess games let you measure it precisely and test whether stronger players exploit it more.
The mathematics you'll need
- Proportions and binomial tests
- Confidence intervals for proportions (HL)
- Chi-squared test of independence (rating band × result)
- Regression of White's score against rating
The statistics, step by step
Worked with every number shown, with what examiners look for and the common mistakes: Chi-squared test for independence · Confidence intervals for a mean. Then run the same steps on your own data in Analyse my data, or start from the statistics workflow.
Where the data comes from
Sample games from one month of the Lichess open database (with ratings and results).
- Lichess open database — Every rated game played on Lichess, monthly PGN files, plus puzzles.
Real data for this idea
- Primary source: Lichess open database: Standard rated games. The files are huge: take one early month and count results by first move. Licence: Check the terms on the page.
Links checked October 2026; we link to the data and never copy it. More free data sets.
A possible outline
- Define score (win = 1, draw = ½).
- Sample games by rating band.
- Test White's score against 50%.
- Compare across rating bands.
- Reflect on time controls and draws.
Pitfalls that cost marks
- Mixing time controls.
- Huge datasets without a sampling plan.
- Ignoring rating differences between players.
Showing personal engagement
- Analyse your own games too.
- Predict the trend with rating before testing.
- Compare with classical over-the-board databases.
See Criterion C: personal engagement for what examiners look for.
Which course is it for?
| Course | Fit | Maths to lean on |
|---|---|---|
| AA SL | Not a natural fit | The core technique sits in the AI course or at HL; an AA SL student could use it only as clearly explained new mathematics. |
| AA HL | Good fit | Proportions and binomial tests; Confidence intervals for proportions |
| AI SL | Good fit | Proportions and binomial tests; Chi-squared test of independence (rating band × result) |
| AI HL | Good fit | Proportions and binomial tests; Confidence intervals for proportions |
Level: Solid. Needs some independent work beyond class examples. 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: mixing time controls; and huge datasets without a sampling plan. Say how each one affects your answer.
Use of mathematics (E)
SL: proportions and binomial tests; chi-squared test of independence (rating band × result); regression of White's score against rating, each explained in your own words and carried out correctly.
HL adds: confidence intervals for proportions, each explained in your own words and carried out correctly.
How games & puzzles explorations reach the top bands in general: Games & puzzles IA ideas. Guides: A · B · C · D · E · self-grade sheet.
Taking it further
Control for rating difference by only using games between similarly rated players.
Extending it for HL
This idea already has HL mathematics in it: Confidence intervals for proportions. Make that the centre of the exploration and use it with full rigour.
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 games & puzzles exploration, marked on every criterion.
Frequently asked questions
Which IB Maths course is this IA idea for?
It works for AI SL, AI HL and AA HL. We rate it Solid: it needs some independent work beyond class examples.
What mathematics does this IA use?
Proportions and binomial tests, confidence intervals for proportions (HL), chi-squared test of independence (rating band × result) and regression of White's score against rating.
Where can I get data for this IA?
Sample games from one month of the Lichess open database (with ratings and results). Checked sources and tools: Lichess open database.
Turn this idea into your IA
The planner opens with “How big is White's advantage in chess, and does it depend on skill?” filled in: the question, the maths and the data sources.
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Writing it up: how to write a Maths IA, step by step · structure and format · mistakes that cost marks · annotated exemplars, marked on every criterion
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