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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
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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
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Schema-based predictive eye movements support sequential memory encoding
Investigating human priors for playing video games
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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
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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
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DOI: https://doi.org/10.1038/s41586-023-06124-2
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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
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