Valet: A Standardized Testbed of Traditional Imperfect-Information Card Games

We introduce BluffJAX: an open-source suite of adversarial imperfect information games in JAX. We provide canonical implementations of games designed for high simulation throughputs and parallelization on GPU accelerators. Our suite consists of well-studied benchmarks such as Texas Hold'Em Poker and Kuhn Poker, as well as games that have not been previously studied in reinforcement learning research, such as Bluff, Stud Poker, and Kemps. We hope that implementing a variety of game mechanics and difficulties will introduce new challenges and foster novel research directions in game-theoretic methods for RL. We benchmark the throughput performance and memory usage of our environments in single and multi-GPU settings, demonstrating scaling of up to hundreds of millions of samples per second, and motivating the usage of BluffJAX over related GPU and CPU-based libraries. We benchmark reinforcement learning, tree search, and game-solving algorithms in JAX in order to provide users with baseline results and facilitate future comparisons.

Decision-time search in perfect and imperfect information games with enumerable belief states are effective methods for game AI. Collectible card games are imperfect information games with large belief states. Legends of Code and Magic is a collectible card game competition where the belief states are $2^{101}$. The Legends of Code and Magic (LoCM) champion, ByteRL, plays with no search. Other works claim sound enumeration-based search is unusable in the genre due to the number of belief states. We measured three previously defined properties that predict where theoretically unsound perfect information Monte Carlo's defects are cheap and found LoCM sits in the favorable region. Starting with imitation learning of the runner-up policy, NeteaseOPD, we created a policy and value feed-forward network. Our agent searches over worlds sampled from a prior over the opponent's deck built from the runner-up's drafts. Using our strictest configuration in the battle phase we beat ByteRL with a win percentage of 51.35% 95% CI [50.37, 52.33], over 10,000 pre-registered games using the LoCM official referee and time limit. Search is not a minor factor on the matchup between our agent and ByteRL. Without search this agent scores 26.8% and adding search adds +24.6 points. Unsound search in imperfect information games could be exploitable. We replicate a published best-response attack against ByteRL. We then apply the same attack protocol to two search configurations of our agent, and each one resists it better than ByteRL at every iteration. In LoCM unsound search gives us a stronger and more resilient agent.

Deciding which of two agents is stronger means playing games until skill outweighs luck, and every game costs money, model inference, or expert time. Since the number of games needed is unknown, fixed-budget evaluations either keep paying after the result is settled or stop before the agents can be told apart, while naive optional stopping with an ordinary confidence interval invalidates the stated level. We make such an evaluation stop as soon as its evidence suffices, with the guarantee intact. The Action-Informed Value Assessment Tool (AIVAT) reduces variance in imperfect-information games through conditional mean-zero corrections, by a median $54\times$ across 15 LLM agent configurations spanning 71,439 paired Heads-Up No-Limit Hold'em (HUNL) hands, but does not say when to stop. We combine AIVAT with continuously monitored Confidence Sequences (CSs) into anytime-valid AIVAT (AV-AIVAT), whose online value model learns only from past games so that no game scores its own correction. At the nominal 95% level and a target precision of $\pm1$ Big Blind, raw outcomes need a median $74\times$ as many hands as AIVAT-corrected outcomes to stop under the Asymptotic CS (AsympCS). Exact finite-sample certification uses the Empirical-Bernstein CS (EB-CS), which needs an independently justified bound on corrected payoffs. We establish such a bound structurally for Leduc hold'em and characterize a width floor set by the CS's bet cap and that bound, which governs how much of a variance gain becomes earlier stopping; the descriptive HUNL EB-CS runs show a median $1.37\times$ stopping-time ratio. AV-AIVAT turns variance reduction into efficient, auditable early stopping while separating asymptotic screening from exact certification, so an evaluation can stop the moment its evidence suffices and hand a third party everything needed to recheck the verdict at that very stopping time.