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Solving Wordle using information theory

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Re: Solving Wordle using information theory

#21

Post by mcphage »

dredmorbius wrote: post #8

I'd quickly realised that a set of words which covered most of the alphabet (20 words, leaving b, g, j, q, v, and z excluded) allowed solving virtually all Wordle puzzles. The game quickly lost any challenge. wimpy crowd thank fuels Altering order might give faster results. The order presented leaves the most common letters (e, t) for last. Z is quite uncommon, q is virtually always followed by u, similarly common pa…

> I'd quickly realised that a set of words which covered most of the alphabet (20 words, leaving b, g, j, q, v, and z excluded) allowed solving virtually all Wordle puzzles. The game quickly lost any challenge.

You can even go further—there's a set of 5 words which uses 25 out of 26 possible letters, leaving you one more word to enter the right answer.

But here's the thing: while that means you'll almost always win, your # of guesses will always be high.

> but if your goal is simply to solve (rather than minimise attempts)

Pretty much nobody's goal is to simply solve. Once they've played it for a few days, everybody's goal is to minimize guesses. That's the flaw in having a long word list—you always do badly.

Re: Solving Wordle using information theory

#22

Post by lkbm »

Brendinooo wrote: post #18
dredmorbius wrote: post #8

I'd quickly realised that a set of words which covered most of the alphabet (20 words, leaving b, g, j, q, v, and z excluded) allowed solving virtually all Wordle puzzles. The game quickly lost any challenge. wimpy crowd thank fuels Altering order might give faster results. The order presented leaves the most common letters (e, t) for last. Z is quite uncommon, q is virtually always followed by u, similarly common pa…

gotta see how your strategy holds up in sexaginta-quattuordle

This is how I played Quordle and Octordle, but with just three words (doubt, glyph, raise). Might not scale for all combinations.

Re: Solving Wordle using information theory

#23

Post by boothby »

I crushed wordle within a few days of its popularity entering my sphere. It was pretty easy to brute-force a decision tree minimizing the average number of guesses using a lowly python script and a few days of qpu time.

Don't Wordle[1] is significantly more interesting; I've got a solver but the maximum score takes my lowly python script upwards of a day (per day) to solve using brute force. For now, I solve it with a heuristic that terminates in about 20 minutes. My old wordle solver was useful to find a good but suboptimal tree for identifying the answer in 5 undos or less.

Today:

  Don't Wordle 1491 - SURVIVED
  Hooray! I didn't Wordle today!
  ..... 8089
  ..... 4647
  ..... 2492
  ..... 1026
  .Y... 231
  ..G.. 100
  Undos used: 3

    100 words remaining
  x 10 unused letters
  = 1000 total score
My puzzle ethics are: you can and should download the dictionaries of valid answers and valid guesses, you're allowed to keep them separate, but you must not keep the list of answers in its original order.

[1] https://dontwordle.com/

Re: Solving Wordle using information theory

#25

Post by topaz0 »

mcphage wrote: post #21
dredmorbius wrote: post #8

I'd quickly realised that a set of words which covered most of the alphabet (20 words, leaving b, g, j, q, v, and z excluded) allowed solving virtually all Wordle puzzles. The game quickly lost any challenge. wimpy crowd thank fuels Altering order might give faster results. The order presented leaves the most common letters (e, t) for last. Z is quite uncommon, q is virtually always followed by u, similarly common pa…

> I'd quickly realised that a set of words which covered most of the alphabet (20 words, leaving b, g, j, q, v, and z excluded) allowed solving virtually all Wordle puzzles. The game quickly lost any challenge. You can even go further—there's a set of 5 words which uses 25 out of 26 possible letters, leaving you one more word to enter the right answer. But here's the thing: while that means you'll almost always win,…

The only virtuous goal is to type some fun words imo.

Re: Solving Wordle using information theory

#26

Post by empath75 »

dieselgate wrote: post #19
magneticnorth wrote: post #11

Earlier quoted context omitted.

> The game quickly lost any challenge. I only play on hard mode for this reason. My next guess must always be a possible answer based on my current information, and that varies the puzzle enough from day to day that I still find it enjoyable to play occasionally.

I haven't played wordle much since it was purchased but NYTimes ran a story in the last couple days saying how "Hard mode" is actually easier based on their research. Just throwing it out there as food for thought not in a "gotcha" sort of way. https://www.nytimes.com/2026/06/18/upshot/wordle-hard-mode.h...

It's not "easier", it just forces a more guess-efficient strategy.

Re: Solving Wordle using information theory

#27

Post by cvoss »

boothby wrote: post #23

I crushed wordle within a few days of its popularity entering my sphere. It was pretty easy to brute-force a decision tree minimizing the average number of guesses using a lowly python script and a few days of qpu time. Don't Wordle[1] is significantly more interesting; I've got a solver but the maximum score takes my lowly python script upwards of a day (per day) to solve using brute force. For now, I solve it with…

Another great variant is Unfair Wordle [1]. The opponent does not fix the answer upfront but instead evades the player's guesses as long as possible, providing you with the least information it legally can give (according to the usual rules) while still preserving a valid game completion path. The result is that your guesses end up looking extremely unlucky in retrospect.

[1] https://tweakimp.github.io/unfairwordle/

Re: Solving Wordle using information theory

#28

Post by arcastroe »

cvoss wrote: post #27
boothby wrote: post #23

I crushed wordle within a few days of its popularity entering my sphere. It was pretty easy to brute-force a decision tree minimizing the average number of guesses using a lowly python script and a few days of qpu time. Don't Wordle[1] is significantly more interesting; I've got a solver but the maximum score takes my lowly python script upwards of a day (per day) to solve using brute force. For now, I solve it with…

Another great variant is Unfair Wordle [1]. The opponent does not fix the answer upfront but instead evades the player's guesses as long as possible, providing you with the least information it legally can give (according to the usual rules) while still preserving a valid game completion path. The result is that your guesses end up looking extremely unlucky in retrospect. [1] https://tweakimp.github.io/unfairwordle/

Woah. I was surprised to win on the first try: cramp, ghost, blind, bulky, bevel, bezel

Re: Solving Wordle using information theory

#29

Post by cvoss »

arcastroe wrote: post #28
cvoss wrote: post #27

Earlier quoted context omitted.

Another great variant is Unfair Wordle [1]. The opponent does not fix the answer upfront but instead evades the player's guesses as long as possible, providing you with the least information it legally can give (according to the usual rules) while still preserving a valid game completion path. The result is that your guesses end up looking extremely unlucky in retrospect. [1] https://tweakimp.github.io/unfairwordle/

Woah. I was surprised to win on the first try: cramp, ghost, blind, bulky, bevel, bezel

Nice! I'm not actually sure what its mechanism is for providing the "least information". It could be smart and reply in a way that maximizes the number of remaining consistent answers. Or it could be greedy and try to report as many "grays" as possible, then as many "yellows" as possible, then resorting to "greens". The latter seems more likely to me, since its easier to implement.

Re: Solving Wordle using information theory

#30

Post by adamgordonbell »

It's trivial to determine the best guess at any point based on what options it cuts out.

But I ended up building an alphaWordle, using MCTS and a reinforcement loop just to get a feel for how AlphaGo approach to solving games works.

It's not a 'smart' way to solve it, but its pretty instructive and I could compare its moves to the theoretical best move to see it progress.

https://github.com/adamgordonbell/bitter-lesson-demos

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