Wordle Lovers - Play the NYT Daily Game

[OmCheeto]

Wordle 1,287 3/6

 

[jack action]

Wordle 1,287 3/6

[RENAL] 10 left
[BIPOD] filter - 2 left: CAIRN GRAIN
[GRAIN] most probable (again with the rare occurring letter G)

most-probable method count update (Success/Fail): 46/26 - 63.9%/36.1%

 

[dwarde]

Wordle 1,287 5/6

 

[Orodruin]

Wordle 1 288 3/6

 

[jack action]

Wordle 1,288 3/6

[DEALT] 9 left
[CURNY] filter - 1 left
[DECRY]

Between all 9 possible solutions, with today's solution as a 2nd guess, I could have solved it for 4 different solutions but I went with the suggested word by my program that could solve it for 5 different solutions instead.

 

[kuruman]

Wordle 1,287 4/6






Forgot to post yesterday.

 

[kuruman]

Wordle 1,288 4/6

 

[gmax137]

Wordle 1,288 5/6

BLUNT
SHEEP
CAROM
DEIFY
DECRY

 

[dwarde]

Wordle 1,288 3/6

 

[OmCheeto]

Wordle 1,288 4/6

 

[Orodruin]

Wordle 1 289 3/6





6/7 in three guesses this week (I think I got EAGLE in 4, but it seems I forgot to post it …)

Two weeks to go to 1000 played!

 

[jack action]

Wordle 1,289 3/6

[SNORE] 50 left
[MALTY] filter - 2 left: MACHO MAMBO
[MAMBO] most probable (MACHO is not politically correct)

most-probable method count update (Success/Fail): 47/26 - 64.4%/35.6%

 

[kuruman]

Wordle 1,289 4/6

 

[kuruman]

I have been curious from the start about how this might end so I constructed a spreadsheet-based WORDLE simulator. I used it to "complete" the game by running through the limited list of 2331 words from beginning to end ignoring what has been used in the actual game. Here are the main points of what I did and the rules I followed.

• The target word is chosen randomly from the list and is removed after successfully finding it.
• The seed word is always the same, in this case SLATE.
• The spreadsheet is used strictly for bookkeeping, (a) to search for words containing desired letters for filter generation, (b) to generate a list of candidates with already used words removed and (c) to provide a "frequency spectrum" of the letters in this list of candidates. These are tedious tasks that can also be done by hand except that it would take much longer.
• I use the frequency spectrum to devise the next filter. The task is to find a 5-letter word consisting of the highest ranking letters in frequency. The spreadsheet does not suggest filters. In looking for a suitable filter I consider the balance between finding letters that might belong against excluding candidates that don't belong. Letters whose exact position is known are avoided.
• Every guessed word is a justified filter, never a random guess.
• When the search boils down to two words, I use the alphabetically first word as a filter for the second.
• When the search boils down to three or more words, I go for the guaranteed solution.

The table on the right shows the score distribution for the entire search. All words were completed in ≤ 6 tries. There are two scores of 1, when the target word matched the constant seed SLATE and when I reached the last word that was its own filter.

The graph below shows snapshots of the mean as a function of already used words. It has a negative first derivative and a negative second derivative that becomes more apparent near the end. There are 100 data points recorded in intervals of 1%.

Finally, the bar graph below shows the distribution of scores for each quarter. The shift to lower scores is clear. In the 4th quarter there is a marked increase in the scores of 2 from under 10% to almost 30% of the total.

So there you have it.

 

[OmCheeto]

Wordle 1,289 4/6

 

[gmax137]

Wordle 1,289 3/6

 

[dwarde]

Wordle 1,289 5/6

 

[Orodruin]

I have been curious from the start about how this might end so I constructed a spreadsheet-based WORDLE simulator. I used it to "complete" the game by running through the limited list of 2331 words from beginning to end ignoring what has been used in the actual game. Here are the main points of what I did and the rules I followed.

