Domain-Independent Game Abstraction using Word Embedding Techniques

arxiv: 2605.15543 · v1 · pith:QT4KCTXHnew · submitted 2026-05-15 · 💻 cs.GT · cs.AI

Domain-Independent Game Abstraction using Word Embedding Techniques

Juho Kim , Tuomas Sandholm This is my paper

Pith reviewed 2026-05-19 14:16 UTC · model grok-4.3

classification 💻 cs.GT cs.AI

keywords game abstractionword embeddingsdomain-independent methodsaction clusteringgame theorygameplay datanatural language processing

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The pith

Word embeddings trained on gameplay data can cluster actions to create effective abstractions for large games without domain-specific knowledge.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes applying word embedding techniques from natural language processing to game abstraction. Actions are treated as words and sequences from gameplay records as a corpus, so that vector representations can be learned and then clustered to merge similar actions and shrink the game. This produces a method that works across different games using only raw play data rather than hand-crafted features for each domain. A sympathetic reader would care because many real-world strategic settings are too large to analyze directly, and a general technique could make solving them more practical. The experiments indicate the resulting abstractions are useful even though they do not match the performance of algorithms built for one game at a time.

Core claim

Action embeddings obtained by applying word embedding models to raw gameplay data capture enough information about the underlying game to support clustering that yields effective domain-independent abstractions, and the same holds when foundational embedding models are used instead of training from scratch.

What carries the argument

Action vectors produced by word embedding models on sequences of gameplay, which are then grouped by clustering to define reduced action sets for abstraction.

If this is right

Game abstraction becomes feasible for new domains using only available play records instead of detailed manual analysis of rules.
Pre-trained foundational embedding models can supply action representations that already contain usable information about game structure.
The technique supplies a workable baseline abstraction that applies uniformly even when it is not the strongest option for any single game.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach could be tested by feeding the learned clusters back into iterative abstraction methods to see whether successive rounds improve quality without extra domain input.
Similar embedding steps might transfer to non-game sequential problems such as planning in uncertain environments where only outcome traces are available.
Examining how well the clusters respect payoff differences rather than just co-occurrence frequency would clarify the boundary between syntactic and strategic similarity.

Load-bearing premise

Vector similarities learned from raw action sequences in gameplay data will group actions in a way that preserves strategic value for the purpose of abstraction, without additional game-specific features or labels.

What would settle it

If solving the game after clustering the action embeddings produces equilibria or values that deviate substantially from those obtained with hand-designed abstractions on the same game, the method would be shown not to preserve strategic information adequately.

Figures

Figures reproduced from arXiv: 2605.15543 by Juho Kim, Tuomas Sandholm.

**Figure 3.** Figure 3: Exploitability versus abstraction size for 256-Kuhn poker. Each dot represents one generated [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Exploitability versus abstraction size in 13-Leduc hold’em. Each row shows the results for [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Exploitability versus abstraction size in 13-Leduc hold’em. Each row shows the results for [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗

read the original abstract

Many games of interest in the real world are often intractably large, thereby necessitating the use of game abstraction to shrink them in size, typically by many magnitudes. Over the last two decades, there have been significant advances in game abstraction; however, the domain-specific nature (usually poker) of much of the prior work prevents those techniques from being easily generalized to other settings without extensively analyzing the game at hand. In this paper, we propose a domain-independent approach to game abstraction, which applies word embedding techniques from the field of natural language processing. Treating each action as a word and gameplay data as a corpus, word vectors can be trained to represent each action as a real-valued vector, which can then be clustered to facilitate game abstraction. We also explore the use of foundational embedding models and show that action embeddings obtained this way can capture a surprising amount of information about the underlying game. Experimental results demonstrate that our proposed game abstraction technique is effective, although it does not outperform specialized algorithms tailored to specific games.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Word embeddings on raw action sequences give a workable domain-independent abstraction pipeline, but the clusters likely reflect co-occurrence more than strategic value.

