Exploring the space of human exploration

Abstract

What drives people's exploration in complex scenarios where they have to actively acquire information? How do people adapt their selection of queries to the environment? We explore these questions using Entropy Mastermind, a novel variant of the Mastermind code-breaking game, in which participants have to guess a secret code by making useful queries. Participants solved games more efficiently if the entropy of the game environment was low; moreover, people adapted their initial queries to the scenario they were in. We also investigated whether it would be possible to predict participants' queries within the generalized Sharma-Mittal information-theoretic framework. Although predicting individual queries was difficult, the modeling framework offered important insights on human behavior. Entropy Mastermind opens up rich possibilities for modeling and behavioral research.

Digital Learning Games for Mathematics and Computer Science Education: The Need for Preregistered RCTs, Standardized Methodology, and Advanced Technology

“…We are currently developing a game, Entropy Mastermind (Figure 1; Schulz et al, 2019), to promote students' entropy intuitions by providing experiential access to the relationship between probability distributions and the mathematical concept entropy (Crupi et al, 2018). Entropy is not only an important concept in cognitive science, computer science, mathematics, the philosophy of science, and information theory but it also has many practical applications (Martignon et al, 1991;Mana et al, 2018) and educational relevance (Haglund et al, 2010).…”

“…Figure 2 displays a low entropy (left game environment) and a high entropy (right game environment) Entropy Mastermind game. The level of entropy in the underlying probability distribution affects the difficulty of the game (the number of queries needed to guess the secret code; Schulz et al, 2019), and the resulting variations in difficulty give experiential access to the concept entropy.…”

“…First studies using Entropy Mastermind in educational contexts have been conducted: these include the development and implementation of a roadmap for an instructional unit aimed at fostering elementary students' intuitions about entropy using a non-digital version of Entropy Mastermind (Özel et al, n.d., submitted). Based on insights from this first study, a digital version of Entropy Mastermind was developed (Figure 1), and first pilot studies conducted using this digital version of the game (Bertram et al, 2019;Schulz et al, 2019;). Yet, further research is needed to evaluate the effect of playing Entropy Mastermind on entropy intuitions, knowledge about probabilities, and learning-related psychological variables, and to further validate the developed test items for assessing entropy intuitions.…”

Emotion, entropy evaluations and subjective uncertainty

“…The number of queries needed is a measure of the difficulty to break the code. In empirical data from a previous experiment, the number of queries needed to break the code was an increasing function of the entropy in the generating distribution (Schulz, Bertram, Hofer, & Nelson, 2019).…”

The Paradox of Help Seeking in the Entropy Mastermind Game

“…From their guesses the player then tries to deduce the correct color and position of every item in the code. We use an app-based version of Entropy Mastermind, a recently developed, customizable computer-based version of the game (Schulz et al, 2019). Figure 1 displays the gameplay and feedback in more detail.…”