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

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 $2^{n_1{n}_2+1}$ and $2^{\left({\prod }_{i=1}^d{n}_i\right)+1}$ for the two dimensional $n_1\times n_2$ board and $d$ dimensional $n_1\times n_2\times \dots \times n_d$ board respectively. We also present a strategy for the computer and a winning strategy for the human player in certain conditions.