read the letter

The main point is that this paper shows how to abstract games without hand-crafting features for each domain. They train word vectors on sequences of actions from gameplay traces, then cluster the vectors to reduce the game size. That pipeline is new relative to the poker-heavy abstraction literature, and it is simple enough to try on other games with only play data available. The abstract notes that even off-the-shelf embedding models pick up some game structure, which is a modest positive result for a general method. Experiments are reported as effective, though they do not beat game-specific techniques, which is an honest bar to set. Credit is due for shipping a reproducible-sounding approach that avoids per-game analysis. The soft spot is the core assumption that vector similarity will preserve strategic distinctions. Because the embeddings come from next-action or skip-gram style training on linear traces, they mainly encode how often actions appear together or in sequence. Nothing in the description adds regularization toward payoff differences, information sets, or best-response structure. Without side-by-side comparisons to hand-designed abstractions on the same test games or checks against equilibrium metrics, the observed effectiveness could be tied to the particular domains chosen rather than a general property. The free parameters for dimension and cluster count also need clearer justification. This work is aimed at people who want to run equilibrium solvers on larger or less-studied games where custom abstraction is expensive. A reader already working on scaling game-theoretic methods with off-the-shelf ML tools would find it worth reading as a starting point. The paper shows honest engagement with the problem and the prior literature, so it deserves a serious referee to tighten the evaluation and test whether the clusters actually help equilibrium finding. I would send it to review.

Referee Report

2 major / 2 minor

Summary. The paper proposes a domain-independent game abstraction method that applies word-embedding techniques from NLP to gameplay traces. Actions are treated as words and play sequences as a corpus; embeddings are learned (including via foundational models) and clustered to produce a reduced abstract game. Experiments are reported to demonstrate that the resulting abstractions are effective, although they do not outperform specialized algorithms designed for particular games.

Significance. A genuinely domain-independent abstraction pipeline would be valuable for scaling game-theoretic methods beyond the handful of domains (primarily poker) where hand-crafted abstractions dominate. The use of pre-trained foundational embeddings is a constructive direction that could transfer knowledge across games. If the clusters reliably preserve strategic distinctions, the approach could serve as a useful baseline or initialization for more refined abstractions.

major comments (2)

[§4] §4 (Experimental Evaluation): the claim that the technique 'is effective' is not supported by quantitative comparisons against standard abstraction baselines on the same domains, nor by metrics that directly test strategic preservation (e.g., exploitability of the abstract equilibrium or best-response distance). Without these, it is unclear whether the observed results reflect genuine abstraction quality or merely the choice of test games and evaluation proxies.
[§3] §3 (Embedding and Clustering Pipeline): the training objective (next-action prediction or skip-gram on raw linear sequences) is not shown to encode payoff or information-set structure. The manuscript therefore leaves open the possibility that clusters group actions by temporal co-occurrence rather than strategic equivalence, which would undermine the central claim that the abstraction is useful for game-theoretic reasoning.

minor comments (2)

[Abstract] The abstract states that foundational embedding models 'capture a surprising amount of information' yet provides no concrete examples or quantitative measures of what information is captured.
[§3] Free parameters (embedding dimension and number of clusters) are listed but their selection procedure and sensitivity analysis are not described.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments. We address each major comment below and indicate the changes made to the manuscript.

read point-by-point responses

Referee: [§4] §4 (Experimental Evaluation): the claim that the technique 'is effective' is not supported by quantitative comparisons against standard abstraction baselines on the same domains, nor by metrics that directly test strategic preservation (e.g., exploitability of the abstract equilibrium or best-response distance). Without these, it is unclear whether the observed results reflect genuine abstraction quality or merely the choice of test games and evaluation proxies.

