2026-10-01
In a preregistered treasure-hunt task with 300 participants across three forms of stochasticity, planning effort fell monotonically: people determinize and compress their policy.
Lab research on planning runs on deterministic tasks: Tower of London, chess, Four-in-a-Row. Real planning is not like that. Restaurant ratings go stale, weather shifts mid-trip, a keypress executes as its opposite. Two literatures touch randomness without answering the core question. Work on risk preferences studies single-shot lotteries, where computing an expected value is trivial. Resource-rational theories, which treat cognition as a limited resource allocated by cost-benefit tradeoffs, predict that people should plan less when the environment is unpredictable, but that prediction had barely been tested in planning. The closest prior result, shorter-horizon crop choices after negative shocks in a farming task, confounds randomness with loss.
Wei Ji Ma's group at NYU built a treasure-hunt task: a triangle of chests labeled 1 to 9, seven binary moves per game, maximize the collected sum. 300 Prolific participants (preregistered) were each assigned one of three stochasticity manipulations, five levels each, announced and confirmed at block start: reliability (each chest is a "mystery" with probability q, its label meaningless and the payoff drawn uniformly from 1 to 9), volatility (at each step, every chest below the current row is redrawn with probability q, so distant chests are less stable), and controllability (the chosen move is flipped with probability q). Each participant played 150 games. The analysis is computational. A model space of up to 30 models crosses a filter (depth cutoff, value threshold, or rank cutoff) with a value function (optimal expected value, best deterministic path, level means, max, or sum) and an effort mechanism: filter adaptation lets the attended scope change with stochasticity while decision sensitivity stays fixed, policy compression holds the filter fixed and lets the sensitivity β vary. Both mechanisms carry 7 parameters, and models were ranked by 5-fold cross-validated negative log likelihood; the six EV variants were dropped in the volatility group, where the state space explodes.
| Measure (LMM slope per level of stochasticity) | Reliability (0-100%) | Volatility (0-100%) | Controllability (0-50%) |
| log first-choice RT | −0.63 (t98=−7.76) | −0.49 (t99=−8.83) | −0.94 (t98=−9.44) |
| log inverse temperature (winning Path model) | −1.86 | −1.76 | −3.96 |
| Points per game | −1.16 (t99=−19.8) | −1.26 (t99=−23.2) | −2.54 (t98=−22.9) |
RT and points rows all p<10^-10; the inverse-temperature row all P<0.001. Per-participant slopes point the same way for 82/100, 83/100, and 85/100 participants on first-choice RT. Part of the earnings drop is mechanical (mystery chests just pay less); the informative fact is that time and sensitivity shrink together. Model comparison adds two findings. First, people are not expected-value machines: where the EV model is tractable, it predicts indifference to label differences at maximum stochasticity, near coin-flip choices, yet participants keep chasing those differences. Treating a stochastic world as a deterministic one is called determinization in AI planning; FF-Replan won an international probabilistic planning competition with it, and this paper is the first to propose it as a model of human planning. Second, effort shrinks through policy compression, not filter adaptation: every winning model combines PC, depth filtering, and a determinizing value function, with the inverse temperature dropping as stochasticity rises. Under the comparably performing Level-Mean model the log-β slopes are −1.71, −1.82, and −4.04, the same conclusion. Model and parameter recovery checks pass; the participant-level Bayesian comparison (RFX-BMC) was sensitive to CV splits, and the authors report that honestly instead of overclaiming.
Resource-rational simulations close the loop on why: with reward R(β,q) estimated on 10,000 random boards at fixed depth 3 and a linear effort cost, the optimal log β falls monotonically with q in all three variants. Cutting effort is what optimal allocation looks like once marginal returns thin out.
For anyone building agents, this is a training-free reference for test-time compute allocation: how much to think should track how predictable the environment is, and human participants implement it by picking a good-enough deterministic approximation first, then tuning sensitivity to uncertainty. Policy compression also connects to information bottlenecks, dopamine responses to policy complexity, and robust agent design, all pointing at one conclusion: policy complexity itself has a cost worth optimizing. For behavioral economics, it is a warning that lottery-style single-shot findings do not extrapolate to branching multi-step decisions.
The authors list several: the individual-differences analysis (RFX-BMC) is sensitive to cross-validation splits, so they make no quantitative claims about strategy heterogeneity; models assume one strategy per person, though mixing within a person is plausible; the branching factor is small and the state space tractable, and more complex environments should push people toward pruning instead; and the findings cover irreducible (aleatoric) uncertainty only, whereas epistemic uncertainty that exploration could remove might justify more effort, not less. The supplement adds one more: the total-RT effect in the volatility group fails a sign test (55/100), attributed to motor delay contaminating total times. Beyond that, RT is a noisy proxy for effort, the simulation's cost parameters are illustrative, and the three manipulations span different ranges (controllability only reaches 50%), so slopes are not directly comparable across groups.