> Q: What simple strategy guarantees a win within 6 guesses?
I've seen a lot of analyses of Wordle that pose this question, and I feel like these are not people who play Wordle (not unlikely - these are seemingly people more interested in analysing the game from a statistical standpoint than simply playing directly).
But while the answer to this question is interesting enough, it's not that interesting. People I've spoken to who play have zero interest in winning in 5 or 6 guesses - in fact most would consider a score of 6/6 a loss (or at least a relatively bad score), unless it was a particularly tricky word.
> (1) If I win in two guesses, am I good or lucky?
Q: What first guess maximizes the number of guaranteed wins on the second guess?
Q: What first guess maximizes the number of expected wins on the second guess?
> The probability of winning in two guesses is about 2%, so the answer is: mostly lucky.
These - and the follow-ups I was hoping for for 3, 4 & 5 guesses respectively - are much more interesting questions.
* Yes I can just clone this and edit to find these things out (& probably will later this week) but I'm just commenting on my confusion around why there's so much focus on the least interesting part of a problem.
I know how to simulate the game and get a very good strategy (or see what others have done), but I use different starting word every day because it makes it more interesting.
I'm using the same strategy and I have to say it mostly is doable. I was afraid for vivid (two repeated letters) but if I remember correctly the next day was quite doable starting from vivid.
> I've seen a lot of analyses of Wordle that pose this question, and I feel like these are not people who play Wordle
Interesting thought. But idunno, I am prettty into wordle, I agree with you, my goal with the daily is to get it in 3 as often as possible, but when it comes to "extracurriculars" I'm interested in all sorts of questions that are divorced with this concern. And I'm actually not that interested in deeply analyzing the part I enjoy most (getting the daily in 3).
> I'm actually not that interested in deeply analyzing the part I enjoy most (getting the daily in 3).
I think I'm similar; I've been using the same starter word since almost day 1, and despite having seen lots of very compelling evidence that it is suboptimal, I have not changed it :D
But I'm still somehow interested in what is optimal (& I guess oddly passionate about the definition of optimality).
Actually yeah, even though I'm trying to get it in 3 every day, I do not optimize my starting word. In fact I get quite some pleasure out of choosing a bad starting word (like MELEE) and then going for a 3. I wouldn't mind if wordle had an option to start with a random word (and everyone who plays that way that day has that same randomized starting word.)
That is a genius idea. Maybe the first row of coloured squares that you share can be a different colour scheme to show to others that you are playing that mode.
This is why I switched off of hard mode, after trying it a few times. For me while it was technically harder, it lost some strategic depth and the games became a lot less interesting.
It's in an important sense actually easier! Sure, good play results in more guesses than in not-hard-mode, but that would be like saying a 100m sprint is easier than a 2-mile race because the latter takes longer. The more interesting measure of difficulty is how hard it is play optimally. And since the search space for not-hard-mode is bigger, I'm pretty sure it's harder.
But more importantly, hard mode is also less fun, and this thread demonstrates exactly why: the creative aspect is coming up with le mot juste for quickly honing in on the right answer. Hard mode takes away your tools to do that and sometimes even results in a thoughtless guessing game.
I kinda like when "hard mode" makes you have to come up with a possible word even if it seems impossible to think of one, which can be a satisfying puzzle, not having the restriction makes it easy to think "okay screw it, I'm going to spend a guess to search for letters".
It only forces you to reuse greens. I like to play in hard hard mode in my head, where each guess must be consistent with everything previous. Still not actually hard though, obviously.
wordle tends to be more familiar words, so I'd ignore blate and blake. So now we have D, M, R, S, Z
Doesn't look like there's a word that has 4 of these letters to guarantee on next guess. So need to try for the most likely 3 letters. Could be 2 more guesses, but still ends up better than a 1 in 5 chance.
> Spending another guess to reduce that search space is the right move (assuming you're not playing hard mode).
This, again, depends what your goal is, or what you consider "winning". If you're only focused on avoiding losing, then yes this is the right move. If you're trying for a low score, it's not as clear, and hard mode may actually be "easier" in many ways.
