A Study of Wordle Games Based on Mathematical Models

This study explores the potential of the daily puzzle game Wordle, as disseminated by The New York Times, as both a leisure activity and an educational tool. Through the analysis of game data shared on Twitter, we develop mathematical models to decode the puzzles and examine player strategies, word selection tendencies, and game difficulty settings, aiming to refine the game's design for an improved user experience. Additionally, we consider Wordle's educational merits, particularly its utility for English vocabulary acquisition. Utilizing a genetic algorithm-based neural network prediction model, we assess player completion times using three-word attribute indicators as input and seven corresponding completion time percentages as output. Employing a 6:2:2 ratio for our sample learning set, training set, and validation set, and selecting five neurons for the hidden layer with Bayesian regularization, we establish an accurate prediction model. We demonstrated its effectiveness by predicting the completion time percentages for the word "EERIE," achieving an MSE of 21.1049 and an R-value of 0.93095. For word difficulty classification, we employed KMeans++ clustering analysis, considering parts of speech, letter repetition, and frequency of common letters in the word. Using the elbow rule, we categorized words into three difficulty levels. Our analysis yielded 114 medium, 107 hard, and 138 easy words, with the word "EERIE" classified as easy. The model's performance, indicated by a silhouette coefficient of 0.4914, DPI of 1.312, and CH value of 174.187, was robust. Future work will focus on refining the BP neural network model parameters to enhance accuracy, robustness, and generalization, thereby improving predictive outcomes.