The emerging paradigm of dialogue interfaces for information retrieval systems opens new opportunities for interactively narrowing down users' information query and improving search results. Prior research has largely focused on methods that use a set of close-ended questions, such as decision tree, to learn about the user's search target. However, when there is a myriad of documents or items to search, solely relying on close-ended questions can lead to long and undesirable dialogues. We propose an adaptive dialogue strategy framework that incorporates open-ended questions at the optimal timing to reduce the length of the dialogue. We propose a method to estimate the information gain of open-ended questions, and in each dialog turn, we compare it with that of close-ended questions to decide which question to ask. We present experiments using several synthetic datasets designed to explore the behavior of such an adaptive dialogue strategy under different environments, and compare the system's performance with that of a close-ended-questions-only strategy.