No it absolutely is the way to win in the fewest moves. When you have more than 2 equally possible words then the next word should be a choice that reduces the search space rather than going for a guess.
It's the way to win in the fewest words on average.
If you want to maximize your number of three-guess-wins even if your 6-guess-failure rate is higher, it is obviously can't be a correct strategy to use your third guess on a word that you know can't be correct.
Sure, my point is that the metric "minimize mean number of guesses to win" isn't axiomatically the objective function: the 6 threshold already suggests that many people would rather have a "guaranteed 6 and average 5" rather than "average 4 but fail 5% percent of the time".
If someone considers a 4 to be a soft-failure then they will prefer (3,6,6) to (4,4,4) even though the latter is a lower mean number of guesses: it's a higher count of 4+ 'failures'. The strategy that considers (3,6,6) a better result than (4,4,4) wouldn't guess "dream" in the above example.
I find it fun because it prompts me to find the optimal guess (given hard mode). Playing easy mode I'm much more happy to do the first word that comes to mind and sort of fits.
Very anecdotal and personal, and non-technical, but I believe wordle words are usually very simple ones, so in your case, BLAME will stand a better chance than the remaining three. BLADE could be second.
'blade', 'blame', 'blare', and 'blaze' are all words that will be used in a wordle puzzle one day, and all equally likely to be used since it uses all words once.
The OP does link to this blogpost[0] which, while frustratingly also focuses heavily on the "worst-case" & seems to treat "winning" as "avoiding the worst-case", it does also have some numbers on decision-trees that produce highest average scores: those are linked here[1] & are much more interesting.
Reading that wiki page brings up a follow-up question:
Given:
- the optimal starter word appears to be the quite obtuse word "SALET"
- while we don't know that "SALET" won't someday be an answer, there's a common assumption among players that the answer list consists of "common" words. If I'm not mistaken this is a founded assumption
What would the rankings of the subset of optimal starter words that are "common" be (i.e. would be likely to be reasonable guesses of typical players)?
It's interesting to see the averages from different decision trees and that the optimal hard mode is only 3.51 -- and that easy/hard mode are so close. It makes me wonder how much of my stats are pure luck. I'm currently sitting at exactly 3.5 after 48 hard modes (0/2/26/14/6/0) starting with SLATE, but while I feel pretty confident playing the game, I definitely have not used the "optimal strategy" every time, if I even knew that strategy in the first place.
Given how close hard mode and easy mode are, and that even when calculating averages, 4, 5 & 6 are still considered "wins", I strongly suspect changing the parameters could show hard mode to be "easier" for a "<4 or bust" goal.
> I definitely have not used the "optimal strategy" every time, if I even knew that strategy in the first place.
It's also worth noting that these models (presumably) assume an equal chance for every word in the provided dictionary, whereas - assuming the answers are "common" words - a human will likely be strongly biased toward the subset of possible answers and therefore can have much higher probabilities of success in practice than the theoretically-optimal strategies.
Was phrasing the statement from the perspective of a model "player", but I guess knowing whether "SALET" is in the answer list is not quite the same as knowing where each word is in the list, so you could semi-cheat and use the answer list as your definition of "common", without gaining too much knowledge.
> The probability of winning in two guesses is about 2%, so the answer is: mostly lucky
That's for any given game, so presumably if your statistics over time are significantly higher than 2% then the answer is mostly good? Or perhaps that's a statistical fallacy akin to tossing a head 5 times in a row?
My dictionary, excluding proper names and words with punctuation, has about 4600 five-letter words. I'd add a question to your list related to how the 2315 Wordle words were chosen as an analysis of this might provide more heuristics for how to win faster.
Once I realized that solving in one guess or two doesn't take any particular skill, I began to wonder what "winning" Wordle really means.
It's a game that you play for fun. If folks want to analyze the dictionaries to develop their strategy because it's fun for them, then they're doing it right. Not cheating.
