APMM: Automated Parlay Market Maker

[2607.18299] LOPMM: A Low-Order Parlay Market Maker Skip to main content Search Submit Donate Log in Computer Science > Computer Science and Game Theory arXiv:2607.18299 (cs) [Submitted on 13 Jul 2026 ( v1 ), last revised 5 Oct 2026 (this version, v3)] Title: LOPMM: A Low-Order Parlay Market Maker Authors: Niusha Moshrefi , Ranvir Rana , Pramod Viswanath View PDF HTML (experimental) Abstract: Parlays - joint contracts on the simultaneous resolution of several events - are among the most heavily traded products in betting markets, but prediction markets have struggled to offer them natively. The family of parlays over $M$ binary events is exponentially large, and the mechanisms that could price it either cannot be computed at that scale or need to pay for the same information multiple times. We start from an empirical observation that reframes the obstacle. On Kalshi order flow, most of the trades are placed on low-order parlays. For example, on Kalshi 7 days of traded parlay data, $87.03\%$ of the trades have at most 13 legs and $95.13\%$ have at most 20, with trade counts bounded by geometrical decay in increasing leg numbers. Given this concentration, and the structural correlation between parlays that share legs, current designs waste most of either their computation or their subsidy. We propose Low-Order Parlay Market Maker (LOPMM), which keeps a separate book for each combination of legs to stay tractable, then shares information from lower-order parlays into the higher-order ones containing them to reduce the market maker's loss. We formalize the observed concentration as a low-order flow condition. Empirically, LOPMM substantially reduces the cost of supporting parlay trading. On synthetic low-order flow, its losses remain close to that of running the base markets alone. On a replay of 83 Kalshi NBA games, independent parlay books lose \$174,050 in aggregate while LOPMM earns \$31 under the same liquidity parameter. Its computational cost depends on the order (m) of the requested parlay rather than the number (M) of base events, requiring $\Theta(4^m)$ work per quote and $\Theta(5^m)$ per full trade. We complement these empirical results with theoretical guarantees ... Subjects: Computer Science and Game Theory (cs.GT) Cite as: arXiv:2607.18299 [cs.GT] (or arXiv:2607.18299v3 [cs.GT] for this version) https://doi.org/10.48550/arXiv.2607.18299 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Niusha Moshrefi [ view email ] [v1] Mon, 13 Jul 2026 19:18:37 UTC (303 KB) [v2] Wed, 26 Aug 2026 21:14:48 UTC (303 KB) [v3] Mon, 5 Oct 2026 23:34:21 UTC (68 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.GT < prev | next > new | recent | 2026-07 Change to browse by: cs References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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