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

lockwood.dev

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

#152
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.

The (exact) optimal EV-minimizing strategies (assuming each target word is equally likely) always solve in 5 of fewer guesses in normal mode, and always solve in 6 guesses in hard mode. If you wish to guarantee 5 guesses in hard mode, there's a different (optimal) strategy with slightly higher EV. See: http://sonorouschocolate.com/notes/index.php?title=The_best_...

I don't think a maximum-number-of-guesses optimizer leads to an equilibrium (if you mean Nash equilibrium), assuming you're playing the game where the score of the game for the setter is the number of guesses. In particular, if the solver's strategy is deterministic, the setter will always pick one of the words that needs 5 guesses. There's no reason to think the nash equilibrium can be easily found.

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

#153

Earlier quoted context omitted.

Kindergarten? https://kidpillar.com/free-rebus-puzzles-for-kids/

This website looks like it's target audience is five year olds, to you?

It was just a random google result, but we definitely did rebuses in pre-school at least.

The rebus concept is actually a precursor to actual writing, historically speaking. Both in Mesopotamia/Egypt and in the Chinese civilisation, writing developed through a rebus phase. So it's a very natural thing, that's why it's so child friendly.

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

#154
post #33

This [1] solves it in 3.4212 average guesses 100% of the time and claims optimality, which is 99% of the difficulty it seems. For the limited 2671-word set of possible words, I think the question is now settled (for the whole 12k-word set, I don't think anyone tried anything). It was posted here four days ago [2]. [1] http://sonorouschocolate.com/notes/index.php?title=The_best_... [2] https://news.ycombinator.com/ite…

It's a bit disappointing that there's been many writeups of heuristic-based solvers make the front page, but the writeup of an exact solver doesn't make it. [Note: I was the person who submitted the link to the exact solver writeup to HN].

https://news.ycombinator.com/item?id=30006724

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

#155

Earlier quoted context omitted.

This website looks like it's target audience is five year olds, to you?

It was just a random google result, but we definitely did rebuses in pre-school at least. The rebus concept is actually a precursor to actual writing, historically speaking. Both in Mesopotamia/Egypt and in the Chinese civilisation, writing developed through a rebus phase. So it's a very natural thing, that's why it's so child friendly.

That's all cool, why's it a common word, though?

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

#156

Earlier quoted context omitted.

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.

I once caused a vague division in my secondary school by writing a (looking back now) horrendously hacky OCR solver for our "world maths day" challenge.

Literally half the teachers thought it was cheating and I should be punished, whilst the other half thought (because I hadn't abused it to win prizes) that it showed a creative use of more modern skills to make up for my renowned weak mental-math.

I saw the joy in writing the solver as much more interesting than the math. Same way I can't focus on sudoku given I always try to "solve" solving it.

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

#157

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…

[deleted]

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

#158

If you like Wordle you should check out https://wordhoot.com/

I thought the UI of Wordle wasn't anything special but this makes me appreciate the subtle attention to detail that went into it That website you linked doesn't lock the viewport so on my phone it's constantly panning or randomly zooming And the grid instead a keyboard layout actually matters more than I expected for how easy it is to type Having to manually start a game is a tiny thing but doesn't feel as smooth

Recreating the game from scratch I noticed a ton of these tiny little details that went into the game which made it even more fun of a challenge.

I'm looking forward to trying to implement these subtle animations, too.

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

#160

See also Absurdle, an adversarial Wordle that is designed to be as difficult as possible: https://qntm.org/files/wordle/ I won't spoil how it works, but click the "?" button on the page if you want to know.

Since it is adversarial, it is also deterministic, I.e, for a given play, its response will always be the same. So the challenge here is no longer, “can you guess THE word?”, but rather, “can you find the shortest play?”. Finding a 5-step solution is reasonably challenging, but try for a 4-step solution, it will drive you nuts :) Some have been posted on Twitter but that’s no fun.
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