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Record W2006791053 · doi:10.1126/science.1259433

Heads-up limit hold’em poker is solved

2015· article· en· W2006791053 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueScience · 2015
Typearticle
Languageen
FieldComputer Science
TopicArtificial Intelligence in Games
Canadian institutionsUniversity of Alberta
FundersNatural Sciences and Engineering Research Council of CanadaUniversity of AlbertaAlberta Innovates - Technology FuturesCompute Canada
KeywordsPerfect informationLimit (mathematics)ImperfectComputationComputer scienceCombinatorial game theoryMathematical economicsExtensive-form gameSequential gameComplete informationGame theoryTheoretical computer scienceMathematicsAlgorithm

Abstract

fetched live from OpenAlex

Poker is a family of games that exhibit imperfect information, where players do not have full knowledge of past events. Whereas many perfect-information games have been solved (e.g., Connect Four and checkers), no nontrivial imperfect-information game played competitively by humans has previously been solved. Here, we announce that heads-up limit Texas hold'em is now essentially weakly solved. Furthermore, this computation formally proves the common wisdom that the dealer in the game holds a substantial advantage. This result was enabled by a new algorithm, CFR(+), which is capable of solving extensive-form games orders of magnitude larger than previously possible.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Other design · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.606
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.002
Science and technology studies0.0000.001
Scholarly communication0.0010.002
Open science0.0030.001
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.002

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.114
GPT teacher head0.335
Teacher spread0.220 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it