I designed and taught a new Game Theory course in spring 2017 (students enrolled from computer science, statistics, bioinformatics, and electrical and computer engineering departments). Here are slides providing an overview of my research from the recent SCIS Information Session. In fall 2017 I designed and taught a new undergraduate class Artificial Intelligence. See related post "3-player Kuhn poker project". See also video from AI workshop at FIU's ShellHacks Hackathon, "Artificial Intelligence: From Poker Agents to Hurricane Prediction."
I have a PhD in computer science from Carnegie Mellon University and A.B. in math from Harvard University (see my CV here). I'm interested in artificial intelligence, game theory, multiagent systems, multiagent learning, large-scale optimization, large-scale data analysis and analytics, and knowledge representation, and applications including poker, education, medicine, socialization, and hurricane prediction. My dissertation was on scalable approaches for computing game-theoretic solution concepts and learning in imperfect-information games.
I created the two-player no-limit Texas hold 'em agent Claudico that competed against top human players in the Brains vs. Artificial Intelligence Competition. See my paper, slides, and video presentation (starting at 1:33). Here is a thread on the Two Plus Two Forum, the most popular poker forum, discussing the event. I describe Claudico's key strengths and weaknesses and address several common questions in this post. I also created the agent Tartanian7 that came in first place in the Annual Computer Poker Competition, beating each opposing agent with statistical significance. A brief description I wrote is available here, and a full description is provided in my paper below. I describe the design of the agent and the current state of research in computer poker in detail in this thread on the Two Plus Two Forum. The Brains vs. Artificial Intelligence Competition was organized by Professor Tuomas Sandholm. Collaborators on Claudico and Tartanian7 were Tuomas Sandholm and Noam Brown.
For takeaways and future directions, see the final chapter of my thesis, the final section of my paper on the Brains vs. Artificial Intelligence Competition, and slides from a talk I gave last year to the Princeton Poker Club. See also slides from my talk at Stanford which includes discussion of how Libratus improved on Claudico and slides from my more recent talk in Einstein's lecture hall at Princeton on the surprising breakthrough that enabled superhuman two-player no-limit Texas hold 'em play. Finally see slides from my talk "Strong Game-Theoretic Strategies: Beyond Two Agents" at the MIT Poker Club, and more recent talk "Successful Nash Equilibrium Agent for a 3-Player Imperfect-Information Game" in 2018 at the Princeton and MIT poker clubs.
I organized the first tutorial on Computer Poker with Marc Lanctot at the 2016 Conference on Economics and Computation. See my slides from part 1 and Marc's from part 2. I organized the AAAI-15 Workshop on Computer Poker and Imperfect Information and co-organized it in 2014 with Eric Jackson. Here is a report summarizing the highlights. I have been a PC member for AAAI ('12, '14, '15, '16, '17, '18), AAMAS ('14, '16, '21), ECAI ('23), IJCAI ('13, '15, '16, '22, '23), NeurIPS ('21), WWW ('18, '19). I have also reviewed for several journals.
I organized the second Computer Poker Tutorial with Johannes Heinrich and Kevin Waugh at AAAI 2017. Here are slides from part 1, part 2, and part 3. I recently gave a 3-part guest lecture at Tsinghua University on computer poker which is available on youtube: part 1, part 2, part 3.
See also recent articles from the Pittsburgh Tribune-Review, front page of the "Tropical Life" section of the Miami Herald, and PokerNews article "Turing and the Poker Endgame," as well as my tv debut as "The Robot" and subsequent commentary on Poker Night in America.
Sam Ganzfried, Kevin A. Wang, and Max Chiswick. 2022. Bayesian Opponent Modeling in Multiplayer Imperfect-Information Games.
Sam Ganzfried. 2022. Random Initialization Solves Shapley's Fictitious Play Counterexample.
Sam Ganzfried. 2022. Stable Relationships.
Sam Ganzfried. 2022. Best Response Computation in Multiplayer Imperfect-Information Stochastic Games. In Proceedings of the Florida Artificial Intelligence Research Society Conference (FLAIRS).
