The Math of Winning Wordle: From Letter Distribution to First-Word Strategies (2023)

In Wordle, players try to find a five-letter word by guessing. After each guess, you learn which letters are in the right place, and which other letters are part of the word but not placed correctly. Then you guess again – but be careful, you only have six guesses.

The Math of Winning Wordle: From Letter Distribution to First-Word Strategies (1)

Variations of this game go back decades. Jotto is a paper version that doesn’t give the information about exact matches. Lingo is a game show that aired from the 1980s through the 2010s, with the same overall rules as Wordle.

What Wordle gets very right is in its community. Everyone gets the same word every day, and those words come from a curated list. Players can share their results, with the coveted goal of finding the correct word quickly.

Using mathematical analysis of the Wordle data, we share some advice that can help you win more quickly!

Use Letter Distribution

Which letter do you think is the most typical last letter in a five-letter word?

The list of words that are eligible for Wordle’s word of the day can be analyzed for patterns, including the most frequent letters in each position. Importantly for our analysis purposes, the list of words eligible for Wordle’s word of the day is hand-picked. The word list can be found here. The full list of 5-letter words you can use as guesses is here.

Over 15% of Wordle's words of the day start with S. Only six other starting letters appear in more than 5% of Wordle words.In order of frequency, they are C, B, T, P, A, and F. These starting letters might seem pretty surprising, but they are close to the order of general five-letter words.

(Video) Winning Wordle: The Best Starting Words To Use and Why | Mashable

In order of frequency, A, O, R, E, I, L, U, H appear in more than 5% of Wordle words as the second letter. There is a steep drop-off after that.

In both the second and third positions, vowels dominate. The following letters appear in more than 5% of Wordle words as the third letter:A, I, O, E, U, R, N, in order of frequency.

The following letters appear in more than 5% of Wordle words as the fourth letter: E, N, S, A, L, I, R, C, T, O, in order of frequency. By a wide margin, the most common fourth letter is E, which is the fourth letter in 1 in 7 Wordle words.

The last letter is the most interesting: E, Y, T, R, L, H, N, D all appear as the last letter in more than 5% of Wordle words. Compare this to the last-letter frequency of general five-letter words: S, E, Y, D, T, A, and R appear in more than 5% of the full set of five-letter words.

Tip alert!: Wordle words rarely end in S – it is the 15th most popular last letter. Wordle words end in S less than 2% of the time, compared to 31% of the full set of five-letter words. This is the result of the Wordle list being made from hand-picking words — and the contrast is surprising.

Interested in courses that explore topics like this?Check out AoPS Online's Introduction to Programming. The work in this article was done through computer analysis.

Use All Five Letters to Eliminate Options

When you start a game of Wordle, you’ve got a blank slate and can enter any five-letter word.

Imagine you’ve played your first word, CHAIR. The game responds by telling you the H is correct AND correctly placed, while all the other letter guesses are not in the word at all. This is actually great progress: There are now only 33 possible target words, including GHOST, SHEEP, and WHOSE. Which word would you play next?

Surprisingly, one of the best words to play next is STOLE, which does not have an H as the second letter. By playing STOLE, we can distinguish between GHOST and SHEEP and WHOSE, all of which will have different responses. In fact, after playing STOLE as the second guess, the worst case scenario is having to pick between three possible words on the third try. (OK, you could also play SWOLE with the same results.)

(Video) The best Wordle strategy – according to science

The important detail here is that playing the H as the second letter is worse than playing another common word, even though it adds the small chance of nailing the word on the next try. One of the best options that keeps the H in place is THOSE, but it’s important to see that this is less useful than playing STOLE. By playing STOLE, we get information about the letter L, which THOSE does not give. The only advantage of playing THOSE is that it has a 1 in 33 chance of being the correct word, while STOLE does not.

In Wordle’s “Hard Mode,” there’s a reason it forces you to play the H where it was found: It is harder. This especially applies when you have 3 or 4 letters placed, but there are many options for the final letters.

Tip alert! If you aren’t playing Hard Mode, rather than guessing one letter at a time, pick a word that cannot be correct, but tells you which of the many options to use next.

What Word to Pick First?

One of the fun things about Wordle is there isn’t one single answer to this question. Some people have a go-to starting word they always play, while others switch it up. Here are some suggestions.

