wordle-solver-benchmarks

Optimal gameplay benchmarks for various algorithms that can be used to solve Wordle puzzles

7920 step solution: https://github.com/caseyho/wordle-solver-benchmarks/blob/main/wordle_perfect_solutions_7920_steps.txt

Problem set

Wordle is a word guessing game available at: https://www.powerlanguage.co.uk/wordle/

The list of possible Wordle words can be determined by peeking at Wordle's source code. There are 2315 potential Wordle games, each of which is a fairly common 5-letter English words. There is also a second, larger set of 12972 words containing the majority of 5-letter words that can be found in an English dictionary from which the user can guess from.

Benchmarks

Total guesses = the total number of guesses required to solve all 2315 potential Wordle puzzles
First guess = the first turn of each game is always the same because there is zero information
Avg turns = the average number of turns required to find a solution
Std. dev turns = the standard deviation in number of turns per game, roughly measuring consistency
Max turns = the maximum number of guesses required to find a solution

Algorithm	Optimal*	Max partitions	Max entropy	Minimax (Knuth)
Total guesses	7920	7949	8023	8245
First guess	SALET	TRACE	SOARE	RAISE
Avg. turns	3.4212	3.4337	3.4657	3.5616
Std. dev turns	0.6105	0.6355	0.6111	0.6528
Max turns	5	6	6	6
By Game Length
2 turn games	96	78	45	67
3 turn games	1201	1249	1240	1011
4 turn games	965	895	943	1108
5 turn games	53	87	81	123
6 turn games	0	5	6	5

(1) Optimal is based on a recusive search of all potential game states with aggressive pruning. There is a slight possibility that the minimum found (7920) may not represent the true minimum due to the way some game states were pruned. Regardless, the value is posted here to provide a benchmark for anyone attempting to fine-tune their own solution or also find the perfect decision tree. Will update in the case this is beaten.

Hard mode benchmarks

Algorithm	Current best*	Max partitions	Max entropy	Minimax (Knuth)
Total guesses	8120	8179	8347	8496
First guess	TBD	TRACE	SOARE	RAISE
Avg. turns	3.5076	3.5330	3.6056	3.6700
Std. dev turns	0.7439	0.7982	0.7962	0.8444
Max turns	7	8	8	8
By Game length
2 turn games	135	124	79	108
3 turn games	1057	1091	1055	908
4 turn games	962	887	945	1014
5 turn games	138	173	184	220
6 turn games	20	31	42	50
7 turn games	3	6	8	13
8 turn games	0	2	2	1

(3) Current best = based on semi-exhaustive search of branches. Likely close to optimal. Can possibly be bested.

Algorithms

Wordle bears a close resemblance to another game, Mastermind. In both games a player makes a series of attempts to guess a hidden codeword from. For each guess the player receieves some sort of feedback on what that guess is. The player can eventually guess the codework by narrowing down the set of possible codes. Games are scored by the number of turns it takes to guess the codeword.

It is possible to write a generalized solver that finds optimal guessing startegies for both Wordle and Mastermind games.

Information on various algorithms to Mastermind algorithms can be found here: https://en.wikipedia.org/wiki/Mastermind_(board_game)#Algorithms_and_strategies

For the purposes of this solver, meta-gaming (comparing against publicly posted results from other players) is ignored.

Code

Code for the solver will be posted at a later time