Metrics details Here we investigate expertise in a complex board game that offers ample opportunity for skilled players to plan deeply We use model fitting methods to show that human behaviour can be captured using a computational cognitive model based on heuristic search We also perform a Turing test and a reconstruction experiment we find robust evidence for increased planning depth with expertise in both laboratory and large-scale mobile data Experts memorize and reconstruct board features more accurately Using complex tasks combined with precise behavioural modelling might expand our understanding of human planning and help to bridge the gap with progress in artificial intelligence Prices may be subject to local taxes which are calculated during checkout Data supporting the findings of this study are publicly available at the Open Science Framework (https://osf.io/n2xjm/) Code used in this study is publicly available at the Open Science Framework (https://osf.io/n2xjm/) in Toward a General Theory of Expertise: Prospects and Limits (eds Anders A pattern-recognition theory of search in expert problem solving Adaptive expert decision making: Skilled chess players search more and deeper Entanglement of perception and reasoning in the combinatorial game of chess: differential errors of strategic reconstruction Model-based influences on humans’ choices and striatal prediction errors Bonsai trees in your head: how the Pavlovian system sculpts goal-directed choices by pruning decision trees The effects of time pressure on chess skill: an investigation into fast and slow processes underlying expert performance Chess players’ eye movements reveal rapid recognition of complex visual patterns: evidence from a chess-related visual search task Expert chess memory: revisiting the chunking hypothesis Mechanisms and neural basis of object and pattern recognition: a study with chess experts Visuospatial and articulatory interference in chess players’ information intake The Psychology of Chess Skill (Lawrence Erlbaum Towards a chess program based on a model of human memory Counting backward during chess move choice in Complex Information Processing 203–228 (Psychology Press Interplay of approximate planning strategies Prospective optimization with limited resources Hippocampal place-cell sequences depict future paths to remembered goals Planning at decision time and in the background during spatial navigation Dorsal hippocampus contributes to model-based planning Chronic exposure to methamphetamine disrupts reinforcement-based decision making in rats The anterior cingulate cortex predicts future states to mediate model-based action selection Combinatorial Games: Tic-Tac-Toe Theory Vol Tasks for aligning human and machine planning Heuristics: Intelligent Search Strategies for Computer Problem Solving (Addison-Wesley Longman Publishing Co. Generalized best-first search strategies and the optimality of A* Rational use of cognitive resources in human planning Unbiased and efficient log-likelihood estimation with inverse binomial sampling Practical Bayesian optimization for model fitting with Bayesian adaptive direct search Proceedings of the 31st International Conference on Neural Information Processing Systems 1834–1844 (2017) and forward search: Effects of playing speed and sight of the position on grandmaster chess errors Krusche, M. J., Schulz, E., Guez, A. & Speekenbrink, M. Adaptive planning in human search. Preprint at BioRxiv https://doi.org/10.1101/268938 (2018) Schema-based predictive eye movements support sequential memory encoding Investigating human priors for playing video games Intennational Conference of Machine Learning (ICML) (2018) The role of deliberate practice in chess expertise Meta Fundamental AI Research Diplomacy Team (FAIR) et al.Human-level play in the game of diplomacy by combining language models with strategic reasoning A general reinforcement learning algorithm that masters chess Combining q-learning and search with amortized value estimates International Conference on Learning Representations (ICLR) (2020) Ma, I., Phaneuf, C., van Opheusden, B., Ma, W. J. & Hartley, C. The component processes of complex planning follow distinct developmental trajectories. Preprint at PsyArXiv https://doi.org/10.31234/osf.io/d62rw (2022) Neurons in the orbitofrontal cortex encode economic value The eyelink toolbox: eye tracking with MATLAB and the psychophysics toolbox Die berechnung der turnier-ergebnisse als ein maximumproblem der wahrscheinlichkeitsrechnung MM algorithms for generalized Bradley-Terry models Reinforcement Learning: An Introduction Vol in Advances in Neural Information Processing Systems 1057–1063 (2000) Unbiased sequential estimation for binomial populations Global optimization by multilevel coordinate search Download references Shu for piloting an early version of the experiment; F Khalidi for assistance with data collection; and A and the other current members and alumni of the Ma laboratory for discussions This work was supported by grant number IIS-1344256 to W.J.M and by Graduate Research Fellowship number DGE1839302 to I.K Center for Neural Science and Department of Psychology All of the authors contributed to conceptualization of the research supervised the project and acquired funding The authors declare no competing interests reviewer(s) for their contribution to the peer review of this work Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations We validate our main model specification by comparing to alternatives in three categories: lesions generated by removing model components (red) extensions generated by adding new model components (blue) and modifications generated by replacing a model component with a similar implementation (green) across all participants in the laboratory experiments of the difference in log-likelihood with the main model Because model fitting is too computationally expense for parameter recovery we assess the reliability of the parameter estimates using less computationally expensive methods Pearson correlation across participants between model