{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/modeling-precomputation-in-games-played-under","title":"Modeling Precomputation In Games Played Under Computational Constraints","arxiv_id":"2105.09145","date":"2021-05-19","proceeding":null,"authors":["Thomas Orton"],"abstract":"Understanding the properties of games played under computational constraints remains challenging. For example, how do we expect rational (but computationally bounded) players to play games with a prohibitively large number of states, such as chess? This paper presents a novel model for the precomputation (preparing moves in advance) aspect of computationally constrained games. A fundamental trade-off is shown between randomness of play, and susceptibility to precomputation, suggesting that randomization is necessary in games with computational constraints. We present efficient algorithms for computing how susceptible a strategy is to precomputation, and computing an $\\epsilon$-Nash equilibrium of our model. Numerical experiments measuring the trade-off between randomness and precomputation are provided for Stockfish (a well-known chess playing algorithm).","url_abs":"https://arxiv.org/abs/2105.09145v1","url_pdf":"https://arxiv.org/pdf/2105.09145v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"modeling-precomputation-in-games-played-under","repo_url":"https://github.com/Thomas-Orton/chess-precomputation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2105.09145","atlas_url":"https://app.syntology.ai/?focus=2105.09145","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}