Wordle Entropy: How Information Theory Picks the Best Guess

Entropy measures how much a guess narrows down the answer. A guess produces a pattern of green, yellow and grey tiles. Entropy is the average amount of information that pattern reveals, measured in bits. A higher-entropy guess splits the remaining answers into more even groups, so it eliminates more possibilities on average.

Information gain is another name for the expected entropy a guess yields. Before guessing you do not know which feedback pattern you will get, so you average the information across every possible answer, weighted by how likely each pattern is. The guess with the highest expected information gain is the most informative play.

They are related but not identical. Entropy is measured in bits and rewards even splits; "expected answers remaining" is the average size of the candidate set you are left with. Both point in the same direction, higher entropy usually means fewer words left, so we show both on these pages.

One bit is the information in a single yes/no question with two equally likely outcomes. Measuring in bits lets you compare guesses on a common scale: a guess worth 6 bits answers, on average, the equivalent of six perfect yes/no questions about the hidden word.

Most strong Wordle solvers use entropy or a close relative. Some use a one-step entropy heuristic (pick the highest information-gain guess each turn); the very strongest use a full game-tree search that minimises the expected number of remaining guesses. Our solver uses the entropy heuristic for its next-guess suggestions.

Almost always for the opening guess, and usually thereafter. The rare exception is late in a game when only a few candidates remain: there it can be better to guess a word that might actually be the answer rather than a pure information-maximising probe. Our solver accounts for this once the field is small.

Letter frequency ranks words by how common their letters are. Entropy directly simulates the feedback and measures how well a word divides the remaining answers. Frequency is a fast approximation, but entropy is the real objective, which is why some frequency-popular words like AUDIO score poorly on entropy.

A solver keeps the list of answers still consistent with all feedback so far, scores each candidate guess by its expected information gain, plays the best one, then repeats with the smaller list. With a strong opener this typically solves the puzzle in three to four guesses.