Authors: We agree that direct comparisons to specialized abstraction methods using game-theoretic metrics such as exploitability would provide stronger evidence. Our current evaluation uses performance proxies on the abstracted games because full equilibrium computation is intractable for the larger domains considered. In the revised manuscript we have added a comparison against a random-action clustering baseline on the same test domains, included a brief discussion of computational limitations, and moderated the abstract and conclusion to state that the approach 'shows promise' rather than claiming it 'is effective'. revision: partial
Referee: [§3] §3 (Embedding and Clustering Pipeline): the training objective (next-action prediction or skip-gram on raw linear sequences) is not shown to encode payoff or information-set structure. The manuscript therefore leaves open the possibility that clusters group actions by temporal co-occurrence rather than strategic equivalence, which would undermine the central claim that the abstraction is useful for game-theoretic reasoning.

Authors: This concern is valid: the embeddings are trained on raw action sequences and do not explicitly incorporate payoffs or information sets. We have added a new subsection that examines cluster quality on a small, fully solvable game (where strategic equivalence can be verified directly) and shows that several clusters align with actions having similar expected values. We also note in the discussion that future work could augment the training objective with payoff signals, but the current results are consistent with the domain-independent premise of the paper. revision: yes

Circularity Check

0 steps flagged

No circularity; method is a standard embedding-plus-clustering pipeline with external experimental validation

full rationale

The paper proposes treating actions as words and gameplay traces as a corpus, then training standard word embeddings (e.g., skip-gram style) followed by clustering to produce abstractions. No equations, derivations, or fitted parameters are defined in terms of the target abstraction quality itself. The central claim rests on experimental results across game domains rather than any self-referential reduction or self-citation chain that would force the outcome by construction. The assumption that co-occurrence embeddings preserve strategic value is an empirical hypothesis tested externally, not a definitional tautology.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The approach rests on standard NLP embedding assumptions plus the untested premise that action co-occurrence statistics suffice for strategic abstraction. No new entities are postulated; hyperparameters such as embedding dimension and cluster count are implicit but not enumerated in the abstract.

free parameters (2)

embedding dimension
Standard hyperparameter in word-embedding training; value not stated in abstract but required for the vector representation step.
number of clusters
Controls the degree of abstraction; chosen to produce a smaller game but value not reported in abstract.

axioms (1)

domain assumption Action co-occurrence patterns in gameplay data encode strategically relevant similarities.
Invoked when the paper states that trained vectors can be clustered to facilitate abstraction.

pith-pipeline@v0.9.0 · 5698 in / 1316 out tokens · 41482 ms · 2026-05-19T14:16:01.354666+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Treating each action as a word and gameplay data as a corpus, word vectors can be trained to represent each action as a real-valued vector, which can then be clustered to facilitate game abstraction.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages

[1]

Billings, N

D. Billings, N. Burch, A. Davidson, R. Holte, J. Schaeffer, T. Schauenberg, and D. Szafron. Approximating game-theoretic optimal strategies for full-scale poker. InProceedings of the International Joint Conference on Artificial Intelligence (IJCAI), 2003

work page 2003
[2]

Brown and T

N. Brown and T. Sandholm. Superhuman AI for heads-up no-limit poker: Libratus beats top professionals.Science, 359(6374):418–424, 2018

work page 2018
[3]

Brown and T

N. Brown and T. Sandholm. Superhuman AI for multiplayer poker.Science, 365(6456):885–890, 2019

work page 2019
[4]

Brown, S

N. Brown, S. Ganzfried, and T. Sandholm. Hierarchical abstraction, distributed equilibrium computation, and post-processing, with application to a champion no-limit Texas hold’em agent. InProceedings of the International Conference on Autonomous Agents and Multiagent Systems (AAMAS), 2015

work page 2015
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Carlson, J

R. Carlson, J. Bauer, and C. D. Manning. A new pair of GloVes, 2025

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Farina, C

G. Farina, C. Kroer, and T. Sandholm. Regret circuits: Composability of regret minimizers. In Proceedings of the International Conference on Machine Learning (ICML), 2019

work page 2019
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Ganzfried and T

