Wordle Back-Solver, for final result and scores, how many legal games are there?

wordle.py

# SPDX-License-Identifier: Unlicense OR CC0-1.0+

words = [w.lower().strip() for w in open("words.txt", "r").readlines()]
print("loaded", len(words), "Words")


def match(word: str, final: str, score: chr, index: int) -> bool:
    return (score == "G" and word[index] == final[index]) or \
        (score == "W" and word[index] not in final) or \
        (score == "Y" and word[index] != final[index] and word[index] in final)


def fits(word: str, final: str, scores: str) -> bool:
    for i, score in enumerate(scores):
        if not match(word, final, score, i):
            return False
    return True


steps = ["WWWWW", "WWWYY", "WWYYW", "WYWGW", "WWGGG", "GGGGG"]
#steps = ["WGGGG", "WGGGG", "WGGGG", "WGGGG", "GGGGG"]
winner = "fires"

if __name__ == "__main__":
    print("playing game with winning word", "'"+winner+"'", "and steps", steps)
    legal_games = 1
    smart_games = 1
    guesses = []
    all = set()
    for step, pattern in enumerate(steps):
        if pattern == "GGGGG":
            print(step + 1, pattern, winner)
            break

        matches = [w for w in words if fits(w, winner, pattern)]
        smart_matches = [w for w in matches if w not in guesses]
        if smart_matches:
            guesses.append(smart_matches[0])
        else:
            smart_games = 0  # nobody could play like this without a repeat!
        unique = [w for w in matches if w not in all]
        all.update(matches)
        legal_games *= len(matches)
        print(step + 1, pattern, len(smart_matches), "sensible candidates out of", len(matches), "with", len(unique), "unique out of", len(matches), matches)
        smart_games *= len(smart_matches)

    print("legal games:", f'{legal_games:,}')
    print("non-stupid games:", f'{smart_games:,}')