parameters estimated in two independent fits Error bars indicate the confidence interval for different sessions in the learning experiment 2-sample Kolmogorov-Smirnov test statistic between the distribution of \({\hat{\theta }}_{j}^{{\rm{lesion}}\,i}\) and \({\hat{\theta }}_{j}^{{\rm{full}}}\) for each pair of parameters we indicate tests that are significant after correcting for multiple comparisons using false discovery rate by *: α = 0.05 we additionally report uncorrected two-sided p-values Trade-offs between model parameters using a Pearson correlation between \({\hat{\theta }}_{i}^{{\rm{full}}}\) and \({\hat{\theta }}_{j}^{{\rm{full}}}-{\hat{\theta }}_{j}^{{\rm{lesion}}\,i}\) for each pair of model parameters Comparing our main model directly to human choices is challenging because the data is high-dimensional and discrete we compute summary statistics as a function of number of pieces on the board to probe for systematic patterns in the time course of people’s games such as a tendency to start playing near the centre of the board and gradually expand outwards We compare moves made in human-vs-human games (green solid lines) the behavioural model with inferred parameters on the same positions (blue solid lines) or random moves (black dashed lines) and the main model closely matches the human data All panels depict cross-validated predictions Each panel shows a scatterplot for the same set of summary statistics as in Extended Data Fig. 3 where each point represents a participant in the human-vs-human experiment the horizontal coordinate the statistic computed on that participant’s moves and the vertical coordinate the statistic computed on moves made by the model with parameters inferred for that participant on out-of-sample choices The Pearson correlation coefficient and two-sided p-value are reported within each panel The model accurately predicts individual differences between participants To investigate which patterns in the data are explained by tree search and feature dropping we compare the distribution of choices predicted by the main model against lesion models Example positions from human-vs-human games in which the model with (right column) and without tree search (left column) make highly different predictions (red shade) as quantified by Jensen-Shannon divergence we also show the models’ preferred move (with an x) and the move made by the human participant (open circle) These predictions are averaged across simulations with 200 different parameter vectors from fits to human data to capture positions with robust differences between planning and no planning we recognize these positions as ones where the player to move has multiple reasonable options but to evaluate their quality one has to calculate many moves ahead the move preferred by the No tree model is losing and the one by the main model is drawn but this relies on a specific 10-move forced sequence that can only be found through explicit search and using the ratio of the predicted probability of the human move as metric for selecting positions The feature drop mechanism is primarily necessary to account for people’s tendency to overlook possibilities to immediately make four-in-a-row or block immediate four-in-a-row threats by the opponent we showed participants video segments of sequences of moves Classification accuracy in the Turing test as a function of video length Participants are at chance level for classification of one-move videos (of which there were 8) and their accuracy only substantially exceeds 50% for sequences longer than 10 moves A mixed effects linear regression with accuracy as dependent variable and observer-specific random intercepts estimates the increase in accuracy per observed move as only 0.33 ± 0.10% Histogram of the percentage of observers classifying a given video as human-vs-human or computer-vs-computer While human games are on average more likely to be classified as human and computer games as computers there are no videos for which all 30 observers agree and there is a considerable fraction of videos (63 out of 180) for which a majority of observers respond incorrectly Coefficients in a linear regression predicting participants’ attentional distribution from the distribution of squares that the model includes in its principal variation at each depth The regression coefficients are significantly greater than zero (one-sample T-test across participants) for depth up to 7 Example positions from the eye tracking data in which the No feature drop model assigns low probability to the participant’s move The right column shows the eye movements while the participant contemplates their move the participant spends no time whatsoever looking at the square preferred by the model suggesting they indeed dropped the relevant four-in-a-row feature Planning depth vs Elo rating of all participants in the learning (green) and time pressure experiments (purple) Playing strength correlates with planning depth (ρ = 0.62 which does correlate with playing strength (ρ = 0.11 Response times for participants in each session of the learning experiment Participants play slightly faster in later sessions our finding of increased planning in later sessions is not confounded by an increase in thinking time The time limit manipulation is effective at increasing participants’ response times even though they use only a fraction of the available time on average Error rates in the memory and reconstruction experiment Although experts are slightly worse than novices in the extra piece error rate (β = 0.0071 ± 0.0031 experts substantially outperform novices in the missed piece (β = 0.037 ± 0.006 p < 0.001) and the wrong colour rate (β = 0.019 ± 0.003 Scatterplot of total reconstruction time for experts and novices Each point represents a board position in the memory in reconstruction experiment the x-coordinate the average time that experts take to finish their reconstruction and the y-coordinate the same but for novices Experts take more time to reconstruct pieces (β = 2.73 ± 0.57 meaning that the error rate result could reflect a