The Best Average

A key measure of the quality of a Wordle word is the information you get from it. Let’s say your first guess is KUZDU. A whole lot of the time, you won’t get any information except that K, U, D, and Z aren’t in the target word. That makes this a terrible choice, and it can be measured.On average, after playing KUDZU, you still have 870 words that could all be correct. A better word would have a lower average number of words remaining.

Many of the best words are not common English words. These are the best 10 options alongside the average number of words remaining in the decision pool IF you choose it as your first word:

The Math of Winning Wordle: From Letter Distribution to First-Word Strategies (2)

Every one of these options uses three vowels and two common consonants.

(Video) Winning at Wordle: Results from 4 different starting words

Avoiding Worst-Case Scenarios

Sometimes, your first guess is bad. But you can pick words that minimize the worst-case options. These words narrow things down to the fewest possible remaining choices. They are especially good choices in Absurdle, an adversarial version of Wordle where the target word can change but still fits the selections made.

These are the best 10 options in terms of the number of lowest maximum possible number of words remaining:

The Math of Winning Wordle: From Letter Distribution to First-Word Strategies (3)

The first five are all anagrams, and their worst-case scenario is that none of the letters are present. 93% of Wordle words have at least one of the letters R, A, I, S, or E.

Going for Green

Earning a green letter (right letter, right position) is very helpful on the first turn. These are the best 10 options for earning green letters, ranked by the average number of green letters found:

The Math of Winning Wordle: From Letter Distribution to First-Word Strategies (4)

While these words can help, they tend to have repeated letters, and don’t generally do well at narrowing down the options if they miss.

Going for a Quick Win

While it’s proven that any Wordle can be won in 5 guesses or less, it’s prestigious to win faster! One measure of this is how likely a guess can narrow the options to fewer than 10 remaining options. For example, if you pick RAISE and you find that the R, S, E are all in the correct spots and the I is correct but in the wrong place, you instantly know the correct word is RINSE.

(Video) Wordle Strategy - Maths is Fun! ;-)

These are the best 10 options that give you the chance of narrowing things to under 10 options in one shot:

The Math of Winning Wordle: From Letter Distribution to First-Word Strategies (5)

All of them use three consonants, and two of three vowels each (among A, E, and I).

Final tip alert!There’s a lot to think about here, but note that the best first words always use five distinct letters and use multiple vowels. After the first word, take into account what the possibilities are, and find a word that distinguishes between the remaining possibilities. And, if you’re stuck, use the word list to figure out what your options are.

What’s your starting word? Tag us at @artofproblemsolving with #wordle.

--

Written by Bowen Kerins, Senior Math Curriculum Developer, Art of Problem Solving

FAQs

What is statistically the best word to start Wordle? ›

Sorry Bill Gates, but AUDIO isn't the best word to start with when you're playing Wordle. A pair of MIT researchers recently set out to find the optimal starting word for the popular online puzzle, discovering that the statistically superior first guess is SALET, which is a 15th century helmet.

What is the mathematical probability of Wordle? ›

Since there are 2,315 possible target words in Wordle, the probability that you will guess the target in exactly one try is 1/2315 = 0.000432. In fact, it doesn't matter which of the 2,315 words in the dictionary you choose to use as your initial guess since the probability of success is always 1/2315.

What is the algorithm for Wordle? ›

The algorithm behind giving that hypothetical score is: Every possible guess is checked against every possible solution. Desirable green letters are worth two points, less certain yellow ones are worth one point, and the useless grey ones are worth zero points.

What is the most common first letter in Wordle? ›

You may intuitively know that the most common starting letter for a daily Wordle is "S". What you may not know is how common it is. Roughly 18% of the possible Wordle answers start with "S".

What is a good average score in Wordle? ›

Wordle in Four

Most people should, on average, get it in at least 4, even on days where it is harder. Especially if you aren't making risky moves, four guesses should supply you with enough information to make a correct guess.

What are the best 3 words to start with in Wordle? ›

If, on the other hand, you're simply trying to win within the allotted six guesses, the top three words to play are “adept,” “clamp” and “plaid.” Using any of these three words will yield an average success rate in winning the game of 98.79 percent, 98.75 percent, and 98.75 percent, respectively, if you're playing the ...

What is the average guess distribution in Wordle? ›

On average 95% of target words can be solved within 6 guesses with average game length is approximately 4 rounds. By the time the third guess has been made, a good player will have located about 4 target letters with 2 or 3 in their correct positions.

