If your next word was a word like paint, it would narrow things down greatly.kuruman said:Wordle 413 2/6*
It occurred to me that if one thinks that getting three letters in the correct place after one attempt is a dream come true, one better think again lest this dream turn into a nightmare. Say you get _ R I _ E.
I could think of 20 common words that fit. I have not figured out the shortest path to each of the words and I hope I will not have to.
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Yes, that would narrow things down. However, I have decided to set the appropriate switch to "hard" mode which forces the use of any revealed hints in subsequent guesses. My decision was based mostly on philosophical reasons. You might think I'm silly, but if one views entering a word as a working hypothesis of what the target word could be, then that hypothesis better fit the facts that are already known. It goes against my grain to propose a hypothesis that I know a priori as incorrect. The Edisonian approach is viable in Wordle because there is a limited amount of solutions. I am trying to see how far the scientific approach can take me.Borg said:
Ah, but the aim is not to guess the correct word immediately but to gain information. As such it is not necessarily about making the guess you think may be correct but the guess that you think will give you the most information.kuruman said:
My decision is based on philosophical belief. I cannot propose a hypothesis for how things are when I am certain that it does not fit the already known observations. If one acted this way as a professional scientist, it would be catastrophic to one's reputation and career. Maybe it's just me, but I don't see why I should alter my methodology when I amuse myself with puzzles. Besides, I am not convinced (yet) that not using a known but misplaced letter in the next guess provides more information than using it but in a different position. That's something that I hope to settle.Orodruin said:
I disagree. We know that Newtonian physics are not applicable everywhere. Still, many branches of science use Newtonian physics rather than relativity and they seem to be doing pretty well. You perform tests that you know will not be applicable at all levels, but it can still give you valuable information on how things behave.kuruman said:
This is not the only option that ”hard mode” prohibits. There is also the case when you know the position of say four letters and there are multiple options for the final one. A guess containing several of the candidates may be able to resolve the degeneracy faster and thereby guarantee solving the puzzle whereas ticking the options off one at a time will be completely reliant on luck (which is something I really dislike in games like Wordle - getting four correctly placed letters on an early guess can actually ruin your chances to solve the puzzle).kuruman said:
I thought that I would do better than my wife today. Nope.Borg said:I don't usually get this lucky.
I think that this is an unfair analogy. I would argue that removing a letter that is known to belong in the word is not an approximation but a step in the wrong direction. How can a next attempt without a known letter be an improved approximation? By keeping the letter in the second attempt, I have a one-in-four chance to put it in the right place. If the letter is not where I thought, I can now eliminate all candidate words with that particular letter in 2 of the 5 locations.Orodruin said:
There will always be a problem with solution degeneracies whether one uses "hard mode" or not. Look at post #145. The sequence T R I _ E is sixfold degenerate. It can be solved with certainty only if the first guess is one of the solutions.Orodruin said:
The problem is however amplified by hard mode. In your specific example, several of the solutions can be ruled out with a single guess if you are allowed any guess such as PRICK.kuruman said:
Except that it may not be game theoretically. Your task is to figure out the word (or maybe to do it in as few guesses as possible). I think our disagreement is mainly what a guess represents. To me it represents an experiment that will lead to an observation. When I design the experiment I want to get as much information as possible about the correct word. But that is all it is. It does not necessarily represent an attempt at the final word.kuruman said:
This exchange has been useful to me. It is often useful to verify the regime where what one is looking for is not the case. That assuages my philosophical objection so I will switch off the hard mode.Orodruin said: