Confident at the moment of action: belief miscalibration in LLM play under hidden information

Abstract

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 ($\geq 0.5$) 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.