Intuitively, we would expect that the efficient split-in-half search would be worthwhile for the player who is ahead in the race, but might be suboptimal for the player who is behind, since he must take a risk at some point in the race to try to overtake his opponent. However, in a search race the situation is complicated by the fact that the goal is to win the race, rather than minimising the expected number of guesses. In a regular search problem without an opponent it is commonly used as the most efficient search method. This search method maximises the expected number of objects eliminated in each guess (equivalently, the expected information gain), and thereby minimises the expected number of guesses taken to complete the search. To avoid this conflation of issues, we instead use the term ‘binary search’ to refer to any search done within the context of a set of items with a single search-for item.) This same method is referred to as the “split-half heuristic” in psychology and information theory (see e.g., ). This is an unfortunate terminology, since it conflates an optimal search procedure within a binary choice setting with the choice setting itself. (Much of the literature in this area uses the term ‘binary search’ to refer to the split-in-half-search. Search algorithms for binary search are studied extensively in computer science and have led to the use of the “split-in-half search” which operates by splitting the remaining objects evenly (or as close as possible if there are an odd number of objects) on each search iteration (see e.g., ). In this regard, the game has two interesting strategic aspects that occur in broader competitive problems: (1) the agents are able to choose between more “conservative” and more “risky” strategies in their moves and (2) the agents are able to observe the progress of their competitor and adjust their own strategy accordingly.įormally, Guess Who is a “search race” in which each player is searching for an unknown item which is known to be equiprobable from a finite group of objects. As an object of academic study, the game is useful because it is a simple discrete “search race” that bears resemblances to more complex problems in sports, industrial competition, and other competitive ventures. These features make the game a good introduction to logical reasoning. As children progress in their understanding of the game they can also learn some basic probabilistic intuition which gives them a higher chance of winning the game.
When one player is able to correctly guess the other player’s character as his question, he wins the game specific variations in rules for the final guess are discussed soon.įor many young children, Guess Who it is their first exposure to the basic logical idea of eliminating a false hypothesis through contradictory information.
By guessing the characteristics of characters, player narrows down the search through this process of elimination. Hence the language “Are you…”.) After receiving a yes or no answer the player asking the question is then able to eliminate incompatible characters on his game-board by placing these face down, so that only the remaining face-up characters are possible characters that might be held by the other player. Taking it in turns, each player asks a question about the other player’s character that can be answered with a simple yes or no-e.g., “Are you wearing glasses?” (Usually the questions are framed as if each player is their character. Each player has a different character from the game-board and keeps this character secret from the other player. (Some versions of the game have characters that are exclusively white, and other versions have characters that differ by race.) Each player randomly selects a character from a set of cards that matches the characters on the game-boards. These characters have various different characteristics-some are men, some are women, some have facial hair, some are wearing hats, some have glasses, and so on. Each player has an identical game-board showing the faces of twenty-four named characters. For readers unfamiliar with the game, we set out a brief explanation. Guess Who is a two-player guessing game teaching children rudimentary skills in logic. The structure of the game has remained the same since its initial design and has been a staple in toy stores for over forty years. The game has been redesigned several times and re-released in many forms. At the time of publication of this paper it is presently manufactured and distributed by Hasbro. The game was designed by Theora Designs and was first manufactured by Milton Bradley in 1979. Most readers will already be familiar with the children’s game Guess Who which forms the basis for this article, either through having played the game during childhood, or having had children who have done so, or perhaps both.
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