We propose InfoChess, a symmetric adversarial game that elevates competitive information acquisition to the primary objective. There is no piece capture, removing material incentives that would otherwise confound the role of information. Instead, pieces are used to alter visibility. Players are scored on their probabilistic inference of the opponent's king location over the duration of the game. To explore the space of strategies for playing InfoChess, we introduce a hierarchy of heuristic agents defined by increasing levels of opponent modeling, and train a reinforcement learning agent that outperforms these baselines. Leveraging the discrete structure of the game, we analyze gameplay through natural information-theoretic characterizations that include belief entropy, oracle cross entropy, and predictive log score under the action-induced observation channel. These measures disentangle epistemic uncertainty, calibration mismatch, and uncertainty induced by adversarial movement. The design of InfoChess renders it a testbed for studying multi-agent inference under partial observability. We release code for the environment and agents, and a public interface to encourage further study.
Figures & tables
Figure 1. The mechanics of InfoChess. (a) The starting configuration on an 8×8 board, where the king is placed randomly among the four indicated squares on each side. A turn consists of a non-king piece movement, a king movement, and then an inference about the location of the opponent’s king. Probability is assigned to all squares on the board, and the oracle records a score equal to the probability mass placed on the correct (ground truth) square where the opponent’s king is located. (b) Movement is the same for all pieces: one square in any direction, respecting exclusive occupancy. There are no piece captures in InfoChess. Visibility is piece-dependent: all pieces have visibility over their immediate vicinity, but the bishop and rook have viewing rays that match their movement in standard chess. (c) An example board state with annotations. Note that pawns obstruct the opponent’s vision: viewing rays end at a pawn’s square. The mechanics of InfoChess
Agent Name
Piece policy
King policy
King belief
Opponent visibility belief
Random
Random
Random
Uniform
Uniform
VisMax (V)
Greedy info gain
Random
Uniform
Uniform
BeliefMax (B)
Greedy info gain
Random
Learned
Uniform
HidingVisMax (HV)
Greedy info gain
Greedy concealment
Uniform
Learned
HidingBeliefMax (HB)
Greedy info gain
Greedy concealment
Learned
Learned
RL Agent
Learned
Learned
Learned
Learned
Table 1. Agent definitions in terms of movement policies and belief models. King and opponent visibility belief models are trained with privileged full-state supervision but operate on partial observations at evaluation.
Figure 2. Pairwise score distributions. Each scatter plot displays the final scores for 100 self-play matches (diagonal) or 200 cross-agent matches (100 for black-white and 100 for white-black). The horizontal axis represents the score for the agent corresponding to the label at the top of the column, and the percentage reflects the proportion of games won by the agent listed to the left of each row (whose score is on the vertical axis). Pairwise score distributions
Figure 3. Per-turn characterization. The curves show the mean of the quantity, averaged per turn per agent over 250 games per matchup, and the shaded regions indicate one standard deviation in either direction. “ Δ score” refers to the change in score earned during that turn. Per-turn characterization of all matchups against the VisMax and RL agents.
Figure 4. Non-king movement by agent. For each agent in 1,000 matches against randomly selected opponents (including self-play), the allocation of non-king movement is shown across the three types of pieces. Breakdown of non-king movement.
Real-world decision-making generally involves hidden information, that is, information that is unknown to one agent but possessed by another. Unfortunately, the presence of large amounts of hidden information renders established reinforcement learning and search approaches ineffective. Even with multimillion-dollar industrial research efforts, top-human-level play at Stratego---a board wargame with hidden information on a massive scale---has remained beyond the reach of artificial intelligence (AI). Here we introduce Ataraxos, an AI for Stratego based on general techniques that we developed for both self-play reinforcement learning and test-time search under hidden information. Ataraxos defeated the most decorated human Stratego player of all time by a large margin---achieving, to our knowledge, the first superhuman result in the game's history---while consuming orders of magnitude less compute and data than previous efforts. Using the same techniques, we built a superhuman AI for Barrage Stratego and state-of-the-art AIs for Hanabi and dou dizhu, all with low cost and high sample efficiency. The success of this approach across adversarial, cooperative and team games establishes a design pattern for reinforcement learning and search that is effective under large amounts of hidden information, a longstanding desideratum of the field of strategic decision-making.
Samuel Sokota, Eugene Vinitsky, Hengyuan Hu +3
Carnegie Mellon University · NYU Tandon School of Engineering · Stanford University +1
Agentic systems increasingly gate actions on a model's own stated confidence, which assumes confidence tracks correctness at the moment of acting. We test this in a hidden-information chess variant where royal status can be secretly, repeatedly relocated between pieces, and where an agent's stated probability distribution over the opponent's hidden royal piece -- elicited every turn, separately from the move it chooses -- is scored against ground truth recoverable after the game. Across two independent batches, captures made at high stated confidence (≥0.5) about the hidden piece's location were correct in 1 of 62 cases. The calibration deficit is concentrated almost entirely in these events: 99.3% of it in the original batch, 98.7% in the replication. The same pattern, in weaker form, orders consistently (point estimates only; most pairwise gaps are not statistically distinguishable at this sample size) across four further model configurations spanning a second provider -- reported as scope for the finding, not as evidence that capability predicts calibration: a same-model comparison at a fixed external leaderboard score shows a deliberation-budget change alone moves the metric by nearly as much as a large cross-model gap. In a separate seat, conventional evaluation axes -- legality, cost, latency, completion rate -- can dissociate entirely from belief quality, with the configuration winning on every conventional axis producing the worst belief quality tested. A model exhibiting this pattern can still win the game its belief was about, which is why outcome-only evaluation would not detect it.
We evaluate artificial intelligence (AI) systems without ground truth by exploiting a link between strategic gaming and information loss. Building on established information theory, we analyze which mechanisms resist adversarial manipulation. This motivates mutual evaluation, where the overseer is treated as a strategic player estimating mutual information by prompting, making truthful agent reporting an optimal strategy. We show that certain f-divergences, such as total variation distance (TVD), maintain polynomial guarantees under attack, building on an established exponential barrier for estimating mutual information (MI) in worst-case certification settings. Under adversarial attacks, TVD-MI maintains effectiveness (area under the curve 0.70--0.77) while other approaches can decay toward chance, demonstrating that prompting the same system for information relationships rather than quality judgments can improve robustness. The mechanisms decompose pairwise evaluations into reliable item-level detection scores without ground truth, addressing a key limitation of standard peer prediction. Pre-registration: https://osf.io/c7pum .
Zachary Robertson, Sanmi Koyejo
Department of Computer Science Stanford University