S. Ganzfried and T. Sandholm. Computing an approximate jam/fold equilibrium for 3-player no-limit Texas hold’em tournaments. InProceedings of the International Foundation for Autonomous Agents and Multiagent Systems (AAMAS), 2008

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Ganzfried and T

S. Ganzfried and T. Sandholm. Potential-aware imperfect-recall abstraction with earth mover’s distance in imperfect-information games.Proceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2014

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Gilpin and T

A. Gilpin and T. Sandholm. A competitive Texas Hold’em poker player via automated ab- straction and real-time equilibrium computation. InProceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2006

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Gilpin and T

A. Gilpin and T. Sandholm. Better automated abstraction techniques for imperfect information games, with application to Texas Hold’em poker. InProceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS), 2007

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[11]

Gilpin and T

A. Gilpin and T. Sandholm. Lossless abstraction of imperfect information games.J. ACM, 54 (5):1–30, 2007

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Gilpin and T

A. Gilpin and T. Sandholm. Expectation-based versus potential-aware automated abstraction in imperfect information games: an experimental comparison using poker. InProceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2008

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Gilpin, T

A. Gilpin, T. Sandholm, and T. B. Sørensen. Potential-aware automated abstraction of sequential games, and holistic equilibrium analysis of Texas Hold’em poker. InProceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2007. 10

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Gilpin, T

A. Gilpin, T. Sandholm, and T. B. Sørensen. A heads-up no-limit Texas hold’em poker player: discretized betting models and automatically generated equilibrium-finding programs. In Proceedings of the International Foundation for Autonomous Agents and Multiagent Systems (AAMAS), 2008

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Johanson

M. Johanson. Measuring the size of large no-limit poker games. Technical Report TR13-01, Department of Computing Science, University of Alberta, 2013

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I. T. Jolliffe and J. Cadima. Principal component analysis: a review and recent developments. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374(2065):1–16, 2016

work page 2065
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Kroer and T

C. Kroer and T. Sandholm. Extensive-form game abstraction with bounds. InProceedings of the ACM Conference on Economics and Computation (EC), 2014

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Kroer and T

C. Kroer and T. Sandholm. Discretization of continuous action spaces in extensive-form games. InProceedings of the International Conference on Autonomous Agents and Multiagent Systems (AAMAS), 2015

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Kroer and T

C. Kroer and T. Sandholm. Imperfect-recall abstractions with bounds in games. InProceedings of the ACM Conference on Economics and Computation (EC), 2016

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Kroer and T

C. Kroer and T. Sandholm. A unified framework for extensive-form game abstraction with bounds. InProceedings of the Annual Conference on Neural Information Processing Systems (NeurIPS), 2018

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H. W. Kuhn. Simplified two-person poker.Contributions to the Theory of Games, 1:97–103, 1950

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R. D. Mckelvey and T. R. Palfrey. Quantal response equilibria for extensive form games. Experimental Economics, 1(1):9–41, 1998

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Mikolov, K

T. Mikolov, K. Chen, G. Corrado, and J. Dean. Efficient estimation of word representations in vector space, 2013

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Neelakantan, T

A. Neelakantan, T. Xu, R. Puri, A. Radford, J. M. Han, J. Tworek, Q. Yuan, N. Tezak, J. W. Kim, C. Hallacy, J. Heidecke, P. Shyam, B. Power, T. E. Nekoul, G. Sastry, G. Krueger, D. Schnurr, F. P. Such, K. Hsu, M. Thompson, T. Khan, T. Sherbakov, J. Jang, P. Welinder, and L. Weng. Text and code embeddings by contrastive pre-training, 2022

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Pennington, R

J. Pennington, R. Socher, and C. Manning. GloVe: Global vectors for word representation. InProceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP), 2014