If you prize Wordle solution patterns that are symmetrical or aesthetically pleasing because it's fun, then you're doing it right.
If you try to see how many consecutive hard-mode guesses you can make with NO correct letters because it's fun, then you're doing it right.
If you try to see how far you can skew your distribution towards six without ever losing because it's fun, then you're doing it right.
Very well put, especially with the focus on the fact that having fun means different things for different people.
I played the game maybe twice, the game itself is just very boring and hard for me (though generally, I hate playing games, so it's not a critique on the game).
But!
I read the source code and checked the implementation. I read many different strategies optimizing for different aspects of the game. I implemented a very naive solver in JavaScript, then I thought about more advanced data structures and algorithms I could use to improve my naive solver (both from the game's POV and from the computational POV). I watched videos cloning the app with different frameworks (or without) and technologies (mobile, command line, web) and I listened to the author on a podcast.
I'm having fun and I'm learning while doing these things, so I appreciate Wordle, even if I can't be bothered to solve the daily word.
Agreed, I like discovering interesting patterns and strategies, but always using the same 'best' openers is less exciting.
I made a browser extension to show remaining solution counts and make it easier to restart the game without losing my streak - I usually use it to play around more after solving the day's word.
A related question is: "What is the smallest fixed set of guesses which always solve Wordle, narrowing down possible hidden words to just one?". So far the answer is 8: MODEL LEVIN TAPPA GRABS DURGY FLYTE CHAWK SPOOR [1].
Bringing this down to 5 would mean that one could always win at Wordle with the same set of 5 guesses. Seems unlikely that such a solution exists, but interesting question nonetheless.
There are probably hundreds of writeups on strategies to play Wordle. I play it for fun and I play it random. My first word is whatever comes to mind. I know I can increase my chances by selecting a word with more vowels in it but where is the fun in it. :-)
I once got it on second word - it was pure chance. I am now waiting for the day when I get it on the first attempt. :-)
I think this is something the numerical analysts are missing. They are looking at probability and frequency, which tells you about an outcome given a perfect, logical player with unbounded matching skills.
But a human player though might do better by priming their pattern matcher with something more likely to trigger good hints, such as knowing more vowels. My start word is often AEONS
Developed it looking at the answer and guess lists and finding words that maximize frequency and placement. E.g. Y and E are very commonly seen in fifth position. No code, just excel and searching the word lists with regular expressions.
It's so effective the game lost a lot of its fun :( I almost always get the answer on guess #4. The days I struggle and get it on guess 5 or 6 are fun though! :)
Ah nice, I was using SALET CHIMP BOUND or would go for something with a Y in it for the third if there looked like a lack of vowels so far. I hadn't gotten around to doing an analysis on what 3 words would be good for a slightly more dynamic/complex strategy than 4 fixed words.
Wordle is the only thing I haven't tried to outsmart by learning about its math, programming, and tricks that increase your chance of winning. I think those things take away all the joy that I get from Wordle.
It matters for the precise statements these analysis papers are making.
That is, the math is clearly accurate and describes how you can do with perfect knowledge. If you want to grade yourself against that, by all means consider it. For casual play, though, these numbers are not at all a reflection on what your rates will be.
Strongly agree. For me, there are several levels of 'assistance' with the game, and at some point it becomes cheating.
1. Guessing the first word(s) randomly, and then solving from there. Not cheating at all, but frustrating for me, as I am terrible at anagrams.
2. Using a generic dictionary to check possible answers against. Not cheating. I use the standard dictionary in my Linux distro, filtered by 5-letter words.
3. Using the dictionary from the source code to check against. Skirting dangerously close to cheating, but probably OK.
4. Using the list of possible answers. Clearly cheating.
5. Using starting guesses that I concocted myself by studying a generic letter frequency table. Not cheating.
6. Using optimal starting guesses, generated by someone else, based on the WORDLE letter frequencies. Cheating.
7. Using software that I wrote to automate my elimination process based on the dictionary in (2). Again, skirting close to cheating, but possibly OK.