• The target word is chosen randomly from the list and is removed after successfully finding it.
• The seed word is always the same, in this case SLATE.
• The spreadsheet is used strictly for bookkeeping, (a) to search for words containing desired letters for filter generation, (b) to generate a list of candidates with already used words removed and (c) to provide a "frequency spectrum" of the letters in this list of candidates. These are tedious tasks that can also be done by hand except that it would take much longer.
• I use the frequency spectrum to devise the next filter. The task is to find a 5-letter word consisting of the highest ranking letters in frequency. The spreadsheet does not suggest filters. In looking for a suitable filter I consider the balance between finding letters that might belong against excluding candidates that don't belong. Letters whose exact position is known are avoided.
• Every guessed word is a justified filter, never a random guess.
• When the search boils down to two words, I use the alphabetically first word as a filter for the second.
• When the search boils down to three or more words, I go for the guaranteed solution.

View attachment 355056The table on the right shows the score distribution for the entire search. All words were completed in ≤ 6 tries. There are two scores of 1, when the target word matched the constant seed SLATE and when I reached the last word that was its own filter.

The graph below shows snapshots of the mean as a function of already used words. It has a negative first derivative and a negative second derivative that becomes more apparent near the end. There are 100 data points recorded in intervals of 1%.

View attachment 355057
Finally, the bar graph below shows the distribution of scores for each quarter. The shift to lower scores is clear. In the 4th quarter there is a marked increase in the scores of 2 from under 10% to almost 30% of the total.

View attachment 355058
So there you have it.

How is $n_1 = 2$ if the seed is always the same?

 

[kuruman]

How is $n_1 = 2$ if the seed is always the same?

When 2330 words are eliminated, what is word 2331 in a list of 2331 words?

 

[Orodruin]

When 2330 words are eliminated, what is word 2331 in a list of 2331 words?

Ah, but then the seed is not always the same!

 

[kuruman]

Ah, but then the seed is not always the same!

Can the last word be called a “seed” when nothing can sprout from it?

 

[Orodruin]

I would say no seed violates the rule of always using the same seed. If you want to change the rule of always using the same seed then you might as well guess between the two remaining words at the penultimate word. Or check if one of the words is a filter at the first guess when there are between 2 and 10 left, etc.

 

[kuruman]

It looks like we understand the meaning of “seed” differently. To me it is more than just the first word in a sequence of at most 6 words. It is a word the letters of which provide new information about the component letters in the target word. When I’m down to two words left, choosing either one provides information about the other. One is a perfect filter for the other. The cat is either alive or dead. Choosing one of the two opens the box.

When I’m down to the last word, there is no more new information to be provided by choosing it. It is the alpha and the omega. The cat is alive. Meow!

 

[Orodruin]

It looks like we understand the meaning of “seed” differently. To me it is more than just the first word in a sequence of at most 6 words. It is a word the letters of which provide new information about the component letters in the target word. When I’m down to two words left, choosing either one provides information about the other. One is a perfect filter for the other. The cat is either alive or dead. Choosing one of the two opens the box.

When I’m down to the last word, there is no more new information to be provided by choosing it. It is the alpha and the omega. The cat is alive. Meow!

But that’s my point! It is arbitrary to say the seed is always SLATE and then not use it for the first word in one or more games. You will get a better outcome by adapting your seed to the remaining pool of words.

Also I did not get a 3/6 today …

…

…

…

Wordle 1 290 2/6

 

[jack action]

But that’s my point! It is arbitrary to say the seed is always SLATE and then not use it for the first word in one or more games. You will get a better outcome by adapting your seed to the remaining pool of words.

So your point is that @kuruman 's data are skewed because he found $n_1 = 2,\ n_2 = 271$ instead of $n_1 = 1,\ n_2 = 272$? Seems rather trivial to me.

