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kuruman said:
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
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:
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.
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).
 
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Borg said:
I don't usually get this lucky.
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I thought that I would do better than my wife today. Nope.
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Orodruin said:
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.
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.

My method relies on a list of candidate words that remain in contention following an attempt. After the Wordle algorithm evaluates my entry, I update the list according to the following sequence of steps: (a) cross out all candidate words that contain rejected letters; (b) cross out all candidate words with a known letter at its initially incorrect position; (c) cross out all candidate words that do not contain a letter in its known correct position; (d) review the remaining candidates and make the next guess. Of course, this looks like a daunting process with 12972 starting candidates. That is why I gave up using pencil and paper and use a spreadsheet instead.

Mind you, I am not dismissing your method. I am trying to ascertain if including all the information at each step can do just as well if not better. I have not field-tested it sufficiently to be able to draw a conclusion. I am still discovering refinements.
Orodruin 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).
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.
 
kuruman 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.
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:
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.
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.

I think the Newtonian physics analogy is very fair. By ignoring relativistic effects you are trying to find out some of the properties of your system in the non-relativistic limit. If your end goal is to include relativistic effects as well, knowing the non-relativistic limit can be of great help in guessing what the end result may look like rather than trying to conjure up a relativistic theory in a vacuum.
 
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.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.

I think the Newtonian physics analogy is very fair. By ignoring relativistic effects you are trying to find out some of the properties of your system in the non-relativistic limit. If your end goal is to include relativistic effects as well, knowing the non-relativistic limit can be of great help in guessing what the end result may look like rather than trying to conjure up a relativistic theory in a vacuum.
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.