Analysis of the Game "2048" and its Generalization in Higher Dimensions

2018/04/19 by Madhuparna Das, Das, Madhuparna, Goutam Paul +1
Computer Science · #Artificial Intelligence in Games #Computational Physics and Python Applications #Discrete Mathematics (cs.DM) #Distributed and Parallel Computing Systems #FOS: Computer and information sciences

paper · pdf · doi:10.48550/arxiv.1804.07393

openalex publication_date 2018/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We theoretically analyze the popular mobile app game `2048' for the first time in n-dimensional space. We show that one can reach the maximum value 2^n₁n₂+1 and 2^(∏_i=1^d n_i)+1 for the two dimensional n₁× n₂ board and d dimensional n₁× n₂× … × n_d board respectively. We also present a strategy for the computer and a winning strategy for the human player in certain conditions.

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