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Solving Wordle in 3.64 guesses on average, 99.4% of the time

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Re: Solving Wordle in 3.64 guesses on average, 99.4% of the time

#91

Post by jeffomatic »

Humphrey wrote: post #78

I have also hacked around on solving this problem. However, I decided that using the shorter list of answers was cheating, since end users wouldn't have access to this list. From a user's perspective, any word that Wordle lets you guess could be a valid solution. It's still a work in progress, but my code died when I tried to generate a complete game tree for the full list. However, in theory it could be done once, t…

No slight to anyone pursuing this strategy, but I also felt like using the shorter list for ranking candidate words was cheating. On the other hand, my solver ends up making silly suggestions that might be appropriate for early on in the game, but not for late guesses.

I've tried to think of what might be a good way of approximating a human's own sense of which words are viable Wordle answers. One thing I attempted was using a word frequency table to help bias the algorithm away from less common words. The funny thing is that some words rank low in word frequency but are otherwise count as "common knowledge". For example, "tapir" was a Wordle solution a few weeks ago, but it ranked lower than some obvious non-answers like "grovy". It could be that the frequency table I was using was weird, but I can believe that there are well-known words that aren't used that often. Maybe I could come up with a better corpus (e.g. only use the NYT or some other newspaper) to use as the basis for a custom frequency table. Seems like a lot of work!

Re: Solving Wordle in 3.64 guesses on average, 99.4% of the time

#92

Post by ycombobreaker »

npinsker wrote: post #16

I wrote a solver a few weeks ago that solves easy mode in 3.45 guesses and hard mode in 3.55 guesses. Rather than using heuristics, it explored a large portion of the game tree (with a little pruning) and I'm hopeful that it's optimal. Interestingly, the EV-optimal hard mode strategy takes 3.52 guesses on average, but requires 7 guesses a tiny fraction of the time, so I instead exposed the best strategy that always r…

I've seen a number of solvers; but my partner has forbidden me from writing one, forcing me to do everything in wetware. 3-4 guesses seems right intuitively. I saw some speculation that the dictionary was well-known, is that true?

Seems to me that the problem as-stated allows the guesser to discover a nonword "for free", but otherwise expects the dictionary to be "all five letter words" which is much larger than the real solution space. Though, maybe in practice that doesn't change the solvability by much.

Re: Solving Wordle in 3.64 guesses on average, 99.4% of the time

#93

Post by hgibbs »

hervature wrote: post #60
hgibbs wrote: post #31

Earlier quoted context omitted.

As a point of curiosity, what do you mean by optimal? To me, I can see at least two (potentially different) cost functions that a Wordle strategy can aim to minimise. Firstly, you can try to minimise the expected number of guesses, and secondly you can try to minimise the expected number of guesses conditional on never losing the game. In principle you could optimise for the first but not the second by allowing a sma…

Funnily enough, I think neither of those notions are the correct thing to optimize. For me, you want to minimize the maximum number of guesses. This leads to an equilibrium. Otherwise, your opponent can just abuse your strategy.

My point is exactly that though - the choice of cost function is subjective. There is no best cost function, just a mapping from costs functions to optimal strategies.

Re: Solving Wordle in 3.64 guesses on average, 99.4% of the time

#94

Post by tomlockwood »

Grustaf wrote: post #87
tomlockwood wrote: post #25

Earlier quoted context omitted.

I think it's chosen based on a random number generated from the date - but one of the most recent games had the answer "REBUS", which I've never heard or read before. But yeah, the target list has many more common words in it than the list of all possible guesses.

That is not an uncommon word though, I'd venture most school children know it. You probably read rebuses in school but just forgot about it!

It's a common word? What's your source for that claim?