 

[kuruman]

But that’s my point! It is arbitrary to say the seed is always SLATE and then not use it for the first word in one or more games. You will get a better outcome by adapting your seed to the remaining pool of words.

I think we are talking past each other. I never said or implied that I did not use SLATE for the first word in one or more games. I played 2331 games and SLATE was the first word in all but game 2331. Shown below is the spreadsheet record of the last 15 games.

Adapting the first word (what you call seed) to the remaining pool of words may seem like a good strategy but, after my survey, I don't think that it is. The second word, tied to a constant first word, is more important, in my opinion. Let me illustrate with a concrete example.

Suppose after SLATE as the first guess the result is the letter pattern $\text{ _ _ A _ _}$, i.e. the target word has A fixed in position 3 and does not contain SLTE . The spreadsheet tells me that there are 49 words that fit this pattern. If I use CHORD as the second word, the spreadsheet tells me that there are only two words in the subset of 49 (AGAIN & GUAVA) that have no letter overlap with CHORD. This makes CHORD a good filter to be used every time $\text{ _ _ A _ _}$ appears in response to starting with SLATE. Excepting AGAIN & GUAVA, it guarantees either finding additional letter(s) or excluding whole words. Both outcomes are desirable.

A key step of using the same seed is following it with a second word that serves as a filter for the candidates matching the letter pattern generated by the constant seed. This second word is semi constant in the sense that it can and should be reused but also re-examined periodically as the pool of words changes in order to confirm its relevance. Thus, the general idea is to subdivide the pool of 2331 words to a finite number of sub-pools identified by the response to the constant seed, e.g. $\text{ _ _ A _ _}$. Then find an appropriate filter for each sub-pool to trim it down.

You can see in the spreadsheet record above that entry 2318 BOAST is the last survivor of $\text{ _ _ A _ _}$ and, as such, a guaranteed score of 2. At entry 2319 the pattern was $\text{ _ _ _ _ _}$ (no overlap with SLATE) with a sub-pool of 2 members, DYING and ROBIN. Following my protocol, I chose alphabetically and ended up with a score of 3. However, that reduced the sub-pool for that pattern to a population of 1 which I got for a score of 2 at the penultimate entry. The penultimate entry DYING was not a 50-50 toss-up with the ultimate entry. I think it shows the value of using the same seed to subdivide the big pool into sub-pools that can be dealt with separately.

 

[Orodruin]

My point, and the most obvious example was that when you had HAUTE and DYING left, starting with either of them is a 50-50 to solve it in 1. Starting with SLATE is a guaranteed 2 so picking randomly between your remaining words is an obviously better strategy. The pool of remaining words is already manageable.

The same goes for when you had 3 or 4 left. You could have had a shot at a one and still guaranteed at most two. Etc.

 

[jack action]

Wordle 1,290 4/6

[SHALE] 4 left: SPARE STARE STAVE SUAVE
[SUAVE] most probable
[SPARE] most probable (ever so slightly!)
[STARE] finally!

I went for the gold and failed twice with the most-probable method.

most-probable method count update (Success/Fail): 47/28 - 62.7%/37.3%

 

[Orodruin]

Meanwhile, both STARE and STAVE were perfect filters …

 

[kuruman]

The same goes for when you had 3 or 4 left. You could have had a shot at a one and still guaranteed at most two. Etc.

I could have, but I didn't because that would be inconsistent with my (self-imposed) protocol. As I stated in post #6,064

• Every guessed word is a justified filter, never a random guess.
• When the search boils down to two words, I use the alphabetically first word as a filter for the second.
• When the search boils down to three or more words, I go for the guaranteed solution.

My goal for playing the game this way was not to get as many low scoring words as possible but to have as tight (low $\sigma$) distribution as possible. For example, if I am faced with a third guess and 3 candidates left, I can always (a) pull one of the three candidates randomly out of a hat until I get the right one or (b) use the third guess to give me a guaranteed solution as the fourth guess.