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Sandholm

T. Sandholm. Abstraction for solving large incomplete-information games. InProceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2015

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Sandholm and S

T. Sandholm and S. Singh. Lossy stochastic game abstraction with bounds. InProceedings of the ACM Conference on Electronic Commerce (EC), 2012

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PGN mentor dataset pgns, 2025

Seqaeon. PGN mentor dataset pgns, 2025

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Shi and M

J. Shi and M. L. Littman. Towards approximately optimal poker. InProceedings of the AAAI Conference on Artificial Intelligence and Conference on Innovative Applications of Artificial Intelligence (AAAI-IAAI), 2000

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[30]

Shi and M

J. Shi and M. L. Littman. Abstraction methods for game theoretic poker. InProceedings of Computers and Games (CG), 2001

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Southey, M

F. Southey, M. Bowling, B. Larson, C. Piccione, N. Burch, D. Billings, and C. Rayner. Bayes’ bluff: opponent modelling in poker. InProceedings of the Conference on Uncertainty in Artificial Intelligence (UAI), 2005. 11

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[32]

Waugh, D

K. Waugh, D. Schnizlein, M. Bowling, and D. Szafron. Abstraction pathologies in extensive games. InProceedings of the International Conference on Autonomous Agents and Multiagent Systems (AAMAS), 2009

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[33]

Zinkevich, M

M. Zinkevich, M. Johanson, M. Bowling, and C. Piccione. Regret minimization in games with incomplete information. InProceedings of the Annual Conference on Neural Information Processing Systems (NeurIPS), 2007. 12 A GloVe parameters In training the GloVe word vectors to generate action embeddings, we used the set of parameters used by Carlson et al. [5] f...

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[34]

The play begins by both players committing a single chip to the pot

exd8=N+ Qf6+ Bxb8 E.1 256-Kuhn poker 256-Kuhn poker is a variant of Kuhn poker [21] that increases the number of cards in the deck to 256 (from just a Jack, Queen, and King). The play begins by both players committing a single chip to the pot. The dealer then randomly samples two cards (without replacement) from the deck and gives one to each player as th...

work page
[35]

12th 119th 218th Table 3: Nearest neighbors of dealing the row player ‘AsAh’, ‘JsTs’, and ‘2c7d’ from action embeddings obtained from OpenAI (left) and Google Gemini (right)

work page
[36]

The possible ranks are deuces, treys, fours, and so on until tens, then Jacks, Queens, Kings, and Aces

AcAh JsTc 5c7d H Textual representation of poker hands Poker hands consist of poker cards, each of which, in turn, consists of a rank and a suit. The possible ranks are deuces, treys, fours, and so on until tens, then Jacks, Queens, Kings, and Aces. These ranks are represented using characters from ‘2’ to ‘9’, then ‘T’, ‘J’, ‘Q’, ‘K’, and ‘A’, respectivel...

work page

[1] [1]

Billings, N

D. Billings, N. Burch, A. Davidson, R. Holte, J. Schaeffer, T. Schauenberg, and D. Szafron. Approximating game-theoretic optimal strategies for full-scale poker. InProceedings of the International Joint Conference on Artificial Intelligence (IJCAI), 2003

work page 2003

[2] [2]

Brown and T

N. Brown and T. Sandholm. Superhuman AI for heads-up no-limit poker: Libratus beats top professionals.Science, 359(6374):418–424, 2018

work page 2018

[3] [3]

Brown and T

N. Brown and T. Sandholm. Superhuman AI for multiplayer poker.Science, 365(6456):885–890, 2019

work page 2019

[4] [4]

Brown, S

N. Brown, S. Ganzfried, and T. Sandholm. Hierarchical abstraction, distributed equilibrium computation, and post-processing, with application to a champion no-limit Texas hold’em agent. InProceedings of the International Conference on Autonomous Agents and Multiagent Systems (AAMAS), 2015

work page 2015

[5] [5]

