Get the state of a Wordle game before any guess has been made.

Call this at the START of a game, before the first guess: it returns the size of the guess dictionary, how many words are eligible answers, and the starting uncertainty in bits. Do not call recommend_guesses with an empty guess history - scoring the full dictionary is too expensive, so open with a standard high-information first word instead.

Get ranked next-guess recommendations for an in-progress Wordle game.

Call this AFTER each guess, passing the full game so far: every guessed word and its color feedback, in order. Feedback is one string per guess, one character per letter: 'g' green (right letter, right spot), 'y' yellow (in the word, wrong spot), 'x' gray (not in the word).

Example: the guess CRANE showing gray-yellow-gray-green-gray is words=["crane"], feedback=["xyxgx"].

Returns the top recommendations ranked by expected information gain (lower bits = better guess), the best guesses that are also eligible answers, and game-state statistics including remaining possibilities and uncertainty in bits. Prefer a word from best_answers when few answers remain; prefer best_overall when many remain and you want to maximize information.