Start with the idea, not the formula
A good guess leaves you with a useful next step
Wordle does not simply tell you which letters are common. Its five tiles give you a pattern. That pattern rules out every answer that could not have produced it.
The most useful guesses tend to spread the possible answers across many small feedback groups. The name for those groups is buckets. Everything on this page grows from that one idea.
By the end, you will be able to:
- explain what a feedback bucket is;
- read probability and entropy in plain English;
- compare entropy, expected remaining answers and worst case;
- understand what the site's six-turn ranking is trying to do.
Feedback buckets
One pattern can stand for several answers
Imagine that the answer could be any word in a short list. Try one guess against every word in that list. Answers that produce the same five tiles go into the same bucket.
After the real game shows a pattern, you keep its bucket and discard all the others. If a bucket holds one answer, the pattern identifies it. If a bucket holds ten, you still have ten candidates to separate.
Right letter, right place
Right letter, different place
No unused copy of this letter
A two-answer example
Suppose only AWAKE and EVADE remain. Guessing SLATE gives the same result for both: A and E are correct, while S, L and T are absent. The two answers stay together in one bucket.
That guess helped, but it did not finish the job. A later guess has to split this last bucket.
Try it
Sort 12 sample answers into buckets
Choose a guess, then open any bucket to see which sample answers share that feedback. Each tile includes a text label, so color is not required.
The sample list contains 12 answers.
Candidate shrinkage
Keep only words that fit every row
The candidate list shrinks by exact feedback, not by a loose checklist of letters. A word survives only if it would give the same greens, yellows and grays for every guess already played. This detail matters when a guess or an answer repeats a letter.
For example, one gray E does not always mean there is no E in the answer. It can mean that another E in the same guess already used the answer's only copy. The matching calculation follows the game's two-pass rule: place greens first, then place yellows from the letters still unused.
Try it
Follow a candidate list through three clues
Pick a pretend hidden answer. Reveal one row at a time and watch the sample list keep only words that match the feedback.
Start with all 12 sample answers, then reveal the first clue.
Answers still possible: 12
- CIGAR
- REBUT
- SISSY
- HUMPH
- AWAKE
- BLUSH
- FOCAL
- EVADE
- NAVAL
- SERVE
- HEATH
- DWARF
Probability and information
Build entropy one step at a time
Now we can put numbers on the buckets. The site treats each answer in its current working pool as equally likely. Under that assumption, a bucket's probability is simply its size divided by the total number of answers.
Find the chance of a pattern
If a bucket contains si answers out of N, its probability is:
Measure how surprising that pattern is
A rare pattern tells you more than a common one. Its information is measured in bits:
Average over every possible pattern
Entropy is the average information you expect from the row:
A bit has a practical meaning here. If a split leaves two equally likely groups, learning which group contains the answer gives you one bit. Four equal groups give two bits. Eight equal groups give three bits.
Try it
Compare ways to split eight answers
Choose a split. The bars show bucket sizes, while the table gives the same information in numbers.
Four equal buckets give 2 bits of entropy.
Entropy
Expected answers left
| Bucket | Answers | Probability | Information if seen |
|---|
What to notice: even splits have more entropy because no single result is much more likely than the others. That usually means a smaller shortlist, but entropy is not the whole game.
Three useful measures
“Best” depends on what you count
Entropy asks how much information a row should give. Two other measures make the trade-offs easier to see.
Expected remaining answers
This is the average shortlist size after the guess. A bucket of size si occurs with probability si/N, so:
Lower is better for this measure.
Worst case
This is the size of the largest bucket. It asks how many answers could remain if you receive the least helpful pattern.
Lower is better for this measure too.
Six-turn result
A first-row score cannot tell you how every later branch will play out. A solver can continue each branch and count failures and turns across the full answer pool.
This is the site's default opener objective.
What the site's solver actually ranks
The current bounded six-turn policy ranks exact misses first. If two opening guesses miss the same number of answers within six rows, it then compares their average guesses among wins. A tiny improvement in speed never makes up for an extra recorded failure.
When only a few answers remain, the solver can test every accepted guess. That lets it find a separating word even when that word is not itself a likely answer. For small endgames that fit the response limit, it can search to the end of the board. In larger branches, lookahead is capped at three rows. The result is a practical, bounded calculation, not a claim that one opener is perfect under every rule or word list.
One important assumption
These first-row calculations give equal weight to every word in the working answer pool. They describe that captured list and the site's solver rules. They do not claim to know how the New York Times selects future answers, and they do not include a player's vocabulary or Hard Mode preferences.
Live comparison
Test two guesses on the current answer pool
Enter any two accepted five-letter guesses. The demonstration simulates every answer in the current pool, then compares their feedback groups. It does not add your choices to the URL.
Try it
Compare first-row splits
Use five letters in each box. Higher entropy is better for information. Lower expected remaining and lower worst case mean smaller buckets.
Ready to compare SLATE and ADIEU.
| Measure | First guess | Second guess |
|---|
Use this comparison to ask a precise question, such as “Which word leaves the smaller average shortlist?” To compare complete six-turn simulations, use the Opener Lab.
Knowledge check
Can you read the numbers now?
Choose one answer for each question. You can also open the answer key and check them yourself.
Answer all three questions when you are ready.
Read the answers and explanations
- 2 answers. Every bucket has size 2, so every possible result leaves 2.
- Guess A. Lower is better when you compare expected remaining answers.
- No. Entropy scores the first split. Later guesses, large trap groups and the six-row limit can change the six-turn result.
You have the main idea
Small buckets make the next decision easier
Feedback buckets are the bridge between a colored row and the next shortlist. Entropy measures the average information in those buckets. Expected remaining answers measures their average size. Worst case watches the largest one. Six-turn simulation carries the process through the remaining rows.