# 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.

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.

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.)

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:

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

#### 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 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:

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.

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

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 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 best Wordle algorithm? ›

After conducting extensive testing, Sanderson found that the best word for players to try on Wordle is 'Crane'. By using the word Crane first in every puzzle, Sanderson's testing results in an average score of 3.438.

What are the odds of solving Wordle on first line? ›

Wordle has about 2314 possible answers. So the probability of getting it right on the first try is 1/2314 = 0.0004=0.04% approximately.

What are the most common letters in Wordle strategy? ›

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.

What is a good Wordle distribution? ›

Canberra, Australia is the global city with the best Wordle average: 3.58 guesses. Sweden is the world's best country at Wordle, with an average of 3.72. The US is ranked #18 in the world for Wordle, with a national average of 3.92. The American state with the best Wordle average is North Dakota (3.65).

What is a good average score on 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 is the number one most guessed word on 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 most used first word in Wordle? ›

Most common Wordle starting words

ADIEU — ADIEU was the most common response, with a total of 21 submissions.

What is the best first word to guess in Wordle? ›

Mathematician Alex Selby devised an algorithm that determined “SALET” is the best word to start Wordle off. Reason: Alex's algorithm determined that Salet took the least average guesses of 3.4212 to guess the word of the day.

Does the average person solve Wordle? ›

Human Statistics Playing Wordle. On average, Wordle players can guess the correct word on their first try in only 0.02% of games.

### How many tries does it take the average person to solve Wordle? ›

On average 95% of target words can be solved within 6 guesses with average game length is approximately 4 rounds.

What is the average Wordle distribution? ›

The United States ranked No. 18 in the world for Wordle, with a national average of 3.92. The U.S. state with the best Wordle average was North Dakota, with an average of 3.65. The U.S. city with the best Wordle score was Saint Paul, Minnesota, with an average of 3.51.

What are the 3 best 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 are the 7 most used letters in Wordle? ›

As for the letters that begin the most English words, the top five are T, O, A, W, and B. For the end letter, the most common are E, S, T, D, and N.

What is the rarest letter? ›

The rarest letters in English are j, q, x, and z.

What is the guess distribution chart in Wordle? ›

Guess Distribution is a representation of the number of guesses you make to successfully solve each challenge. The guess distribution chart, like the other elements on the scoreboard, sheds light on your whole gaming history on Wordle and not just the current game.

Has anyone ever got 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.

Who has the highest score on Wordle? ›

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.

Who has the longest streak on Wordle? ›

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

What is the hardest Wordle on word? ›

Research has revealed that “Parer” has been the hardest word to guess in the NYTimes game Wordle. A study conducted by online gaming site im-a-puzzle.com utilised and examined data collected by a Twitter API called WordleStats that has been analysing players' Wordle tweets since the start of 2022.

### 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's the best 5 letter word to start Wordle with? ›

Some Wordle players have found success in starting with a word that has several vowels in it. “Adieu,” “audio” or “canoe,” for instance, may be good words to start with because at least three out of the five letters are vowels.

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.

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 is the easiest way to solve Wordle? ›

12 Wordle Tips and Tricks to Improve Your Score
1. Don't Try to Guess the Word on Your First Turn. ...
2. Your First Guess Should Contain "Popular" Letters. ...
3. Use the Same First Word for Every Wordle Game. ...
4. Take Time With Your Turns. ...
5. Don't Be Afraid to Use the Same Letter Twice. ...
6. Don't Forget the Less Popular Letters.
Sep 29, 2022

What percentage of people fail Wordle? ›

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%. In fact, WordleBot claims that today's puzzle has an average solve rate of 6.3 answers....which means that most players aren't getting the puzzle correct.

Does anyone get 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).

Do most people get Wordle in 4 tries? ›

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 5 letter word has the most vowels? ›

Top-Words with 5 Letters with mostly vowels
• MIAOU. ...
• AUDIO. ...
• AULOI. ...
• LOUIE. ...
• AUREI. ...
• OURIE. ...
• URAEI.

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%. In fact, WordleBot claims that today's puzzle has an average solve rate of 6.3 answers....which means that most players aren't getting the puzzle correct.

### Is there an algorithm for Wordle? ›

The various Wordle algorithms all take slightly different approaches in how they solve the puzzle. Some start with knowledge of the solution list; others do not. Some allow any of the almost 13,000 five-letter English words as valid guesses; others (like WordleBot) use a smaller set.

What is the best word to start Wordle with? ›

“If you play SALET and you play intelligently you can assuredly win the game within five guesses,” researcher and MIT Ph. D. student Alex Paskov tells CNBC Make It. “You don't even need that last guess.”

What is the best first word in Wordle? ›

The best Wordle start word according to WordleBot

And by that measure, the best Wordle start word is apparently CRANE. That's surprising to me — not least because STARE actually fares better in terms of average number of solutions, scoring 71.8 to CRANE's 78.7.

What is the best word to use after Crane in Wordle? ›

The New York Times' Wordlebot originally recommended Wordle users on regular mode start with the word CRANE. But, as of August 2022, Wordlebot now recommends the word SLATE. If you're on hard mode, the recommended word has gone from LEAST to DEALT.

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