Relationship between the Difficulty of Words and its Distribution of Numbers of Tries in Wordle

In this paper, we aim to explore the relationship between the difficulty of words and the distribution of the number of tries (DNT) in Wordle, a popular word-guessing puzzle game around the world. To do so, we first define and extract six attributes of words, namely Information Entropy (IE), Word Frequency (WF), Letter-Pair Frequency (LPF), Letter Frequency (LF), Vowel Rate (VR), and Repeat Letter Rate (RLR), and use Principal Component Analysis (PCA) to assess the redundancy of these features. Then, we employ a self-supervised learning method to train an Autoencoder (AE) for learning the DNT features, with a 3-dimensional latent variable in the bottleneck section. Subsequently, we use this latent variable as a supervised label and the word attributes as input to train a Multilayer Perceptron (MLP) to approximate the latent variable. Finally, the MLP-AE Fusion Model can predict the DNT for an arbitrary given word. Based on experimental results, our model achieves an MAE of 3.53 and a JS divergence of 99.45% in tests, highlighting the significance of our work in offering an effective prediction approach for the correlation between word difficulty and the distribution of the number of attempts.