speed-accuracy trade-off as opposed to an overall improvement experts reconstruct game-relevant features such as 3-in-a-row more accurately in the same amount of time Example position of the memory and reconstruction experiment The original board contains a 3-in-a-row feature on the bottom row (yellow shading) each circle indicates the distribution of pieces placed by different observers black and white wedges indicating the probability for that square to be empty Novices correctly reconstruct the 3-in-a-row feature 42.1% of the time these results suggest that players represent boards in memory in terms of game-relevant features a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law Download citation DOI: https://doi.org/10.1038/s41586-023-06124-2 Anyone you share the following link with will be able to read this content: a shareable link is not currently available for this article Sign up for the Nature Briefing newsletter — what matters in science 2024 1:00 PM(Credit: Tsuguliev/Shutterstock) NewsletterSign up for our email newsletter for the latest science newsSign Up Wouldn’t it be great to be able to know someone’s next move and beat them to it but it may also be that we were better at these skills in the first place According to research, expertise lays the groundwork when it comes to thinking farther ahead. The more skill you have in something like chess, the better equipped you are to think steps farther ahead when compared to a novice. In a study published in the journal Nature researchers found that participants are better able to think multiple moves ahead because they have a better handle on the game you can teach yourself to think farther ahead Lead study author Bas van Opheusden wanted to choose a methodology that could accurately assess how far participants were able to think ahead Using board games like chess has typically been more difficult because study participants might not know the rules of the game or how to play it researchers used a game called “four-in-a-row” to gauge abilities Think of it as a game of tic-tac-toe but with an added row there are a number of moves from which to choose making it a good choice for assessing the ability to think ahead “The rules are simple but the gameplay itself is actually quite complicated,” says van Opheusden a research scientist at the AI company Imbue who previously worked in Princeton University’s Griffiths Computational Cognitive Science Lab and it’s not known (and rather unlikely) that the same is true of chess He says that study participants would come back to the lab again and again Read More: Where Do Thoughts Occur? Jumping steps ahead has any number of benefits and it’s long been tied to human intelligence This was not part of van Opheusden’s research and participants did not take IQ tests or other intelligence assessments but we’ve previously known that thinking ahead is an aspect of intelligence “I don’t think it’s controversial to say that planning is a component of intelligence,” van Opheusden says the study also found that learning a skill helps you improve your ability to think ahead Researchers had the same participants come in four times to assess how practice improved their ability to win games Read More: The Science Of A Wandering Mind It was previously thought that the ability to think ahead was part of what makes us human, but new research disputes this. A July 2017 study published in the journal Science found that ravens were well-versed in thinking ahead The bottom line is that if you want to get better at a skill and master your opponent expertise is the best way to jump steps ahead the more likely you’ll be able to think steps ahead of your opponent Read More: Could Positive Thinking Do More Harm Than Good? Our writers at Discovermagazine.com use peer-reviewed studies and high-quality sources for our articles and our editors review for scientific accuracy and editorial standards Review the sources used below for this article: Nature. Expertise increases planning depth in human gameplay Bas van Opheusden Science. Ravens parallel great apes in flexible planning for tool-use and bartering PBS. Dolphins Plan Ahead Sara Novak is a science journalist based in South Carolina She graduated with a bachelor’s degree in Journalism from the Grady School of Journalism at the University of Georgia She's also a candidate for a master’s degree in science writing from Johns Hopkins University Register or Log In Want more?Keep reading for as low as $1.99 Subscribe Save up to 40% off the cover price when you subscribe to Discover magazine This website is using a security service to protect itself from online attacks The action you just performed triggered the security solution There are several actions that could trigger this block including submitting a certain word or phrase You can email the site owner to let them know you were blocked Please include what you were doing when this page came up and the Cloudflare Ray ID found at the bottom of this page XFASTINDEX Cooperation between Van Oord, GMB, BAM Speciale Technieken and RoyalHaskoningDHV has led to the development of the dyke pins as a new reinforcement method Client organisation Rivierenland Water Board is backing Van Oord and GMB’s use of the new method for the Hagestein-Opheusden Dike Improvement Project Installing the pins is an effective way of making dykes safer The innovation has been further improved on the back of a number of tests and pilot projects Rivierenland Water Board director of innovation Johan Bakker said: “Innovation succeeds more often than not To keep the Netherlands safe and to keep safety affordable we – in a joint effort – have to pull out all the stops.” managing director of GMB's flood prevention and construction division added: “Dyke pins are a simple and environmentally friendly way for us to reinforce dykes Their modular structure means they can be extended in future We use this valuable innovation in order to work considerately and safely on projects within the flood protection programme.” Got a story? 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