Sam Ganzfried. 2022. Human Strategic Decision Making in Parametrized Games. Mathematics, 10(7), 1147. Special Issue "Game Theory and Artificial Intelligence."
Sam Ganzfried. 2021. Algorithm for Computing Approximate Nash Equilibrium in Continuous Games with Application to Continuous Blotto. Games, 12(2), 47. Special issue "Economics of Conflict and Terrorism." First algorithm for solving continuous Blotto game. The Blotto game is a well-studied model of resource allocation with applications to national security, voting, and auctions. Initial work constructed analytical solutions of continuous models, and recently efficient algorithms have been developed for a discrete model. Algorithm applies to both perfect and imperfect information, and applies to continuous games in general beyond Blotto games. Experiments on a continuous Blotto game with asymmetric imperfect information.
Sam Ganzfried. 2021. Computing Nash Equilibria in Multiplayer DAG-Structured Stochastic Games with Persistent Imperfect Information. In Proceedings of the Conference on Decision and Game Theory for Security (GameSec). First algorithm for computing Nash equilibrium in multiplayer stochastic games with imperfect information that extends throughout game play, applied to a realistic national security scenario. Best paper award.
Sam Ganzfried. 2020. Fast Complete Algorithm for Multiplayer Nash Equilibrium. New algorithm for computing Nash equilibrium in normal-form games with three or more players that outperforms all prior algorithms. Video presentation.
Sam Ganzfried. 2020. Fictitious Play Outperforms Counterfactual Regret Minimization.Presentation.
Sam Ganzfried, Conner Laughlin, and Charles Morefield. 2020. Parallel Algorithm for Approximating Nash Equilibrium in Multiplayer Stochastic Games with Application to Naval Strategic Planning. In Proceedings of the International Conference on Distributed Artificial Intelligence (DAI). Video presentation.
Max Chiswick and Sam Ganzfried. 2020. Prediction of Bayesian Intervals for Tropical Storms. In Proceedings of the Florida Artificial Intelligence Research Society Conference (FLAIRS). Short version and oral presentation in Proceedings of the 2020 ICLR Workshop Tackling Climate Change with Machine Learning.
Sam Ganzfried and Max Chiswick. 2020. Most Important Fundamental Rule of Poker Strategy. In Proceedings of the Florida Artificial Intelligence Research Society Conference (FLAIRS). New human-understandable rule that outperforms the popular "Minimum Defense Frequency" (MDF) rule by over 60%. MDF is used to justify a high-stakes poker decision in this recent video clip (11:55).
Sam Ganzfried, Austin Nowak, and Joannier Pinales. 2018. Successful Nash Equilibrium Agent for a Three-Player Imperfect-Information Game. Games, 9(2), 33. Feature article.
Sheila Alemany, Jonathan Beltran, Adrian Perez, and Sam Ganzfried. 2019.
Predicting Hurricane Trajectories using a Recurrent Neural Network. In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI).
Sam Ganzfried and Farzana Yusuf. 2018. Optimal Weighting for Exam Composition. Education Sciences 8(1), 36. Special issue "Artificial Intelligence and Education."
Sam Ganzfried. 2017. Reflections on the First Man versus Machine No-Limit Texas Hold ‘em Competition. AI Magazine 38(2) summer issue. See SIGecom Exchanges version below.
Sam Ganzfried. 2017. Endgame Solving: The Surprising Breakthrough that Enabled Superhuman Two-Player No-Limit Texas Hold 'em Play. International Conference on Game Theory.
Sam Ganzfried and Farzana Yusuf. 2017. Computing Human-Understandable Strategies: Deducing Fundamental Rules of Poker Strategy. Games, 8(4), 49. Invited feature article.
New approach for computing strong game-theoretic strategies that can be easily understood by humans. This approach has enabled us to conclude several new fundamental rules of poker strategy, for example when to make a very small bet and when to make an extremely large one. Unconventional bet sizes were critical for recent poker agents such as Claudico (which I created) and Libratus.
Sam Ganzfried and Farzana Yusuf. 2019. Optimal Number of Choices in Rating Contexts. Big Data and Cognitive Computing, 3(3), 48. Special Issue "Computational Models of Cognition and Learning." Theory, simulations, and experimental results for the optimal number of choices to use from a small discrete set (which is used to approximate a large underlying choice set), with applications including online dating, paper reviewing, and exam grading. Counterintuitively, allowing more options is not always best, and fewer options is optimal surprisingly often. Editor's Choice article.
Sam Ganzfried and Qingyun Sun. 2018. Bayesian Opponent Exploitation in Imperfect-Information Games. In Proceedings of the Conference on Computational Intelligence and Games (CIG). See also the extended version containing proofs and additional analysis. First exact algorithm for opponent exploitation in Bayesian setting in imperfect-information games using natural prior models (Dirichlet and uniform).
Sam Ganzfried. 2015. Reflections on the First Man vs. Machine No-Limit Texas Hold 'em Competition. SIGecom Exchanges, Volume 14.2. Feature article. Earlier version from 9/15. Slides from presentation at 2016 World Congress of the Game Theory Society (7/16) and slides/video (starting at 1:33) from presentation at 2016 New York Computer Science and Economics Day (1/16). See AI Magazine version above. Many of the weaknesses of Claudico and future directions for improvement are described in detail in this article, which were used subsequently to implement Libratus that defeated the strongest humans in two-player no-limit Texas hold 'em.
Sam Ganzfried. 2015. Computing Strong Game-Theoretic Strategies and Exploiting Suboptimal Opponents in Large Games. PhD dissertation, Computer Science Department, Carnegie Mellon University. Available as CMU technical report CMU-CS-15-104.
Sam Ganzfried and Tuomas Sandholm. 2015. Endgame Solving in Large Imperfect-Information Games. In Proceedings of the International Conference on Autonomous Agents and Multiagent Systems (AAMAS). Early version appeared in Proceedings of the Workshop on Computer Poker and Imperfect Information at the AAAI Conference on Artificial Intelligence (AAAI), 2013. The best two-player no-limit Texas hold 'em player in the world (Doug Polk) stated that the "endgame solver" was the strongest component of the agent Claudico in the Brains vs. Artificial Intelligence Competition. The approach has been subsequently adopted by popular commercial software such as GTORangeBuilder and PioSOLVER, and extensions of the paradigm introduced in this work were crucial to the success of the recent agents DeepStack and Libratus. The leader of DeepStack has stated that "Deepstack is all endgame solving," and the strongest component of Libratus was an improved endgame solving approach that enabled solving both the turn and river rounds (as opposed to just the river) in real time on a supercomputer. Note that several subsequent papers have used the name "subgame" instead of "endgame" and that this is an identical concept. Some work has also referred to the approach as "unsafe [endgame] solving" (due to the fact that the approach does not have a theoretical worst-case performance guarantee while some of the newer approaches have limited theoretical worst-case guarantees in certain settings). E.g., "Nevertheless, in practice unsafe solving achieves strong performance and exhibits low exploitability, particularly in large games" [paper]. Both the Libratus and Modicum agents use "unsafe endgame solving" in certain situations, and there is no evidence that the "safe" version (which requires more computation) leads to improved head-to-head performance or lower exploitability in no-limit Texas hold 'em. Recent 6-player superhuman agent Pluribus also uses this approach. See also short article above, "Endgame Solving: The Surprising Breakthrough that Enabled Superhuman Two-Player No-Limit Texas Hold 'em Play."
Noam Brown*, Sam Ganzfried*, and Tuomas Sandholm. 2015. Hierarchical Abstraction, Distributed Equilibrium Computation, and Post-Processing, with Application to a Champion No-Limit Texas Hold'em Agent. In Proceedings of the International Conference on Autonomous Agents and Multiagent Systems (AAMAS). Short version appeared in Proceedings of the Demonstrations Program at the AAAI Conference on Artificial Intelligence, 2015. *Listed alphabetically. Describes architecture of two-player no-limit Texas hold 'em agent Tartanian7, which won the 2014 AAAI Annual Computer Poker Competition.
