{"id":"https://openalex.org/W7220729933","doi":"https://doi.org/10.48550/arxiv.2610.06028","title":"Near-Exact Computation of Independent Chip Model Placement Probabilities for Thousands of Players","display_name":"Near-Exact Computation of Independent Chip Model Placement Probabilities for Thousands of Players","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220729933","doi":"https://doi.org/10.48550/arxiv.2610.06028"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.06028","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06028","pdf_url":"https://arxiv.org/pdf/2610.06028","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.06028","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052951841","display_name":"Wataru Inariba","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Inariba, Wataru","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5052951841"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.3059000074863434,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.3059000074863434,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13806","display_name":"Mathematical and Computational Methods","score":0.14429999887943268,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.10610000044107437,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/plackett-luce-model","display_name":"Plackett-Luce model","score":0.8870000243186951},{"id":"https://openalex.org/keywords/poisson-binomial-distribution","display_name":"Poisson binomial distribution","score":0.9440000057220459},{"id":"https://openalex.org/keywords/deconvolution","display_name":"deconvolution","score":0.8610000014305115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.590399980545044},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5656999945640564},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48980000615119934},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4359999895095825},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.4165000021457672},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36239999532699585},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35600000619888306},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.351500004529953},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3479999899864197},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.31679999828338623},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2922999858856201},{"id":"https://openalex.org/C136975688","wikidata":"https://www.wikidata.org/wiki/Q1320634","display_name":"Tournament","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C103275481","wikidata":"https://www.wikidata.org/wiki/Q6787889","display_name":"Matrix representation","level":3,"score":0.2818000018596649},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.27630001306533813},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2554999887943268},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.06028","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06028","pdf_url":"https://arxiv.org/pdf/2610.06028","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.06028","doi":"https://doi.org/10.48550/arxiv.2610.06028","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.06028","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.06028","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06028","pdf_url":"https://arxiv.org/pdf/2610.06028","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220729933.pdf","grobid_xml":"https://content.openalex.org/works/W7220729933.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4413321686","https://openalex.org/W3131327446","https://openalex.org/W7202155629","https://openalex.org/W2146589112","https://openalex.org/W4412806304","https://openalex.org/W2139447213","https://openalex.org/W7027579121","https://openalex.org/W7135897297","https://openalex.org/W88297289","https://openalex.org/W1516597318"],"abstract_inverted_index":{"The":[0,50,126,228],"Independent":[1],"Chip":[2],"Model":[3],"(ICM)":[4],"converts":[5],"the":[6,10,25,59,78,94,103,107,114,121,141,165,170,175,204,217],"chip":[7],"stacks":[8,67],"of":[9,81,97,123,143,209,221],"players":[11,84,144,234],"remaining":[12],"in":[13,28,54,89,133,188],"a":[14,62,73,129,137,152,222],"poker":[15],"tournament":[16,29],"into":[17],"finishing-place":[18],"probabilities":[19,80],"and":[20,39,106,164,216],"prize":[21],"equities.":[22],"It":[23],"is":[24,61,100,146,212],"standard":[26],"model":[27,65],"solvers,":[30],"but":[31],"its":[32,158],"definition":[33],"considers":[34],"all":[35,82,86],"possible":[36],"finishing":[37],"orders,":[38],"exact":[40],"computation":[41],"has":[42],"been":[43],"regarded":[44],"as":[45,68],"intractable":[46],"for":[47,57,85,102,232],"large":[48],"fields.":[49],"same":[51],"mathematics":[52],"appears":[53],"other":[55],"fields;":[56],"instance,":[58],"ICM":[60],"Plackett-Luce":[63],"ranking":[64],"with":[66,199],"weights.":[69],"We":[70],"present":[71],"DE-ICM,":[72],"deterministic":[74],"algorithm":[75,127],"that":[76],"computes":[77],"placement":[79,223,230],"$n$":[83],"paid":[87],"places":[88],"$O(M":[90],"n^{2})$":[91],"time,":[92],"where":[93],"number":[95,142],"$M$":[96],"quadrature":[98,150],"nodes":[99],"fixed":[101],"admissible":[104],"inputs":[105],"target":[108,115],"accuracy.":[109],"Its":[110],"numerical":[111],"scheme":[112],"allows":[113],"to":[116,120,201],"be":[117],"set":[118],"close":[119],"accuracy":[122],"double-precision":[124],"arithmetic.":[125],"evaluates":[128,155],"classical":[130],"integral":[131],"representation":[132],"which,":[134],"conditional":[135],"on":[136,151,238],"player's":[138,185],"exponential":[139],"clock,":[140],"ahead":[145],"Poisson-binomial.":[147],"A":[148,178],"double-exponential":[149],"single":[153],"grid":[154],"every":[156],"integral;":[157],"truncation":[159],"errors":[160],"have":[161],"closed-form":[162],"bounds,":[163],"step":[166],"size,":[167],"which":[168],"controls":[169],"discretization":[171],"error,":[172],"follows":[173],"from":[174,191],"field":[176],"size.":[177],"numerically":[179],"stable":[180],"deconvolution":[181],"then":[182],"recovers":[183],"each":[184],"leave-one-out":[186],"coefficients":[187],"$O(n)$":[189],"time":[190],"one":[192,239],"shared":[193],"product.":[194],"On":[195],"exactly":[196],"solvable":[197],"instances":[198],"up":[200],"4,000":[202],"players,":[203],"worst":[205,218],"observed":[206],"relative":[207],"error":[208,220],"an":[210],"equity":[211],"$4.0":[213],"\\times":[214,226],"10^{-14}$":[215],"absolute":[219],"probability":[224],"$1.1":[225],"10^{-14}$.":[227],"full":[229],"matrix":[231],"1,000":[233],"takes":[235],"0.2":[236],"seconds":[237],"CPU":[240],"core.":[241]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-07T00:00:00"}