What is the average Wordle score distribution? ›

Wordle has 2,308 possible answers and 12,545 allowed guesses. The global average for solving Wordle is 4.016 guesses, with Sweden being the best country (3.72) and Egypt the worst (4.42). The best word to start with is “SALET”, followed by “CRATE”, “TRACE”, “SLATE”, and “REAST”.

What is the average Wordle winning percentage? ›

While most puzzles have a 99% solve rate, and even tough puzzles have a solve rate in the 80% range, today's Wordle has a solve rate of only 45%.

Is there a perfect Wordle strategy? ›

In Wordle, an optimal strategy means avoiding repeating letters as much as possible. Instead of rushing to try to guess the actual solution on your second try, an ideal second word would repeat no letters from your first guess.

What is an impressive Wordle score? ›

A score of three is solidly above average, and it is certainly nothing to frown at. Especially with harder words such as “cynic,” “vivid,” or “swill,” getting it in three is very good. Three takes skill, finesse, and intellect. Only true Wordlers will be able to keep their streak of three and below.

What is the best Wordle strategy? ›

Wordle: The Best Strategy For The Game
  1. 1 Try Even If It Looks Wrong.
  2. 2 Words Rarely End In S. ...
  3. 3 Cross Out One Letter At A Time. ...
  4. 4 Find Go-To Words. ...
  5. 5 Skip The Correct Letters In The Second Guess. ...
  6. 6 Remember The Statistics. ...
  7. 7 Use Distinct Words For First 2 Guesses. ...
  8. 8 Eliminate Vowels First. ...
Jul 9, 2022

What is the least popular letter in Wordle? ›

The least common letters in all words are the usual suspects: J, Q, Z, X, and it's unlikely any five-letter Wordle word would contain any of those characters. F, V, and K are also uncommon, but these letters have higher odds of being in one of the five possible Wordle positions.

What is the most common last letter in Wordle? ›

The last letter is the most interesting: E, Y, T, R, L, H, N, D all appear as the last letter in more than 5% of Wordle words. Compare this to the last-letter frequency of general five-letter words: S, E, Y, D, T, A, and R appear in more than 5% of the full set of five-letter words.

What is the most common ending letter in Wordle? ›

For the end letter, the most common are E, S, T, D, and N.

Who has the longest winning streak on Wordle? ›

Wordle winning streak: An interview with a person who's gone green 83 times in a row.

Has anyone gotten the Wordle on the first try? ›

Based on the data shared by the unofficial account, Wordle Stats, of the 241,489 players who shared their Wordle results on Twitter on January 22, 2022, approximately 1% of them solved it on the first try, 3% on the second try, 17% on the third, 33% on the fourth guess, 29% on the fifth attempt, and 15% on the final .. ...

Can there be plurals in Wordle? ›

Wordle is a popular word-guessing game from the New York Times. Wordle, the popular word-guessing game from the New York Times, will no longer use plural words, according to an announcement made last week. Over the past year, tens of millions of people tried to guess the five-letter word of the day.

What 2 words should you start with in Wordle? ›

From that starting point, we've identified these words as some of the very best first words for Wordle:
  • React.
  • Adieu.
  • Later.
  • Sired.
  • Tears.
  • Alone.
  • Arise.
  • About.
Nov 28, 2022

What letter do most 5 letter words start with? ›

According to one analysis, the letter E appears most frequently in English-language words featured in a condensed version of the Oxford Dictionary, followed by A, R, I, O, T, N, and S. So starting words like “ratio,” “irate,” “stain,” or “stare” that include those commonly used letters are great options.

What are the odds of getting Wordle in 2 tries? ›

So if we guess BIPED to start out with, there's a 91/2315 = 3.93% chance that we get the Wordle in two (so long as our second guess is from the 2315 word answer list). A qajaq!

Which country has the best Wordle score? ›

This European Country Has The Best Wordle Score In The World, Study Shows. According to the study by word site Word Tips, Sweden comes out on top being able to get the right answer in 3.72 guesses. (For anyone unfamiliar with how Wordle works, when it comes to scoring, the lower the better.)

What is a good Wordle distribution? ›

On average 95% of target words can be solved within 6 guesses with average game length is approximately 4 rounds. By the time the third guess has been made, a good player will have located about 4 target letters with 2 or 3 in their correct positions.

What percentage of people get Wordle right every day? ›

Based on the data shared by the unofficial account, Wordle Stats, of the 241,489 players who shared their Wordle results on Twitter on January 22, 2022, approximately 1% of them solved it on the first try, 3% on the second try, 17% on the third, 33% on the fourth guess, 29% on the fifth attempt, and 15% on the final .. ...

