How big is White's advantage in chess, and does it depend on skill?

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

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

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.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

1. Define score (win = 1, draw = ½).
2. Sample games by rating band.
3. Test White's score against 50%.
4. Compare across rating bands.
5. Reflect on time controls and draws.

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.

Taking it further

Control for rating difference by only using games between similarly rated players.