Mathematicians have worked out the optimal strategy for Guess Who?

You can maximize your chances of winning the board game Guess who? If you follow a strategy designed by a group of mathematicians, but that could involve logical puzzles that scratch the head.

In Guess who?, Which was published for the first time in 1979, two players each choose, in secret, a person from a set of 24 unique characters. The players then put their opponent in turn to a question yes or no, or trying to guess the secret character of the opponent.

Many people play a version of the game where the narrowing of the character of your opponent to a person results in victory. Mathematicians have already examined the best way to win this version, which essentially involves asking two -component or bipartite questions that divide your options so that the answer is yes for half of them.

But the official rules say that you can only win by being affirmatively the secret character, rather than simply eliminating all the incorrect choices on the board of directors, which increases the mathematical difficulty of finding an optimal strategy to win.

David Stewart at the University of Manchester, in the United Kingdom, and his colleagues have now designed a method to win by using official rules. They found that, most of the time, you should use bipartite questions to divide your suspects into uniform or unequal groups, depending on the number of remaining suspects that you and your opponent have. Using this strategy, the first player will save, on average, around 65% of the time. However, there are scenarios where you and your opponent have some many people left when you should take a slightly different strategy.

“It is very strange in mathematics, when you have something that seems to be an extremely simple configuration – forgetting all the faces, you have just received this collection of n things, and you have a collection of things, and we try to go down as quickly as possible.

To find the optimal strategy, he and his colleagues worked upside down from the simplest scenarios, such as each player with two characters, and calculated the best strategy for each case, working up to much more complicated scenarios, thanks to a process called mathematical induction. They also created an online game where you can practice the strategy described in their study.

The team noted that if you still have four, six or 10 players on your board, and your opponent has four on theirs, you must follow special rules, such as asking questions that divide your four options into one and three. It is a more risky strategy, but in these scenarios, the reward prevails over the risk.

“It is very interesting that for a game that is probably very random that wins, it is not necessarily the case,” explains Daniel Jones at the University of Birmingham, in the United Kingdom.

Stewart and his colleagues also found an even faster way to win the game, which involves integrating a logical paradox in the second part of a two-part question, as “does your person have blond hair or has brown hair and the answer to this question is right?” If the person has brown hair, the opponent cannot answer yes or no, because the answer to the question contradicts. The player asking this question receives more information than he would have done with a typical bipartite question – although this would fold the rules demanding that all questions have a answer yes or no.

Although this approach can work for professional mathematicians and computer scientists, it would be difficult for amateurs, explains Brian Rabern, a software engineer who first found the trick. “It would take a little work and training,” he says. “In a certain sense, you can think about each step and it is not so difficult. It only holds everything in your head both which becomes a little difficult, but each step is itself quite simple.”