What is the best strategy for Wordle? ›

While picking a new word is a trick, starting Wordle with the same word every day is another strategy players have been using. Choosing words with at least two to three vowels along with most common consonants, such as 'sauce,' 'saute' and 'dance', is an efficient way of arriving at the Wordle of the day.

What is the easiest way to solve Wordle? ›

Starting with a word that has common letters is a good approach, because it lets you quickly eliminate many words: If you pick a word with the most common letters and one or more of those common letters is not in the solution, then you have identified a large number of impossible solutions.

What is optimal strategy in Wordle? ›

Wordle: The Best Strategy For The Game
  1. 1 Try Even If It Looks Wrong.
  2. 2 Words Rarely End In S. ...
  3. 3 Cross Out One Letter At A Time. ...
  4. 4 Find Go-To Words. ...
  5. 5 Skip The Correct Letters In The Second Guess. ...
  6. 6 Remember The Statistics. ...
  7. 7 Use Distinct Words For First 2 Guesses. ...
  8. 8 Eliminate Vowels First. ...
Jul 9, 2022

What are the 10 least used letters in Wordle? ›

The least common letters in all words are the usual suspects: J, Q, Z, X, and it's unlikely any five-letter Wordle word would contain any of those characters. F, V, and K are also uncommon, but these letters have higher odds of being in one of the five possible Wordle positions.

What is the most common letter in 5 letter words? ›

This means the top most commonly used letters in 5-letter words (in terms of total frequency as well as average frequency) were the letters A, E, S, O, R, I, L, T, etc. I decided to focus on the top six letters since the average frequency dropped significantly after the sixth letter.

What percentage of players solve Wordle? ›

“Wordle” players are quite good at the game — or at least that's what they say. Seventy-four percent of players said they successfully solve the puzzle either “always” or “sometimes.” Meanwhile, 17 percent said they solve it “rarely” and only 9 percent said they “never” complete the puzzle.

What are the five words to win Wordle every time? ›

Because, although his system will give players all the correct letters 99.5 percent of the time, it's up to the player to take those letters and win Wordle. "You still have to solve it but this will give you a fantastic lead into solving," said Myles. "Derby, flank, ghost, winch, jumps."

How many people have solved Wordle on the first try? ›

Based on his findings, O'Connor has determined that approximately 1% of the players who post their results to Twitter are guessing the correct word on their first attempt, and somewhere between 3% and 9% guess correctly on the second try.

What 5 letter word has the most vowels? ›

List of 5 Letter Words with the Most Vowels
  • Aurei.
  • Louie.
  • Adieu.
  • Auloi.
  • Miaou.
  • Ouija.
  • Ourie.
  • Uraei.

What is a burner word in Wordle? ›

A letter that isn't in the word in any spot shows up gray. With each “burner” word, you can learn hints about the letter and their placements, and then, you get one chance to guess the Wordle. This simple yet entertaining game became extremely viral within the first two months of 2022.

Who has the longest streak on Wordle? ›

Spencer Evans was the one whose accomplishment impressed me the most: 83 unbroken wins and counting. A wordsmith himself, Evans first discovered Wordle earlier this month.

Videos

1. Wordle: Best Starting Word
(AP Now)
2. Perfect WORDLE algorithm (and how I found it)
(Games Computers Play)
3. Oh, wait, actually the best Wordle opener is not “crane”…
(3Blue1Brown)
4. Simulating Wordle: in search of the perfect strategy
(Games Computers Play)
5. Using Statistics To Beat Wordle
(RandomMathsInc)
6. Wordle! A fun word logic puzzle. Game history, how to play, and strategy!
(Sean Plays)
Top Articles
Latest Posts
Article information

Author: Neely Ledner

Last Updated: 02/18/2023

Views: 5389

Rating: 4.1 / 5 (42 voted)

Reviews: 81% of readers found this page helpful

Author information

Name: Neely Ledner

Birthday: 1998-06-09

Address: 443 Barrows Terrace, New Jodyberg, CO 57462-5329

Phone: +2433516856029

Job: Central Legal Facilitator

Hobby: Backpacking, Jogging, Magic, Driving, Macrame, Embroidery, Foraging

Introduction: My name is Neely Ledner, I am a bright, determined, beautiful, adventurous, adventurous, spotless, calm person who loves writing and wants to share my knowledge and understanding with you.