Note that both (a) and (b) give the same expectation value of 4 over many occurrences. However, (a) has $~\sigma \approx 0.8~$ whereas (b) has $\sigma = 0.$ I, conservatively, chose to exclude gambling by guessing because I did wish to have to provide reasons for choosing one word over another, e.g. KITTY is cuter than HYENA, or end up second guessing myself,

I went for the gold and failed twice with the most-probable method.

My goal for doing this was to demonstrate that it is possible to find all 2331 words on the list with at most 6 guesses by following a consistent and easy to explain protocol without having to guess at any point. The 7 words that I had with a score of 6 were all guaranteed solutions after guess 5. I think I reached my goal.

 

[kuruman]

Wordle 1,290 2/6

SLATE forever!

 

[OmCheeto]

Wordle 1,290 3/6

 

[Orodruin]

Wordle 1,290 2/6

SLATE forever!

I believe ALERT also worked out pretty decently ... (although I did have a 50-50 ...)

 

[jack action]

My goal for doing this was to demonstrate that it is possible to find all 2331 words on the list with at most 6 guesses by following a consistent and easy to explain protocol without having to guess at any point.

That is pretty easy to accomplish. Here is the method I used when doing it without any list:

1. IRATE - 5 most popular letters (in English);
2. CLONS - 5 next most popular letters;
3. DUMPY - 5 next most popular letters (including all vowels at this point);
4. BiGHa - 3 next most popular letters;
5. WaKFs - 3 next most popular letters;
6. The only letters left are JQVXZ

With these guesses, it is impossible not to get the solutions within 6 guesses if you know the remaining words after each guess.

If you don't check any list, it is possible to miss because of a word you cannot think of, but it rarely occurred to me - and English is not even my mother tongue. My average was somewhere between 3 and 4.

One word I remember struggling with was WALTZ. The word just did not pop into my head, even on the 6th guess. But if I had the full list for WORDLE, I would have isolated it after the 2nd second guess. Even with the full list of 5-letter English words, I would have isolated it with my 3rd guess.

 

[dwarde]

My seed word did it all.

Wordle 1,290 2/6

 

[gmax137]

Wordle 1,290 4/6

 

[Orodruin]

With these guesses, it is impossible not to get the solutions within 6 guesses if you know the remaining words after each guess.

It is impossible not to know what the letters are (effectively), but does it guarantee a solution? What about words that have the same letters but in different order? Different double letters? Etc.

 

[jack action]

It is impossible not to know what the letters are (effectively), but does it guarantee a solution? What about words that have the same letters but in different order? Different double letters? Etc.

Let's take an apparently difficult word like JAZZY:

1. irAte - 117 words left
2. clons - 15 words left
3. dumpY - only 1 word left
4. JAZZY

You don't have to wait until the 5th guess to realize the word has J and Z in it. Once the most common letters are eliminated, the range of choices reduces rapidly.

Let's take PENAL and PANEL (same letters):

1. irAtE - 55 words left
2. cLoNs - 5 words left
3. dumPy - 2 words left
4. PENAL or PANEL - 1 word left (or none)
5. PANEL or PENAL

or ALERT, ALTER, and LATER (same letters):

1. iRATE - 14 words left
2. cLons - 2 words left
3. ALERT or ALTER - 1 word left (or none)
4. ALTER or ALERT

1. iRATE - 14 words left
2. cLons - 1 word left
3. LATER

MAMMA:

1. irAte - 117 words left
2. clons - 15 words left
3. duMpy - 2 words left
4. bighA - 1 word left (although it would be smarter to use either MAMMA or GAMMA)
5. MAMMA

I haven't tried them all but there must not be a lot that don't work. One I found that would be tricky is LOLLY - 2 words left for the 6th guess, LOLLY and JOLLY - but it is not on the WORDLE list (JOLLY is though).