8. Using someone else's software to guess, based on solution graphs. Cheating.
For me "cheating" is anything I would not be able to come up with on my own, if I played the game with no prior knowledge, repeatedly, in an offline environment with no external assistance available.
It's not a competition--and all the answers are known--so there's no such thing as cheating. People are free to take whatever approach to it they want to.
I had a similar feeling (though 'cheating' is kinda strong). So I took a dictionary and some letter-frequency stats (also from norvig.com) and computed a three-word opener using the 12 most common consonants and 3 most common vowels: CHAMP GELDS FRONT. (There were more word-sets satisfying the condition; this was the most memorable.)
I guess I'll try this notebook tomorrow and see how it rates my opening.
The first 1-3 words may "strike" early. But victory is inevitable it seems with those. They seem pretty durable against sneaky double-letter words too.
HANDY SWIFT GLOVE CRUMP seem to lack the concentration of "quick strike" letter combos onthe first two words (FEAST and BRING for me). Then CHUMP and DOWLY are "cleanup" guesses if not enough comes out of FEAST / BRING.
But I don't have math behind it so... what do I really know.
- Always start with the same word, one that has the most common letters
- Prefer more common letters to less common letters
- Prefer more common words to less common words
- Starting with round three, never guess until I know all possible common words
- Don't repeat a letter unless the only other possible words are uncommon
- Prefer consonant combinations at the start of the word over staring with a vowel
- Never do plurals (I think the game does not use them)
A guiding principle is maximize learning at each round. I have a manual written process for listing all possible combinations at each step and iterating on each to find all possible words. I usually start that on the third round.
I've written a small program that takes a pattern (like ??EA?) and a list of eliminated letters and spits out all possible words. My wife says it's cheating, so I rarely use it.
I don't think it's cheating because it only saves me time going through all possible combinations on paper. I guess there's some chance it will suggest a common word I would have never hit on manually.
I don't deny that my high rate of second guess wins is partly luck. But I contend that the N is large enough by now that it's at least partly my strategy.
EDIT: I misspoke saying that my strategy maximizes learning. I will explain.
I always apply all learnings to the next guess. That is, with each guess I use all the confirmed letters and put them in the confirmed positions. This DOES NOT maximize learning. That would require using all new letters every time until you know the word for sure. But this would reduce overall performance by eliminating luck in early rounds. So it's more correct to say my strategy balances between learning and serendipity.
Perhaps I'm mistaken, but from an interview with the game author, I gathered that you can use 10k+ words, only ~2300 of those being candidates for the winning word.
But the analysis only uses the latter subset. So in theory there could be a valid 5-letter that could be a good opener, even if it cannot be a winning word.
I saw ROATE PULIS CHYND mentioned here once and have been using it ever since. I find its mechanic precision and usefulness soothing, though it's unhelpful on a few occasions.
It removes a lot of the fog of war and since it leaves me with few guesses remaining, keeps the game tense enough to be fun
It looks like Peter has assumed equal probability for each solution. It would be interesting to apply a probability distribution across the wordlist, assuming the editors pick the words manually. I think this plays into my strategy subconsciously when I’m solving them.
The order was set at the start, the list is visible in the minified source. So a perfect oracle isn't merely possible, it's trivial.
The fun comes from pretending that's not the case and playing it straight. And then from being able to use the oracle as an aid to analysis, if you're into that sort of thing.
I don't agree with Norvig here. The optimal strategy is to reduce the number of degrees of freedom in subsequent guesses as early as possible. Essentially, pick words that would earn you the lowest Scrabble scores.
I used to start with TEARS. Once I realized that they never used plurals, I switched to STARE, since putting the S at the end doesn't appreciably lower the entropy. I usually end up winning with 3 guesses, which is the point where strategy starts to pay off. (I do agree with Peter that 2-guess wins are almost always due to luck.)
With different goals. I try to minimize the number of required guesses, while he is trying to maximize the odds of a 2-guess win. To do that, he deliberately avoids guessing letters that would fit the more-common cases where a 2-guess win is extremely unlikely.
