# Evaluating the Expressive Range of Super Mario Bros Level Generators
## 1 Introduction  
Research on Procedural Content Generation for video games consists of studying procedural generation methods that allow the creation of levels for video games automatically through computational algorithms [1]. Currently, these computational algorithms can potentially save money [2], time, and effort in various areas, such as engineering [1], music [3], and art [4]. The total person-hours needed to complete certain activities can be reduced because these AI-driven systems imitate human action to some degree and deliver results as good as those that a game designer could create [5].  
Thanks to PCG, companies have adapted their workflows to be more competitive and achieve better results. There are even situations where artists have begun to be replaced by these intelligent systems to create games more quickly and economically while maintaining quality [6]. Nowadays, companies not only settle for the initial release but also add new content to keep their audience captive. We know this strategy as \"Downloadable Content\" (DLC) [7], where companies offer additional content that is sold separately, allowing them to generate greater profits. PCG can be a powerful tool for creating DLCs and, thus, offering better services to users.  
In this article, we carry out a study of the expressiveness of open-source automatic level generators for Super Mario Bros (SMB). These are  
1. A Multi-Population Genetic Algorithm [8].
2. A Deep Convolutional Generative Adversarial Network (DCGAN) and Covariance Matrix Adaptation Strategy (CMA-ES) [9].
3. Markov Chains (MCs) ([[https://github.com/hansschaa/MarkovChains_SMB](https://github.com/hansschaa/MarkovChains_SMB)]([https://github.com/hansschaa/MarkovChains_SMB](https://github.com/hansschaa/MarkovChains_SMB)) (accessed on 13 June 2024)).  
This article's main contribution is comparing three generative spaces using Expressive Range Analysis (ERA) [10]. Two of the three evaluated implementations are peer-reviewed [8; 9], the third is our implementation of Markov Chains, and finally, these are contrasted with the SMB levels used as training data. The levels were analyzed with nine metrics through heat charts and box/whisker graphs. As seen in Figure 1, we used the tiles from the video game Super Tux [11] throughout this article because of its GPL license.  
To carry out this study, 200 boards were generated with each generator, and then, for each level, the nine metrics were calculated. Finally, these values are graphed to perform a comparative analysis between generators. The results show that GA and MC have a noticeably wider expressive range than GAN. GA benefits from its exploitation and exploration capacity to find diverse levels, and MC, through the training data, creates levels similar to those that a human can design.  
This document is structured as follows: Section 2 briefly presents the technique's state of the art. Then, in Section 3, the implemented algorithms are reported. In Section 4, the experiments carried out and results obtained are presented, and finally, Sections 5 and 6 show the discussion and conclusions, respectively.