Wordle Winning Strategy

Introduction

Wordle is a relatively new word game that can be played on the New York Times website at https://www.nytimes.com/games/wordle/.

The objective of the game is to guess a five-letter word (the target) in at most six tries using the following rules:

1. On each turn, you make a guess of the target. Your guess must be a valid five-letter word.
2. Wordle then evaluates the quality of your guess using the following colors for each of the letters in your guess:
   1. If the letter in your guess matches the letter in the target in the same location, then a green response is returned for that letter.
   2. If the letter in your guess matches one of the letters in the target but is not in the same location, then a yellow response is returned for that letter in your guess.
   3. Otherwise, a grey response is returned for that letter.

A few more facts are important:

1. The target word is selected, presumably at random, from a basic dictionary of 2,315 five-letter words. See the listing in Figure 1.
2. On each turn, you can select any valid five-letter English word; Wordle uses a dictionary of 12,497 words for this purpose (see discussion following Figure 1).

Winning Strategy Objectives

We describe a practical winning strategy for Wordle that you can use when you play the game each day. The strategy that you use depends on your objective. We consider two such objectives:

1. Maximize the probability that you can win within 3 guesses.
2. Minimize the expected number of guesses required to determine the target word

Strategy to maximize the chances of winning within 3 guesses

We present a strategy for maximizing the probability that you will guess the target word within three tries. In fact, we present three versions of the strategy:

1. Using only words from the basic dictionary
2. Using words from the basic dictionary but where your second guess is one of the words compatible with the colors returned by Wordle to your first guess
3. You can use words from the full dictionary

The key results are:

• Your best initial guess for case 1 is “slate”. Your best initial guess for the other two cases is “trace”
• The probability of winning in case 1 is 59.1%. The probability for case 2 is 51.6% and 60.0% for case 3.
• The basic strategy is to select words that maximize the number of non-zero patterns

Details for winning within 3 guesses

We explain the strategy for winning within 3 guesses (as well as for winning in 1 or 2 guesses) in detail on the following web pages:

• Letter frequency and patterns
• Winning in one or two tries
• Best first and second guesses from the basic dictionary
• Refinement to best second guess
• Winning within three tries
• Best initial guesses from the full dictionary
• Using Excel (Real Statistics support)

Strategy for minimizing the expected number of guesses

We present a strategy for minimizing the expected number of guesses required to identify the target word. In fact, we present four versions of the strategy based on the first guess of “trace”.  With strategies 1, 2, and 3, in addition to minimizing the expected number of guesses, the characteristics described below are also obtained.

1. For any pattern after a first guess of “trace”, minimize the number of targets guessed in 5 tries, and if there is more than one such approach, then pick the one that also minimizes the number of targets guessed in 4 tries.
2. For any pattern after a first guess of “trace”, maximize the number of targets guessed in 2 tries, and if there is more than one such approach, then pick the one that also maximizes the number of targets guessed in 3 tries.
3. For any pattern after a first guess of “trace”, maximize the number of targets guessed in 3 or fewer tries.
4. Minimize the expected number of guesses needed to identify the target word while maximizing the probability of guessing the target word within 3 tries.

The key results are:

• The best results obtained thus far start with an initial guess of “trace”.
• Strategies 1, 2, and 3 achieve an expectation of 3.425; i.e. on average, you will win Wordle in 3.425 guesses.
• Strategy 4 achieves the 59.9568% probability of guessing the target within 3 tries while obtaining an expectation of 3.447.
• For all four strategies, you will never need more than 5 guesses.

Details for minimizing the expected number of guesses

We explain the strategy for winning Wordle in the fewest number guesses in detail on the following web pages:

• Minimizing the expected number of guesses
• Strategy for winning in the fewest number of guesses
• Strategy for winning in the fewest guesses while maximizing the chances of winning within 3 tries

Improved strategy

Bertsimas and Paskov (see reference below) have also worked on determining a strategy for minimizing the expected number of guesses. They concluded that the best initial guesses in order are:

• “salet”  3.42117
• “reast”  3.42246
• “trace”  3.43276
• “crate”  3.43276
• “slate”  3.43462

Wordle Dictionaries

The following figure lists the 2,315 words in the basic Wordle dictionary. 

Figure 1 – Basic Dictionary

In Real Statistics Support for Wordle, we explain how to obtain a list of all the words in the full dictionary consisting of 12,497 words. Many of these additional words are not commonly used, although quite a few of them are (e.g. “acted”, “orate”, “scuff”, “toner”, etc. as well as many plural forms such as “aches”, “lambs”, “myths”, “trees”, etc.).

References

New York Times (2022) Wordle
https://www.nytimes.com/games/wordle/index.html

Scholtes, G. (2022) Wordle dictionary. Github
https://gist.github.com/scholtes/94f3c0303ba6a7768b47583aff36654d

Deangelo, D. (2022) Wordle players are now getting different answers depending on which version they play
https://gamerant.com/wordle-players-are-now-getting-different-answers-depending-on-which-version-they-play/

Bertsimas, D., Paskov, A. (2023) An exact and interpretable solution to Wordle
https://auction-upload-files.s3.amazonaws.com/Wordle_Paper_Final.pdf