Optimal Algorithm for Winning Hangman

Question

In the game Hangman, is it the case that a greedy letter-frequency algorithm is equivalent to a best-chance-of-winning algorithm?

Is there ever a case where it\'s worth

Answer 1

No, this greedy algorithm is not the best at all and I can prove it by giving a better solution:

In each step we know the number of letters and we know some letters. We choose all the words from our set of words which have the given letters at the given positions and their length match the length of the word in question. We select the most frequent letter from the selected subset of words and guess about the given letter. For every guesses the guessed letter will be marked as guessed and they won't be guessed again in the future. This way you have much better chances of survival than in the greedy algorithm described in your question.

EDIT:

After the question was clarified and further specifications were made, I've come to the conclusion that the algorithm is optimal.

If we have n words with the given length, containing all the right guesses ("good letters") and not containing any wrong guesses ("bad letters"), x lives, we can look at the frequency of letters in the still possible words and select the letter with the biggest frequency, let's suppose that y words contained the letter.

In this case, the confidence rate of this guess is y/n, which is bigger than the confidence rate of any other letters, which gives a higher chance of survival. So, such a step is optimal. If you make a series of steps containing only steps in this spirit, the series of steps will be optimal too, so this algorithm is optimal.

But, if we have any extra information (like a description of the word, or knowing that the probability of having the same word twice in a short period), this algorithm can be enhanced based on the extra information, all the words in the set of words will have a fitness value (probability based on the extra information) and all the letter types in the words will be weighted based on the fitness score.