🧬 biology

People use fast and flat simulation to reason about new games

Through large-scale behavioral studies and a computational "Intuitive Gamer" model, this paper demonstrates that humans systematically and adaptively reason about novel games using fast, depth-limited probabilistic simulations, offering insights for developing more flexible, human-like AI systems.

Original authors: Katherine M. Collins, Cedegao E. Zhang, Lionel Wong, Mauricio Barba da Costa, Graham Todd, Adrian Weller, Samuel J. Cheyette, Thomas L. Griffiths, Joshua B. Tenenbaum

Published 2026-07-14

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Katherine M. Collins, Cedegao E. Zhang, Lionel Wong, Mauricio Barba da Costa, Graham Todd, Adrian Weller, Samuel J. Cheyette, Thomas L. Griffiths, Joshua B. Tenenbaum

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine you're handed a brand-new board game you've never seen before. The rules are weird: maybe you win by getting four in a row on a 10x10 grid, or maybe the first person to get three in a row actually loses. You haven't played a single turn. You don't have a strategy guide. You don't have a coach.

So, how do you figure out if the game is fair? How do you decide if it's going to be fun? And if you have to make your very first move, what do you do?

Most people assume that to play a game well, you need to be a grandmaster who has spent years calculating millions of future possibilities, like a supercomputer digging deep into a tree of "what-ifs." But a massive new study suggests that's not how our brains work when we encounter something new. Instead, we are like intuitive gamers who use a "fast and flat" mental shortcut.

The "Intuitive Gamer" in Your Head

The researchers, led by a team from MIT, Princeton, and Cambridge, studied over 1,000 people playing (or just thinking about) 121 different, mostly novel, two-player strategy games. They found that when we face a new problem, we don't run a deep, expensive simulation that looks 20 steps ahead. That would take too much brainpower.

Instead, our brains run a fast, flat, and probabilistic simulation.

Think of it like this: Imagine you are a video game character who can only look one step ahead. You see the board, and you ask yourself two simple questions:

"If I put my piece here, does it get me closer to winning?"
"If I put my piece here, does it stop my opponent from winning?"

You don't calculate the entire game to the end. You just take a quick, shallow peek. Then, you make a guess based on that peek. If you have to decide if the game is fair, you don't solve the math; you just run this quick "peek" simulation in your head maybe 5 to 7 times and see what usually happens. If in most of those quick runs, Player 1 wins, you guess the game is unfair. If they tie a lot, you guess it's balanced.

The paper calls this the "Intuitive Gamer" model. It suggests that humans are surprisingly good at this. When the researchers tested this model against real people, it predicted what people thought about fairness and what moves they would make with 81% accuracy (an R² of 0.81). That's almost as good as the "noise" in the human data itself, meaning the model captures almost everything we can explain about how people think.

What We Are Not Doing

The study explicitly argues against the idea that novices are doing deep, expert-level thinking.

We are not deep divers: The "Expert Gamer" model, which simulates looking about 5 steps ahead (like a chess master), was much worse at predicting what regular people would do. It was also 700 times slower to run on a computer than the simple "Intuitive Gamer" model.
We are not random: We aren't just picking moves by rolling dice. The "Random Gamer" model (which picks moves completely at random) was a terrible fit for how people actually played.
We are not perfect calculators: We don't have a perfect "Oracle" that knows the absolute best move. We are resource-limited. We do the best we can with a tiny amount of mental energy.

The "Fun" Factor

The researchers also asked people: "Before you even play, do you think this game will be fun?"
They found that our guess about funness isn't random either. It's based on the same quick simulations.

Balance: We like games where the winner isn't obvious from the start. If the first player always wins, it's boring. If it always ends in a tie, it's frustrating.
Thinking Reward: We like games where "thinking" actually helps you win more than just moving randomly.
Length: We like games that aren't too short and not too long. It's like a Goldilocks zone for game length.

The "Intuitive Gamer" model could predict these "fun" ratings with 57% accuracy, which is very close to the maximum possible accuracy for human opinions (which varied from person to person).

The Numbers Behind the Magic

The study didn't just guess; they measured it.

They tested 121 distinct games with rules like "3 in a row wins," "4 in a row loses," or "Player 2 gets to move twice on their first turn."
They had 238 people judge the fairness of games without playing them.
They had 302 people actually play 40 of these games for the first time.
They had 314 people watch videos of others playing and predict the next move.
The "Intuitive Gamer" model only needed to run about 6 simulations (k=6) to match human judgment.
In terms of speed, the Intuitive Gamer model was nearly 40,000 times faster than a standard AI method called Monte Carlo Tree Search (MCTS) and 700 times faster than the "Expert Gamer" model.

The Bottom Line

The paper suggests that when we face a completely new situation—whether it's a weird board game or a new kind of problem—we don't need to be geniuses or supercomputers to make a smart guess. We just need to run a few quick, shallow mental simulations, focusing on our goals and blocking our opponents.

This "fast and flat" way of thinking is efficient. It's not perfect, and it's not as deep as what a grandmaster does after years of practice, but it's adaptively rational. It's the perfect tool for a human brain that needs to make a decision now without spending all day thinking about it.

The authors admit this is a model of how we think about games (specifically perfect-information board games), and they suggest it might apply to other areas of life, like how scientists choose which problems to tackle. But for now, the evidence is strong: when we meet a new game, we are all intuitive gamers, running quick mental races to see who wins, and we're pretty good at it.

Technical Summary: People Use Fast and Flat Simulation to Reason About New Games

Problem Statement

While artificial intelligence and cognitive science have extensively studied expert-level and super-human performance in established games (e.g., Chess, Go), a significant gap remains in understanding how humans reason about novel problem settings they have never encountered before. Real-world decision-making often requires individuals to navigate systems of rules and rewards without prior experience, yet existing models of human gameplay typically assume deep tree search and extensive experience, which are computationally implausible for novices. The central question addressed is: How do people rapidly evaluate, select actions, and predict outcomes in entirely new strategic environments with zero prior exposure?

Methodology

Experimental Design

The authors conducted a series of large-scale behavioral studies involving over 1,000 participants and a dataset of 121 distinct two-player strategic board games. These games were derived from the M-N-K family (e.g., Tic-Tac-Toe, Connect-4) but varied systematically in board dimensions, win conditions (e.g., $K$ -in-a-row, misère rules), and transition dynamics (e.g., opening moves, asymmetric rules). Crucially, almost all games were novel to the participants.

The studies assessed reasoning in three distinct settings:

Game Evaluation (Zero-Shot): Participants evaluated games based solely on natural language descriptions and board depictions, before playing. Tasks included estimating the probability of a win/draw (objective fairness) and rating expected "funness" (subjective engagement).
Action Selection: Participants played a single round of a novel game against another novice. Their move choices were recorded to analyze first-time decision-making.
Action Prediction: Participants watched videos of others playing novel games and predicted the likelihood of specific next moves, assessing their ability to simulate others' reasoning.

Computational Model: The "Intuitive Gamer"

The authors propose a computational cognitive model called the Intuitive Gamer to explain human performance. This model is defined by four core mechanisms:

Fast: It relies on a small number of mental simulations ( $k \approx 5\text{--}7$ ) rather than exhaustive search.
Flat (Depth-Limited): The player module performs only a single step of lookahead (depth-1) when selecting actions, rather than deep tree search.
Goal-Directed: Action valuation is based on abstract, locally evaluable heuristic functions that assess immediate progress toward one's own goal ( $U_{self}$ ) and blocking the opponent's progress ( $U_{opp}$ ), plus an auxiliary center-bias heuristic ( $U_{aux}$ ).
Probabilistic: Actions are selected via a softmax distribution over estimated values, and reasoning involves sampling multiple self-play trajectories to estimate outcome distributions.

Comparative Baselines

The Intuitive Gamer was compared against:

Expert Gamer: A model with deeper search (approx. depth-5) and more sophisticated value functions, calibrated to expert human play in specific games.
Random Gamer: A model selecting actions uniformly at random.
Monte Carlo Tree Search (MCTS): A computationally intensive AI algorithm used as an approximate oracle.
Linguistic/Feature Models: Models relying solely on surface-level game descriptions without simulation.

Key Results

1. Game Evaluation (Pre-Play)

Objective Fairness: The Intuitive Gamer model achieved an $R^2 = 0.81$ correlation with human estimates of game payoff (fairness), matching the split-half reliability of the human data ( $R^2 = 0.82$ ). It significantly outperformed the Expert Gamer ( $R^2 = 0.65$ ), MCTS ( $R^2 = 0.60$ ), and Random models.
Subjective Funness: A regression model using features derived from Intuitive Gamer simulations (balance, reward for thinking, and game length) predicted human funness ratings with $R^2 = 0.57$ , approaching the human data's explainable variance ceiling ( $R^2 = 0.60$ ).
Component Analysis: Ablation studies confirmed that removing any of the four core components (fastness, flatness, goal-directedness, or probabilistic simulation) significantly degraded the model's fit to human judgments.

2. Action Selection and Prediction

First-Time Play: The Intuitive Gamer best predicted the actual moves made by novices in single-round gameplay, significantly outperforming the Expert Gamer and Random models in log-likelihood tests ( $p < 0.001$ ).
Distribution Prediction: When predicting the distribution of moves (watch-and-predict task), the Intuitive Gamer's predicted distributions were closest to human judgments (measured by Total Variation Distance), often matching the human noise ceiling.
Draw Decisions: Human decisions to accept or reject draw requests were best modeled by a logistic regression incorporating the Intuitive Gamer's expected value and game length, suggesting players trade objective reward against subjective engagement (fun) and time costs.

3. Efficiency

The Intuitive Gamer is orders of magnitude more computationally efficient than alternatives. It is approximately 700× faster than the Expert Gamer and 40,000× faster than MCTS in wall-clock time, while still capturing human behavior more accurately than these more resource-intensive models.

Significance and Claims

The paper claims to offer a new computational account of pre-expertise reasoning. The authors argue that human cognition in novel domains does not rely on deep, exhaustive search (as seen in experts) nor is it purely random. Instead, people employ a resource-rational strategy: they run fast, flat, goal-directed, and probabilistic mental simulations.

Key contributions include:

Empirical Evidence: Demonstrating that a simple, depth-limited simulation model captures human reasoning across a diverse set of 121 novel games better than complex expert models.
Unified Framework: Showing that the same "Intuitive Gamer" mechanism explains both the evaluation of a game's properties (fairness, fun) and the selection of actions within it.
AI Design Implications: Suggesting that more flexible, human-like AI systems should not just focus on solving tasks with maximum compute, but should incorporate mechanisms to rapidly evaluate whether a task is worth engaging with, mimicking the human ability to reason about novelty with limited resources.

The authors remain modest regarding the scope, noting that their model is currently limited to perfect-information, two-player competitive board games within a familiar genre. They posit that understanding these "intuitive theories of games" is a step toward broader models of human reasoning in complex, novel systems, including scientific inquiry and creative problem-solving.