Entropy-Based Two-Phase Optimization Algorithm for Solving Wordle-like Games

Abstract

In the past, a method called Two-Phase Optimization Algorithm (TPOA) was designed by Shan-Tai Chen to solve the game of Mastermind and the AB game efficiently. In this paper, we proposed a modified version called Entropy-Based TPOA (EBTPOA) for Wordle-like games. It is a combination of his algorithm and our previous work on Nerdle with greedy method. It focuses on not only effectiveness but also efficiency while finding optimal results. In Wordle-like games, EBTPOA performs better with fewer guess times on average than TPOA. In Wordle, EBTPOA hits the answer optimally within 3.42117 times on average, and 5 times in the worst case, and the best opening word is “SALET”. In Nerdle, EBTPOA hits the answer within 3.01947 times on average, and 4 times in the worst case, and the best opening equation is ’’ $52-34=18$ ’’. These are the best results up to date, and particularly none has achieved the result for Nerdle so far. As for efficiency, by expanding with fewer branches and limiting the depth of exploration, EBTPOA can obtain the optimal result with a lower time complexity compared to related works.