The distribution of every dichotomy is intentionally uneven. I think this is the key, though Hasbro’s response did not expand on it. Five characters have glasses, for example, and five characters have blonde hair. Hasbro’s response to the six-year-old included this statement: “You will notice that there are five of any given characteristic” ( source). If two remain, you’ll have to ask a fifth question to reduce it from two to one you’ll then guess it correctly with your sixth question. If only one remains, you’ll guess it on your fifth turn. Three does not halve evenly, so your fourth question may reduce the pool either to one or to two. At the end of your third turn, you want to have three left. You then want your second question to divide the field in half again, down to six.
After the first question, you want to have twelve characters remaining. If you follow this algorithm, you’ll always guess the player correctly after five or six questions. You want the answer to your first question to be “Yes” for twelve of the twenty-four characters and “No” for the other twelve. You do this by asking questions such that either answer will eliminate half of the remaining characters. To discover your opponent’s character in the fewest number of turns (on average over multiple games, of course), you want to make the dichotomic search as efficent as possible. This search algorithm “operates by selecting between two distinct dichotomies at each step” ( source), dichotomies like hat/hatless and male/female. The game itself can be understood as a dichotomic search. The winner is the player who correctly guesses the opponent’s character first. (Here are some sample questions: “Does your character have black hair?” “Does your character have a beard?” “Is your character wearing earrings?”) Each question narrows down the list of possible characters. Players take turns asking a series of Yes/No questions about the other player’s selected character. Each player secretly selects one character. Guess Who? is a simple two-player game that teaches the process of elimination. To make sense of the distribution, let’s explore the best strategy for the game in terms of a computer science algorithm known as a dichotomic search.
Hasbro’s initial response failed to clear up the issue for the six year old - or for her 37-year-old mother ( source). A six-year-old girl sent an email to Hasbro, complaining about the uneven distribution of male and female characters in the game. It’s not every day that a game gets mentioned in the news, but last week a story about the game Guess Who? made the rounds on social media.
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