Deterministic Algorithmic Approaches to Solve Generalised Wordle

TL;DR

This paper develops and analyzes deterministic algorithms, including greedy and clique-based methods, to efficiently solve Wordle under simplified assumptions, aiming to minimize guesses in generalized game settings.

Contribution

It introduces two novel deterministic algorithms for Wordle, expanding beyond probabilistic methods, and analyzes their effectiveness in simplified game scenarios.

Findings

Greedy algorithm effectively reduces guesses in both hard and easy modes.

Clique-based approach performs well in easy mode but not in hard mode.

Deterministic methods provide a new perspective on solving Wordle efficiently.

Abstract

Wordle is a single-player word-based game where the objective is to guess the 5-letter word in a maximum of 6 tries. The game was released to the public in October 2021 and has since gained popularity with people competing against each other to maintain daily streaks and guess the word in a minimum number of tries. There have been works using probabilistic and reinforcement learning based approaches to solve the game. Our work aims to formulate and analyze deterministic algorithms that can solve the game and minimize the number of turns required to guess the word and do so for any generalized setting of the game. As a simplifying assumption, for our analysis of all the algorithms we present, we assume that all letters will be unique in any word which is part of our vocabulary. We propose two algorithms to play Wordle - one a greedy based approach, and other based on Cliques. The Greedy approach is applicable for both hard and easy modes of Wordle, while the Clique formation based approach only works on the Easy mode. We present our analysis on both approaches one by one, next.