Sam Ganzfried and Tuomas Sandholm. 2015. Safe Opponent Exploitation. ACM Transactions on Economics and Computation (TEAC), 3(2), 8:1-28. Special issue on selected papers from EC-12. Algorithms and theory for when it is possible to deviate from just repeatedly playing one-shot equilibrium to exploit opponents' weaknesses.
Sam Ganzfried and Tuomas Sandholm. 2014. Potential-Aware Imperfect-Recall Abstraction with Earth Mover's Distance in Imperfect-Information Games. In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI). Algorithm for game abstraction that takes into account trajectories of private information revelation across all rounds. See discussion on Poker-AI forum.
Sam Ganzfried. 2013. Computing Strong Game-Theoretic Strategies and Exploiting Suboptimal Opponents in Large Games. Thesis proposal.
Sam Ganzfried and Tuomas Sandholm. 2013. Action Translation in Extensive-Form Games with Large Action Spaces: Axioms, Paradoxes, and the Pseudo-Harmonic Mapping*. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI). Algorithm for interpreting opponents' actions that have been removed from game abstraction, which is used by strongest no-limit Texas hold 'em agents. *Note this version contains minor corrections from the published IJCAI version.
Sam Ganzfried and Tuomas Sandholm. 2012. Safe Opponent Exploitation. In Proceedings of the ACM Conference on Electronic Commerce (EC). Succeeded by TEAC paper above.
Sam Ganzfried, Tuomas Sandholm, and Kevin Waugh. 2012. Strategy Purification and Thresholding: Effective Non-Equilibrium Approaches for Playing Large Games. In Proceedings of the International Conference on Autonomous Agents and Multiagent Systems (AAMAS). Theory and experiments for techniques for post-processing approximate equilibrium strategies of game abstractions.
Sam Ganzfried and Tuomas Sandholm. 2011. Game Theory-Based Opponent Modeling in Large Imperfect-Information Games. In Proceedings of the International Conference on Autonomous Agents and Multiagent Systems (AAMAS). Algorithm integrates approximate equilibrium prior with learning from observations and does not require historical data or domain-specific features. First approach for integrating behavioral strategy constraints in the context of opponent exploitation. This approach has recently been further explored by several others.
Sam Ganzfried. 2011. Computing Strong Game-Theoretic Strategies in Jotto. In Proceedings of the Conference on Advances in Computer Games (ACG). Jotto is a word game similar to Wordle. See more recent research on Jotto and Wordle by Peter Norvig.
Sam Ganzfried and Tuomas Sandholm. 2010. Computing Equilibria by Incorporating Qualitative Models. In Proceedings of the International Conference on Autonomous Agents and Multiagent Systems (AAMAS). Extended version as CMU technical report CMU-CS-10-105. Algorithm exploits human-understandable qualitative strategy model to improve equilibrium finding in Bayesian games with application to limit Texas hold 'em.
Sam Ganzfried and Tuomas Sandholm. 2009. Computing Equilibria in Multiplayer Stochastic Games of Imperfect Information. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI). New algorithm with theoretical results for computing approximate Nash equilibrium in multiplayer stochastic imperfect-information games with application to realistic three-player poker tournament. See 2020 DAI conference article above for successful application of extension of the algorithm to a national security scenario for naval strategic planning.
Sam Ganzfried and Tuomas Sandholm. 2008. Computing an Approximate Jam/Fold Equilibrium for 3-Player No-Limit Texas Hold'em Tournaments. In Proceedings of the International Conference on Autonomous Agents and Multiagent Systems (AAMAS). Algorithm computes approximate Nash equilibrium in multiplayer stochastic imperfect-information games, with application to a realistic three-player poker tournament. Similar approach has been subsequently adopted by popular commercial software such as HoldemResources.
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