5 ms·

Why optimize for greens? Better to rule out more first no matter the position. I think it narrows the search space better. If you want to go fancy somehow calc

Why optimize for greens? Better to rule out more first no matter the position. I think it narrows the search space better. If you want to go fancy somehow calculate with bigramms. If you guess c you don't have to guess k blindly too, etc.

tomlockwood 5y ago
> Why optimize for greens? Better to rule out more first no matter the position. I haven't yet experimentally tested this, but I hope to soon! It may be that a green letter in position rules out more possible targets than a grey letter.
- anotheryou 5y ago
  I thought of yellows. Taking frequent letters over words with sub-optimal letters but in the right positions. But manually I'm no where close to 3.6 either :). Also often too lazy.
  - tomlockwood 5y ago
    Yeah, I think my average is closer to 4, ugh! But the program has shown me some strategies that seem interesting. It always guesses "slate" first, and if that has no greys it guesses "crony", and that one-two punch seems to do me well fairly often.
    - anotheryou 5y ago
      interesting :) I go for "torah", "lines", ("ducky", but I think the k is far from optimal) apart from "h" and "i" it's the same letters (and I do have c and y in my optional 3rd).
amluto 5y ago
If you want to get really fancy, a full minimax solution is probably feasible without massive resources. Pretend it’s a two player game with one player guessing and the other player thinking of a potentially different word for each guess subject to the constraint of being consistent with all previous answers.
- ummonk 5y ago
  Somebody had already tweeted about solving it and finding that 3 guesses suffice, using alpha beta search (though he didn’t use the term “alpha beta” because he might have reinvented it). Unfortunately, I can’t seem to dig up the tweet.
- ford 5y ago
  There is a wordle parody (absurdle) [0] that does exactly this. [0] https://qntm.org/files/wordle/ https://qntm.org/files/wordle/
  - pxx 5y ago
    No it does not. It uses a heuristic at every layer of the tree. Specifically, instead of recursing down each subtree, it chooses the set with the maximum number of remaining elements, which isn't necessarily the set that is most difficult to split.
    - ford 5y ago
      I see - I misunderstood the parent comment. I believe you are saying that the best adversary would attempt to maximize the depth of the tree. For example a branch with "{L, B, C, R, ..}ake" requires more guesses than a balanced tree despite the fact that the two trees may have the same number of nodes.
- sdwr 5y ago
  If you want to split hairs, minimax is optimal for worst-case, but not for bringing down the average # of guesses.
canjobear 5y ago
The generally optimal thing is to choose guesses to reduce the set of possible targets as much as possible. This is the same as choosing guesses with maximal entropy over the resulting patterns (that is, the result you get back from the game should be maximally informative). Because greens are rare, by maximizing the probability of greens, you are approximately maximizing the entropy of patterns, by distributing probability mass among rare patterns. This is why going for greens is a good heuristic.
- ascar 5y ago
  This sounds like the optimal strategy for a single guess. But shouldn't the optimal strategy for solving the game include that there are multiple guesses? While some specific word might provide the highest reduce in entropy for the first guess, it might actually negatively impact the entropy reduction of remaining possible words compared to another first guess. E.g. if RAISE is the optimal reduction in search space for the given word list, what's the best 2nd guess for every possible word? Now taking the average 2nd guesses into account, is there a better first guess?
  - canjobear 5y ago
    Good point. Because the set of possible guesses is constrained, the totally general solution needs to take future guesses into account. There doesn't seem to be a way to find the optimal guess other than searching the whole game tree (which it looks like someone in another comment did).

tomlockwood 5y ago

> Why optimize for greens? Better to rule out more first no matter the position. I haven't yet experimentally tested this, but I hope to soon! It may be that a green letter in position rules out more possible targets than a grey letter.

anotheryou 5y ago
I thought of yellows. Taking frequent letters over words with sub-optimal letters but in the right positions. But manually I'm no where close to 3.6 either :). Also often too lazy.
- tomlockwood 5y ago
  Yeah, I think my average is closer to 4, ugh! But the program has shown me some strategies that seem interesting. It always guesses "slate" first, and if that has no greys it guesses "crony", and that one-two punch seems to do me well fairly often.
  - anotheryou 5y ago
    interesting :) I go for "torah", "lines", ("ducky", but I think the k is far from optimal) apart from "h" and "i" it's the same letters (and I do have c and y in my optional 3rd).

amluto 5y ago

If you want to get really fancy, a full minimax solution is probably feasible without massive resources. Pretend it’s a two player game with one player guessing and the other player thinking of a potentially different word for each guess subject to the constraint of being consistent with all previous answers.

ummonk 5y ago
Somebody had already tweeted about solving it and finding that 3 guesses suffice, using alpha beta search (though he didn’t use the term “alpha beta” because he might have reinvented it). Unfortunately, I can’t seem to dig up the tweet.
ford 5y ago
There is a wordle parody (absurdle) [0] that does exactly this. [0] https://qntm.org/files/wordle/ https://qntm.org/files/wordle/
- pxx 5y ago
  No it does not. It uses a heuristic at every layer of the tree. Specifically, instead of recursing down each subtree, it chooses the set with the maximum number of remaining elements, which isn't necessarily the set that is most difficult to split.
  - ford 5y ago
    I see - I misunderstood the parent comment. I believe you are saying that the best adversary would attempt to maximize the depth of the tree. For example a branch with "{L, B, C, R, ..}ake" requires more guesses than a balanced tree despite the fact that the two trees may have the same number of nodes.
sdwr 5y ago
If you want to split hairs, minimax is optimal for worst-case, but not for bringing down the average # of guesses.

canjobear 5y ago

The generally optimal thing is to choose guesses to reduce the set of possible targets as much as possible. This is the same as choosing guesses with maximal entropy over the resulting patterns (that is, the result you get back from the game should be maximally informative). Because greens are rare, by maximizing the probability of greens, you are approximately maximizing the entropy of patterns, by distributing probability mass among rare patterns. This is why going for greens is a good heuristic.

ascar 5y ago
This sounds like the optimal strategy for a single guess. But shouldn't the optimal strategy for solving the game include that there are multiple guesses? While some specific word might provide the highest reduce in entropy for the first guess, it might actually negatively impact the entropy reduction of remaining possible words compared to another first guess. E.g. if RAISE is the optimal reduction in search space for the given word list, what's the best 2nd guess for every possible word? Now taking the average 2nd guesses into account, is there a better first guess?
- canjobear 5y ago
  Good point. Because the set of possible guesses is constrained, the totally general solution needs to take future guesses into account. There doesn't seem to be a way to find the optimal guess other than searching the whole game tree (which it looks like someone in another comment did).