Physics Practical Magic

Mathematicians just dropped the ultimate cheat code for sports betting, showing exactly how to win big on parlays.

March 30, 2026

Original Paper

Optimal Parlay Wagering and Whitrow Asymptotics: A State-Price and Implicit-Cash Treatment

Christopher D. Long

arXiv · 2603.26620

The Takeaway

Parlays are often seen as 'sucker bets' because the odds are so difficult to calculate. This paper provides the first exact mathematical proof for how to balance your bankroll across these bets, explaining a long-observed gambling phenomenon and showing how to grow funds while mathematically minimizing the risk of going broke.

From the abstract

For independent multi-outcome events under multiplicative parlay pricing, we give a short exact proof of the optimal Kelly strategy using the implicit-cash viewpoint. The proof is entirely eventwise. One first solves each event in isolation. The full simultaneous optimizer over the entire menu of singles, doubles, triples, and higher parlays is then obtained by taking the outer product of the one-event Kelly strategies. Equivalently, the optimal terminal wealth factorizes across events. This yie