Media Highlights

Abstract

During the fall of 2021, Josh Wardle, a software engineer in Brooklyn, created a word guessing game “WORDLE” for his partner. After Wardle released the game to the public, it rapidly became a sensation, with players posting progress on social media sites. WORDLE asks you to guess a five letter word in six attempts. Each attempt involves entering an entire five letter word, after which colors indicate whether each letter appears in the word but is incorrectly placed (yellow) or whether it appears and is in the correct location (green). Information theory, pioneered by mathematician Claude Shannon in the 1940’s gives insight about optimal guessing strategies. Rather than trying to build one’s guess around letters one has successfully identified and placed, sometimes substantially more information about the remaining letters can be recovered by guessing words one knows are wrong. Honner illustrates this concretely with an example in which the word is known after several attempts to be ATCH. Because prior guesses have ruled out certain letters, the best next guess is the incorrect word CHIMP, because this guess guarantees to determine the last unknown letter. The key formula is I = log2( 1 p ), where I denotes bits of information obtained from the guessed letter and p is the probability of the event. The article gives an application using a toy WORDLE game with 16 two letter words. Because log2( 16 1 ) = 4, 4 bits of information are needed to know the 2 letter word from the list of 16. Because only 4 of the 16 words contain an A, the information contained in the knowledge of the presence of the letter A is log2( 16 4 ) = 2, which is like halving the possible list of words twice. Similarly the information in knowing the word contains a T is 2, and together, because probability is additive, knowing both A and T are in the word suffice to identify the word at from the list. Of course, 5 letter WORDLE is harder: there are 2315 possible solution words, and an additional 10,657 words that are accepted as guesses. Calculating the actual information yielded by a particular guess would require more information than the average player has at hand, but bearing the information theory concepts in mind may improve your game. KW