In other words, Norvig's approach requires you to guess letters that aren't that likely to appear at all. He will get more 2-guess wins, but I will do better in the long run.
Maybe I misinterpreted what I did read. Is he saying that early-stage guesses that contain uncommon letters is the optimal strategy? If so, I'll go back and try to understand the specific reasoning, because that doesn't sound right.
Wordle is basically gambling, but like a lot of games of chance you can improve your odds using skill. A good vocabulary, good starter words, solid analytical skills. But peeking at the word list, players are often still left with three or four viable options after two or three guesses. Lucky guesses will result in completing the daily game in three or four tries, unlucky guesses will push this up.
for the folks who love playing Wordle, you may also like playing the "Mini" crossword (available on NYT Games iOS app) which is free to play and available daily. Wordle has truly made me interested in word games and I'd love if you have any other recommendations.
I’ve lost completely my lust for Wordle after the NY Times acquisition. Don’t know exactly why. That said, I used to like to come up with my own strategies, to keep things interesting.
The dictionary seems to be from aspell. After a couple stock guesses, I can usually win in another turn or two using `aspell dump master` and some grepping.
The 1970s Mastermind commercials aren't effective, because the mix of vitamins that's injected into bread and pasta no longer has that Gene Rayburn-esque quirk of making everyone crave earth-tone clothes. So Wordle is the next best thing.
LOL. I love me some puzzle games but find Mastermind and Wordle equally boring. Mastermind was fun as a kid but once you learn the algorithm, it's just a chore.
>If I win in two guesses, am I good or lucky? ...The probability of winning in two guesses is about 2%, so the answer is: mostly lucky
>What first guess maximizes the number of expected wins on the second guess? A: FILET gives you 57.5 expected wins (out of 2,315)
Note that 57.5 / 2315 = 2.4%, so being "good" at the first word can only improve your chances of a two-guess win by at most ~20%. Not that much.
I believe that stat illuminates a MAJOR factor for why Wordle is so popular that I haven't seen discussed yet: it's a game of (almost) pure luck, that successfully gives every man, woman and child of diverse intelligence the perception of being very smart, occasionally. It's a pat-on-the-back generator that works for everyone, not just those with high aptitude.
It's a lottery ticket, if winning the lottery meant you could show off how smart you are.
That assumes a two word guess is the only objective. (And, yes, that's luck.) But wins in the 3, 4, 5 turn category are pretty common absent a lack of luck.
That said, it's probably easier than it looks at first glance and given a decent vocabulary and some sense for word and word pair frequencies in different positions you'll probably finish at 6 turns or less unless you really go down a bad path.
I realized just last week that I had been playing in hard mode without knowing it. I had definitely had some games where I was almost had it but there were a lot of options.
I really am finding new layers to this game. I play hard mode, and when entering my initial guess, I try to put common letters in uncommon positions. I'd much rather get a bunch of yellows than a bunch of greens at this stage.
> Q: What simple strategy guarantees a win within 6 guesses?
I've seen a lot of analyses of Wordle that pose this question, and I feel like these are not people who play Wordle (not unlikely - these are seemingly people more interested in analysing the game from a statistical standpoint than simply playing directly).
But while the answer to this question is interesting enough, it's not that interesting. People I've spoken to who play have zero interest in winning in 5 or 6 guesses - in fact most would consider a score of 6/6 a loss (or at least a relatively bad score), unless it was a particularly tricky word.
> (1) If I win in two guesses, am I good or lucky?
Q: What first guess maximizes the number of guaranteed wins on the second guess?
Q: What first guess maximizes the number of expected wins on the second guess?
> The probability of winning in two guesses is about 2%, so the answer is: mostly lucky.
These - and the follow-ups I was hoping for for 3, 4 & 5 guesses respectively - are much more interesting questions.
* Yes I can just clone this and edit to find these things out (& probably will later this week) but I'm just commenting on my confusion around why there's so much focus on the least interesting part of a problem.