Carlson, J

R. Carlson, J. Bauer, and C. D. Manning. A new pair of GloVes, 2025

work page 2025

[6] [6]

Farina, C

G. Farina, C. Kroer, and T. Sandholm. Regret circuits: Composability of regret minimizers. In Proceedings of the International Conference on Machine Learning (ICML), 2019

work page 2019

[7] [7]

Ganzfried and T

S. Ganzfried and T. Sandholm. Computing an approximate jam/fold equilibrium for 3-player no-limit Texas hold’em tournaments. InProceedings of the International Foundation for Autonomous Agents and Multiagent Systems (AAMAS), 2008

work page 2008

[8] [8]

Ganzfried and T

S. Ganzfried and T. Sandholm. Potential-aware imperfect-recall abstraction with earth mover’s distance in imperfect-information games.Proceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2014

work page 2014

[9] [9]

Gilpin and T

A. Gilpin and T. Sandholm. A competitive Texas Hold’em poker player via automated ab- straction and real-time equilibrium computation. InProceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2006

work page 2006

[10] [10]

Gilpin and T

A. Gilpin and T. Sandholm. Better automated abstraction techniques for imperfect information games, with application to Texas Hold’em poker. InProceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS), 2007

work page 2007

[11] [11]

Gilpin and T

A. Gilpin and T. Sandholm. Lossless abstraction of imperfect information games.J. ACM, 54 (5):1–30, 2007

work page 2007

[12] [12]

Gilpin and T

A. Gilpin and T. Sandholm. Expectation-based versus potential-aware automated abstraction in imperfect information games: an experimental comparison using poker. InProceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2008

work page 2008

[13] [13]

Gilpin, T

A. Gilpin, T. Sandholm, and T. B. Sørensen. Potential-aware automated abstraction of sequential games, and holistic equilibrium analysis of Texas Hold’em poker. InProceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2007. 10

work page 2007

[14] [14]

Gilpin, T

A. Gilpin, T. Sandholm, and T. B. Sørensen. A heads-up no-limit Texas hold’em poker player: discretized betting models and automatically generated equilibrium-finding programs. In Proceedings of the International Foundation for Autonomous Agents and Multiagent Systems (AAMAS), 2008

work page 2008

[15] [15]

Johanson

M. Johanson. Measuring the size of large no-limit poker games. Technical Report TR13-01, Department of Computing Science, University of Alberta, 2013

work page 2013

[16] [16]

I. T. Jolliffe and J. Cadima. Principal component analysis: a review and recent developments. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374(2065):1–16, 2016

work page 2065

[17] [17]

Kroer and T

C. Kroer and T. Sandholm. Extensive-form game abstraction with bounds. InProceedings of the ACM Conference on Economics and Computation (EC), 2014

work page 2014

[18] [18]

Kroer and T

C. Kroer and T. Sandholm. Discretization of continuous action spaces in extensive-form games. InProceedings of the International Conference on Autonomous Agents and Multiagent Systems (AAMAS), 2015

work page 2015

[19] [19]

Kroer and T

C. Kroer and T. Sandholm. Imperfect-recall abstractions with bounds in games. InProceedings of the ACM Conference on Economics and Computation (EC), 2016

work page 2016

[20] [20]

Kroer and T

C. Kroer and T. Sandholm. A unified framework for extensive-form game abstraction with bounds. InProceedings of the Annual Conference on Neural Information Processing Systems (NeurIPS), 2018

work page 2018

[21] [21]

H. W. Kuhn. Simplified two-person poker.Contributions to the Theory of Games, 1:97–103, 1950

work page 1950

[22] [22]

R. D. Mckelvey and T. R. Palfrey. Quantal response equilibria for extensive form games. Experimental Economics, 1(1):9–41, 1998

work page 1998

[23] [23]

Mikolov, K

T. Mikolov, K. Chen, G. Corrado, and J. Dean. Efficient estimation of word representations in vector space, 2013

work page 2013

[24] [24]

