Information Gain: How Good Questions Reduce Uncertainty

Information gain is a way of thinking about how much new information a question could provide. Before asking, several answers may still be possible. After receiving a useful response, fewer candidates should remain or the remaining candidates should be organized more clearly.

You do not need a formula to use the idea. Look at the candidates still under consideration and ask which yes-or-no question would separate them into useful groups. A question that could eliminate many candidates regardless of whether the answer is yes or no will usually reduce more uncertainty than a narrow question about one favorite candidate.

Consider eight candidates: African elephant, blue whale, Great Barrier Reef, Moon, Eiffel Tower, telephone, printing press, and International Space Station. Four are human-made and four are not. Asking “Is it human-made?” divides the candidates into two equal groups.

Now suppose you suspect the telephone and ask, “Is it the telephone?” A yes answer would solve the mystery, but a no answer would leave seven candidates. Unless strong earlier evidence already favors the telephone, the broader human-made question is usually more useful because either response removes half of the listed candidates.

Early in a game, the possible answer may belong to a very broad range of categories. Opening questions should usually test large distinctions rather than minor details. A good opening question might separate living things from nonliving things, human-made answers from natural ones, or places from answers that are not places.

The best opening question depends on the candidates you are considering. Do not ask a familiar question automatically. First consider whether its possible answers would actually divide your current candidate set.

As the candidate set becomes smaller, broad questions may stop helping. If every remaining candidate is an animal, asking whether the answer is alive provides no new information. The next question should focus on a difference within the animal group, such as habitat, size, movement, or physical features.

Later questions can be narrower than opening questions without becoming identity guesses. Their purpose is to separate the specific candidates still in play. A question is useful because of how it divides the current set, not because it is broadly useful in every mystery.

A question can greatly reduce uncertainty without identifying the final answer. Dividing eight candidates into two groups of four is useful, but four possibilities still remain after the response. More questions or stronger evidence will be needed before the identity is certain.

Information gain also differs from an interesting detail. Asking whether a historical person had a pet may be entertaining, but it is not useful when every remaining candidate had one or when you do not know how the possible answers would affect the list. A useful question must help distinguish candidates, not merely produce an appealing fact.

Some custom questions do not produce a clean yes or no. A response of Sometimes usually means the property depends on circumstances, life stage, version, location, or interpretation. Do not count it as a full yes or full no. Mark the clue as conditional and replace it with a narrower question.

Not Applicable means the question does not sensibly describe the answer. It should not automatically be treated as no. Not Appropriate means the question should not be used to draw conclusions about the answer. In that case, move to a respectful question about category, function, location, time period, physical properties, or another relevant characteristic.

A balanced division is a useful practical goal, but it is not always available. Five candidates cannot be divided into two equal whole groups, and the known properties may produce only uneven divisions. Choose the question that creates the clearest useful separation rather than delaying indefinitely for a perfect split.

The candidate list may also be incomplete. Eliminating every candidate you wrote down does not prove that no answer fits; it may show that the correct candidate was never listed. Answers can also be uncertain or depend on wording. Information gain is therefore a tool for organizing uncertainty, not a guarantee that the candidate list or conclusion is correct.

Before submitting a question, briefly predict how each remaining candidate would answer it. This does not require formal scoring. You are checking whether the question creates useful groups and whether the wording is clear enough to trust the result.

Is It This? does not need to calculate a formal information-gain score for players to use this strategy. Players can compare possible questions themselves, choose the one that appears most likely to reduce uncertainty, and revise their candidate list after each response.