Estimating Human Difficulty for SameGame Puzzles

Authors

  • Motoki Miura Chiba Institute of Technology

DOI:

https://doi.org/10.52731/liir.v006.347

Keywords:

Difficulty Estimation, Puzzle Game, SameGame, Clickomania

Abstract

SameGame is a computer puzzle game in which players must select adjacent blocks of the same color vertically and horizontally to remove them from the screen. Generally, initial blocks are arranged randomly, but it is known that the difficulty varies depending on the initial blocks. It is also known that it can be impossible to completely remove all blocks on small boards. As a way to quantitatively estimate the difficulty of SameGame puzzles, we devised an index that quantifies the correspondence between blocks when they are removed and the discrete state of those blocks. We compared our proposed index with a random success rate, which examines the ratio of the number of answer steps divided by the number of all possible steps. By investigating the correlation with the clear rate based on human play data, we analyzed the effectiveness of several indices including the proposed method.

References

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Frank W Takes and Walter A Kosters. Solving SameGame and its Chessboard Variant. In Proceedings of the 21st Benelux Conference on Artificial Intelligence, BNAIC, pages 249–256, 2009.

Aviv Adler, Erik D Demaine, Adam Hesterberg, Quanquan Liu, and Mikhail Rudoy. Clickomania is Hard, Even with Two Colors and Columns. The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, 2:325, 2017.

Motoki Miura. A basic study of game characteristics of the SameGame puzzle in which all the blocks can be erased. In WISS2023 Web Proceedings [3-C05],2 pages, 2023. (in Japanese).

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Published

2025-02-22