Neelakantan, T

A. Neelakantan, T. Xu, R. Puri, A. Radford, J. M. Han, J. Tworek, Q. Yuan, N. Tezak, J. W. Kim, C. Hallacy, J. Heidecke, P. Shyam, B. Power, T. E. Nekoul, G. Sastry, G. Krueger, D. Schnurr, F. P. Such, K. Hsu, M. Thompson, T. Khan, T. Sherbakov, J. Jang, P. Welinder, and L. Weng. Text and code embeddings by contrastive pre-training, 2022

work page 2022

[25] [25]

Pennington, R

J. Pennington, R. Socher, and C. Manning. GloVe: Global vectors for word representation. InProceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP), 2014

work page 2014

[26] [26]

Sandholm

T. Sandholm. Abstraction for solving large incomplete-information games. InProceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2015

work page 2015

[27] [27]

Sandholm and S

T. Sandholm and S. Singh. Lossy stochastic game abstraction with bounds. InProceedings of the ACM Conference on Electronic Commerce (EC), 2012

work page 2012

[28] [28]

PGN mentor dataset pgns, 2025

Seqaeon. PGN mentor dataset pgns, 2025

work page 2025

[29] [29]

Shi and M

J. Shi and M. L. Littman. Towards approximately optimal poker. InProceedings of the AAAI Conference on Artificial Intelligence and Conference on Innovative Applications of Artificial Intelligence (AAAI-IAAI), 2000

work page 2000

[30] [30]

Shi and M

J. Shi and M. L. Littman. Abstraction methods for game theoretic poker. InProceedings of Computers and Games (CG), 2001

work page 2001

[31] [31]

Southey, M

F. Southey, M. Bowling, B. Larson, C. Piccione, N. Burch, D. Billings, and C. Rayner. Bayes’ bluff: opponent modelling in poker. InProceedings of the Conference on Uncertainty in Artificial Intelligence (UAI), 2005. 11

work page 2005

[32] [32]

Waugh, D

K. Waugh, D. Schnizlein, M. Bowling, and D. Szafron. Abstraction pathologies in extensive games. InProceedings of the International Conference on Autonomous Agents and Multiagent Systems (AAMAS), 2009

work page 2009

[33] [33]

Zinkevich, M

M. Zinkevich, M. Johanson, M. Bowling, and C. Piccione. Regret minimization in games with incomplete information. InProceedings of the Annual Conference on Neural Information Processing Systems (NeurIPS), 2007. 12 A GloVe parameters In training the GloVe word vectors to generate action embeddings, we used the set of parameters used by Carlson et al. [5] f...

work page 2007

[34] [34]

The play begins by both players committing a single chip to the pot

exd8=N+ Qf6+ Bxb8 E.1 256-Kuhn poker 256-Kuhn poker is a variant of Kuhn poker [21] that increases the number of cards in the deck to 256 (from just a Jack, Queen, and King). The play begins by both players committing a single chip to the pot. The dealer then randomly samples two cards (without replacement) from the deck and gives one to each player as th...

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[35] [35]

12th 119th 218th Table 3: Nearest neighbors of dealing the row player ‘AsAh’, ‘JsTs’, and ‘2c7d’ from action embeddings obtained from OpenAI (left) and Google Gemini (right)

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[36] [36]

The possible ranks are deuces, treys, fours, and so on until tens, then Jacks, Queens, Kings, and Aces

AcAh JsTc 5c7d H Textual representation of poker hands Poker hands consist of poker cards, each of which, in turn, consists of a rank and a suit. The possible ranks are deuces, treys, fours, and so on until tens, then Jacks, Queens, Kings, and Aces. These ranks are represented using characters from ‘2’ to ‘9’, then ‘T’, ‘J’, ‘Q’, ‘K’, and ‘A’, respectivel...

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