 

[Orodruin]

Let's take an apparently difficult word like JAZZY:

1. irAte - 117 words left
2. clons - 15 words left
3. dumpY - only 1 word left
4. JAZZY

You don't have to wait until the 5th guess to realize the word has J and Z in it. Once the most common letters are eliminated, the range of choices reduces rapidly.

Let's take PENAL and PANEL (same letters):

1. irAtE - 55 words left
2. cLoNs - 5 words left
3. dumPy - 2 words left
4. PENAL or PANEL - 1 word left (or none)
5. PANEL or PENAL

or ALERT, ALTER, and LATER (same letters):

1. iRATE - 14 words left
2. cLons - 2 words left
3. ALERT or ALTER - 1 word left (or none)
4. ALTER or ALERT

1. iRATE - 14 words left
2. cLons - 1 word left
3. LATER

MAMMA:

1. irAte - 117 words left
2. clons - 15 words left
3. duMpy - 2 words left
4. bighA - 1 word left (although it would be smarter to use either MAMMA or GAMMA)
5. MAMMA

I haven't tried them all but there must not be a lot that don't work. One I found that would be tricky is LOLLY - 2 words left for the 6th guess, LOLLY and JOLLY - but it is not on the WORDLE list (JOLLY is though).

I am not saying there are many words that would cause issues. I am requesting verification that your strategy cannot possibly fail to give the solution in 6, because that was the claim:

With these guesses, it is impossible not to get the solutions within 6 guesses if you know the remaining words after each guess

 

[Orodruin]

Wordle 1 291 4/6






And so the 3 or fewer guesses streak ends … it was down to a choice between two words at the end …

 

[jack action]

Let's end the year on a good note:

Wordle 1,291 2/6

[SAUCE] 14 left
[LEMUR] possible answer + suggested filter

 

[OmCheeto]

Wordle 1,291 4/6

 

[kuruman]

Wordle 1,291 3/6

 

[OmCheeto]

Interesting thing I discovered after playing yesterdays game. Of the top 15 global seed words, only one remained as a valid solution after the game.

12/30/2024 STARE​

rank	seed	%	notes
1	ADIEU	7.3	vowel rich
2	STARE	5.9	high value solution for this game
3	AUDIO	4.3	vowel rich
4	RAISE	2.8	high value
5	CRANE	2.7	high value
6	SLATE	2.6	high value
7	ARISE	1.8	high value only remaining valid solution on this list
8	TRAIN	1.4	high value
9	IRATE	1.3	high value
10	HEART	0.9	high value
11	GREAT	0.9	high value
12	HOUSE	0.9	high value
13	TRACE	0.8	high value
14	AISLE	0.7	high value
15	LEAST	0.7	high value
total	---	35%	---

Also, I don't think I've ever seen such symmetry in the scoring.
Compare percentages for 1 vs 5, and 2 vs 4 guesses.

Guess	% that got it right	12/30/24
1​	5.9%​
2​	24%​
3​	39%​
4​	24%​
5​	6.0%​
6​	0.57%​
7​	0.016%​
σ​	1.0074​	standard deviation​
μ​	3.016​	mean​

 

[gmax137]

Wordle 1,291 3/6

BREAK - picked today for its "uncommon" letters B and K
LEMON - I use this one frequently, a nice mix of common letters
turns out LEMON was a very good guess today

 

[dwarde]

Nutz

Wordle 1,291 6/6

 

[Orodruin]

Wordle 1 292 4/6






New Year’s and it is not NEWER over NERVE … what is wrong with Wordle!?!?

 

[kuruman]

Wordle 1,292 3/6

 

[jack action]

Wordle 1,292 4/6

[PASTE] 48 left
[LINUM] filter - 4 left: BORNE DRONE NERVE OZONE
[DRONE] most probable, filter - 1 left
[NERVE]

most-probable method count update (Success/Fail): 47/29 - 61.8%/38.2%

 

[OmCheeto]

Wordle 1,292 3/6