Which Mathematicians Have Developed the Best Strategies for Guessing?

You can enhance your odds of winning a board game. By employing a strategy crafted by mathematicians, you may encounter some challenging logical puzzles.

Originally launched in 1979, Zenkon allows players to secretly choose characters from a collection of 24 distinct figures. Players then take turns questioning each other to deduce a yes or no or make a guess about the hidden character.

Numerous individuals engage in a variant of the game, successfully narrowing down their opponent’s character to a single option to win. Mathematicians have explored the optimal approach for this variant, which involves posing two-part questions.

However, official game guidelines stipulate that victory can only be achieved by directly guessing the secret character, rather than merely eliminating incorrect options from the board.

David Stewart from The University of Manchester, UK, and his team devised techniques for winning within the parameters of official rules. They discovered that, in most situations, both players must utilize two-part questions to divide potential suspects into equal or unequal groups based on the remaining suspects. This approach results in the first player winning about 65% of the time. Nevertheless, certain scenarios exist where the number of remaining characters necessitates alternative strategies.

“Mathematics often presents peculiarities. What appears to be a straightforward setup, stripped of all visuals, turns into a mere collection of n objects; you’re striving for efficiency. It’s fascinating to uncover these exceptional cases.

To unearth the best strategy, he and his colleagues began with the most basic scenario, such as having two characters left for each player, calculating optimal strategies for each case, and progressively tackling more intricate scenarios through a method known as mathematical induction. They also created Online Games, a platform for applying the strategies outlined in their research.

The research team identified that when four, six, or ten characters remain on the board and only four players are left, specific rules must be followed—like asking questions that split the four possibilities into one and three. While this is a riskier approach, the potential rewards are significant in these situations.

“It’s intriguing that this isn’t always applicable to games where outcomes seem purely random,” remarked Daniel Jones at the University of Birmingham, UK.

Stewart and his collaborators also uncovered an even quicker method to win the game: “Is your character blonde? If the answer is no, and the character has brown hair, the opponent cannot respond with ‘yes’ or ‘no.’ This creates a contradiction, as the question’s response contradicts itself. By posing this type of question, players gain more insights than with standard two-part inquiries, though it bends the rule that all questions must yield a YES or NO answer.

This method may prove effective for professional mathematicians and computer scientists, yet tends to challenge amateurs. Brian Laverne, a software engineer who developed this clever tactic, notes, “It requires some effort and practice. While you can conceptualize each step, keeping everything organized in your mind simultaneously is the real challenge, even though each step is quite simple.”