Procedural Maze Generation Considering Difficulty from Human Players’ Perspectives

Abstract

In video game development, creating maps, enemies, and many other elements of game levels is one of the important processes. In order to improve players’ game experiences, game designers need to understand players’ behavioral tendencies and create levels accordingly. Among various components of levels, this paper targets mazes and presents an automatic maze generation method considering difficulty based on human players’ tendencies. We first investigate the tendencies using supervised learning and then create a test player considering human-likeness by exploiting the tendencies. The test player simulates human players’ behaviors when playing mazes and judges difficulty according to the simulation results. Maze evaluation results from subject experiments show that our method succeeds in generating mazes where the difficulty estimated by the test player matches human players’.

Appendix A Input Features of Prediction Models

The following are 23 features, mainly related to each branch point b. Directions are represented by integers, 0 for right, 1 for down, 2 for left, and 3 for up.

(1) maze_size: The maze size (0 for Small, 1 for Medium, or 2 for Large). (2)(3) x, y: The x- and y-coordinates of b. (4) ent: The direction from which players enter b. (5) proc: The proceeding direction at b. (6)–(9) proc_$\uparrow$, proc_$\downarrow$, proc_$\rightarrow$, proc_$\leftarrow$: Whether each direction is an uncertain proceeding direction. (10)–(13) dist_edge_$\uparrow$, dist_edge_$\downarrow$, dist_edge_$\rightarrow$, dist_edge_$\leftarrow$: Distance from b to the edge in each direction. (14) is_straight: Whether ent and proc are in a straight line. (15) straight_depth: The number of passages that follow the straight line. (16) promisingness: The number of passages on the succeeding paths of proc regardless of the view range. (17) promisingness_sum: The sum of the promisingness values of all directions, excluding ent, at b. (18) general_direction: The general direction of the paths extending from proc. (19) num_branch: The number of other branch points in the narrow view range, which was used for both wide and narrow view mazes. (20) dist_start: The minimum number of steps from the start point to b. (21) avg_step: The number of steps taken to reach b. We used the average number of steps of the experiment participants when building the prediction models. (22)(23) cos_start, cos_goal: The $cos\theta$ of the angle between the start point or end point and proc.