Re: Solving Wordle in 3.64 guesses on average, 99.4% of the time

#95

Post by kevlened »

ycombobreaker wrote: post #92
npinsker wrote: post #16

I wrote a solver a few weeks ago that solves easy mode in 3.45 guesses and hard mode in 3.55 guesses. Rather than using heuristics, it explored a large portion of the game tree (with a little pruning) and I'm hopeful that it's optimal. Interestingly, the EV-optimal hard mode strategy takes 3.52 guesses on average, but requires 7 guesses a tiny fraction of the time, so I instead exposed the best strategy that always r…

I've seen a number of solvers; but my partner has forbidden me from writing one, forcing me to do everything in wetware. 3-4 guesses seems right intuitively. I saw some speculation that the dictionary was well-known, is that true? Seems to me that the problem as-stated allows the guesser to discover a nonword "for free", but otherwise expects the dictionary to be "all five letter words" which is much larger than the…

The wordlist is more than well-known, the word for each day is predetermined. The entire game runs in the browser and the selected word is based on the date. Here’s a quick script based on any date you select: https://codepen.io/kevlened/full/NWaOmPw

Re: Solving Wordle in 3.64 guesses on average, 99.4% of the time

#96

Post by forrestthewoods »

npinsker wrote: post #16

I wrote a solver a few weeks ago that solves easy mode in 3.45 guesses and hard mode in 3.55 guesses. Rather than using heuristics, it explored a large portion of the game tree (with a little pruning) and I'm hopeful that it's optimal. Interestingly, the EV-optimal hard mode strategy takes 3.52 guesses on average, but requires 7 guesses a tiny fraction of the time, so I instead exposed the best strategy that always r…

Neat!

The graph of every possible game for Hard mode should be pretty tractable. Sounds like you wrote almost exactly what I started but have been too lazy to finish.

> but requires 7 guesses a tiny fraction of the time, so I instead exposed the best strategy that always requires 6 or fewer guesses.

That's awesome. My question is "what is the minimum number of guesses to solve every word while guaranteeing it never loses". For hard mode I'm pretty sure this can be provably brute forced. Easy mode requires enough pruning I'm not sure it can be proved.

Re: Solving Wordle in 3.64 guesses on average, 99.4% of the time

#98

Post by tomlockwood »

ycombobreaker wrote: post #92
npinsker wrote: post #16

I wrote a solver a few weeks ago that solves easy mode in 3.45 guesses and hard mode in 3.55 guesses. Rather than using heuristics, it explored a large portion of the game tree (with a little pruning) and I'm hopeful that it's optimal. Interestingly, the EV-optimal hard mode strategy takes 3.52 guesses on average, but requires 7 guesses a tiny fraction of the time, so I instead exposed the best strategy that always r…

I've seen a number of solvers; but my partner has forbidden me from writing one, forcing me to do everything in wetware. 3-4 guesses seems right intuitively. I saw some speculation that the dictionary was well-known, is that true? Seems to me that the problem as-stated allows the guesser to discover a nonword "for free", but otherwise expects the dictionary to be "all five letter words" which is much larger than the…

This program actually inadvertently created a quite philosophical discussion amongst my friends! Some of them contended that writing a program to solve wordle sucked the joy out of the process of solving it, even if I solved the puzzle myself, first.

Re: Solving Wordle in 3.64 guesses on average, 99.4% of the time

#99

Post by Edman274 »

muti wrote: post #52
Edman274 wrote: post #12

If you right off the bat guess "bound" and then positions 2, 3, 4, and 5 all come up green, then your goal needs to then be to use words like 'morse' to rule out (in one fell swoop) words like 'sound', 'mound' and 'round'. Then, if it's not ruled out, you can then choose words that just have m and s, or s and r.

This is a valid strategy in easy (default) mode, but in "hard" mode, you must use all yellow/green letters in subsequent guesses

Oh, good point. I didn't know that there was a hard mode - I've only played twice.

Re: Solving Wordle in 3.64 guesses on average, 99.4% of the time

#100

Post by davchana »

You guys are all here real programmers, but I am just good with Excel & a bit of javascript. I made this sheet to get best possible words, & I am trying to get this converted into a bookmarklet.

My excel sheet is explained in this different hn thread about same game https://news.ycombinator.com/item?id=30037065

The whole word list is available in the javascript code of the game page. I know all of that can can be accessed by javascript runtime, but the javascript wordle uses is not the one I can understand, could somebody please have a look at wordle page source & let me know how can I access the variables defined in his code in js file https://www.powerlanguage.co.uk/wordle/main.e65ce0a5.js in variable named La

My some of the basic js apps I have made for myself are hosted on gitlab at username davchana

In manual mode I try to use first word with 3 vowels & no repeat letters. Hard mode is good for not letting the tryies go waste.

Thanks

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