Information Theory and the Game of JOTTO
The word game, JOTTO, has attracted the interest of several computer programmers over the years, not to mention countless devoted players. Rules are: 1.) Each of 2 players selects a 5-letter English word, or a proper noun, as his "secret word." 2.) Play consists of alternate turns of naming a "test word, whose constraints are the same as ton the secret words, and the opponent answering how close the test word is to his secret word. 3.) Closeness is measured in jots; each jot is a one-to-one letter match, and independent of which word is the test word. GLASS versus SMILE or SISSY is 2 jots. 4.) The first payer to guess his opponent's secret word wins. Constraints on a JOTTO program are; First, it must have a dictionary of all possible words at the outset of each game. (The modification of adding newly experienced words to its dictionary is trivial in practice ad not worth the programming efforts, especially since one wants to avoid adding word-like typing errors, etc.) the 9unacceptable) alternative is to have a letter-deducing algorithm and then a "word-proposer" to order the 5 factorial = 120 combinations (perhaps based on diagram frequencies and vowel constraints) once all 5 letters are found. Second, the most use the program can make of the jots from a given test word is to eliminate from its list of "possible secret words of opponent" all those which do not have that number of jots against that test word. Hence, each test word should be chosen to maximize the expected information derived.