The Research Lab

Deep dives into betting mathematics, probability theory, and the data science behind finding value.

5 articles
05 March 2026 ⏱ 17 min read 3302 words

Sensitivity, Conjugates, and the Spread: Convex Optimisation for Sports Trading (Part 2)

Part 1 ended with a claim: the dual variables from your optimisation solver tell you where your system is bottlenecked. Constitution Hill's liquidity constraint had a shadow price of £0.09 per pound. ...

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05 March 2026 ⏱ 14 min read 2716 words

Why Your Optimal Bet Is Provably Optimal: Convex Optimisation for Sports Trading (Part 1)

You have three edges on this Saturday's card. Frankel to win the 2:30 at 5% edge, Constitution Hill in the 3:15 at 12% edge, and Enable in the 4:00 at 3% edge. Your bankroll is £3,000. Liquidity caps ...

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01 March 2026 ⏱ 10 min read 2098 words

Odds, Probabilities, and the Hidden Structure of a Betting Market

You look at a horse race on Betfair and see a column of decimal odds. Behind those numbers is a precise geometric structure — one that determines whether the market is fair, whether the bookmaker is t...

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01 March 2026 ⏱ 9 min read 1840 words

The Geometry Hiding Inside Your Betfair Screen

Every set of odds on Betfair describes a point in space. If that point is inside a particular shape — a polytope — the prices are consistent with reality. If the point is outside, someone is offering ...

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01 March 2026 ⏱ 14 min read 2724 words

From Triangles to Polytopes: The Shape of a Fair Market (Part 2)

In Part 1, we converted Betfair odds into implied probabilities and discovered that those probabilities live inside a triangle — the probability simplex. A bookmaker's overround pushes the point outsi...

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