APMM: Automated Parlay Market Maker cuts prediction market losses to O(M²)
New algorithm lets prediction markets offer full combinatorial parlays without massive losses.
Prediction markets have long struggled to offer parlay contracts—joint bets on multiple events simultaneously—despite their popularity in sports betting. The core challenge is that each specific parlay attracts few traders, creating inherently thin markets. The logarithmic market scoring rule (LMSR) works well for thin markets, but running a separate LMSR for each of exponentially many parlays forces the market maker to pay for the same information multiple times.
A team from the University of Illinois at Urbana-Champaign (Moshrefi, Rana, Viswanath) proposes the Automated Parlay Market Maker (APMM), which uses a hierarchical parameterization: the state of each low-leg parlay (e.g., a single event) is shared into every higher-leg parlay that contains it. This means pricing one contract automatically updates all related contracts coherently. The key result: when informed trading concentrates on parlays with few legs, the market maker's worst-case loss is O(M²) for M binary events, and it falls to O(M) if trades spread across different clusters. Simulations and tests on real Kalshi order flow confirm low-leg changes dominate belief updates, validating APMM's advantage.
- APMM uses hierarchical parameterization to share state across related parlays, avoiding redundant information costs.
- Worst-case market maker loss is O(M²), dropping to O(M) with diversified trading across clusters.
- Validated on historical Kalshi order flow—real belief updates are dominated by low-leg (simple) parlay changes.
Why It Matters
Prediction markets can finally natively offer the full combinatorial parlay space, attracting more traders and better price discovery.