In addition to Mastermind, Wordle also falls into the same category.

Optimal play to reduce the search space in both follow the same general pattern - the next check should satisfy all previous feedback, and included entries should be the most probable ones, both of those previously tested, and those not. If entries are equally probable, include the one which eliminates the largest number of remaining possibilities if it is correct.

For wordle, «most probable» is mostly determined by letter frequency - while in Mastermind, it’s pure probability based on previous guesses. For instance, if you play a Mastermind variant with 8 pegs, and get a 2/8 in the first test - each of your 8 pegs had a 1/4 chance of being correct. So you select 2 at random to include in the next guess.

If you then get a 2/8 from the second - you would include 4 previous entries in the next guess, 2 entries from the first that was not used in the second, as well as 2 entries from the 2nd - because the chance you chose the correct entries twice, is less than the chance the two hits are from the 6 you changed.

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Majromax 11 hours ago | parent | next [-]

> In addition to Mastermind, Wordle also falls into the same category.

> Optimal play to reduce the search space in both follow the same general pattern - the next check should satisfy all previous feedback, and included entries should be the most probable ones, both of those previously tested, and those not.

The "next check should satisfy all previous feedback" part is not exactly true. That's hard-mode wordle, but hard mode is provably slower to solve than non-hard-mode (https://www.poirrier.ca/notes/wordle-optimal/) where the next guess can be inconsistent with previous feedback.

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codeflo 12 hours ago | parent | prev | next [-]

> For wordle, «most probable» is mostly determined by letter frequency

I don't think that's a justified assumption. I wouldn't be surprised if wordle puzzles intentionally don't follow common letter frequency to be more interesting to guess. That's certainly true for people casually playing hangman.

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CmdDot 11 hours ago | parent | next [-]

When it comes to quickly reducing the search space of possible words, it is - that’s how you solve it optimally, even if (or in fact, especially) if the word they chose intentionally does not use the most frequent letters.

The faster you can discard all words containing «e» because of a negative match, the better.

If you want to be really optimal, you’ll use their list of possible words to calculate the actual positional frequencies and pick the highest closest match based on this - that’s what «mostly» was meant to imply, but the general principle of how to reduce the search space quickly is the same

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IAmBroom 11 hours ago | parent | prev | next [-]

I would guess Wordle picks from a big bag'o'words. The words are all fairly common - "regel" is not going to show up - but I see no evidence the list favors "zebra" over "taint" (which has occurred, BTW).

	▲	andrewaylett 3 hours ago \| parent [-]
		The original Wordle had a hard-coded ordering that was visible in the source. I had a toy around with the list (as did many other people) a few years back, you can see my copy of the word list here: https://github.com/andrewaylett/wordle/blob/main/src/words.r...

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Bratmon 9 hours ago | parent | prev [-]

It's not an assumption- it's a factual statement about how wordle works

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kruffalon 11 hours ago | parent | prev [-]

> Optimal play to reduce the search space in both follow the same general pattern - the next check should satisfy all previous feedback

Thank you! I might look into this once I break my current streak of the localised wordle clone I'm playing now.

I always try to use as many different bits for the first few rounds...

But then again, maybe I'm not so good at these kinds of games as I think.

	▲	calfuris 4 hours ago \| parent [-]
		It's not actually optimal. Each check should account for all previous feedback, but it may be optimal to make a known-incorrect guess and trade the chance of winning with that guess for additional information. For example, if your first guess on wordle is BOUND and you learn that the word is _OUND, you know the answer is one of FOUND, HOUND, MOUND, POUND, ROUND, SOUND, WOUND. Satisfying all previous feedback leaves you checking those one at a time and losing with probability 2/7. Or you could give up the 1-in-7 chance of winning in 2 and trade it for certainly winning in either 3 or 4: HARMS checks four of those options, and WHOOP identifies the remaining three.