Large language models (LLMs) are impressive, but they sometimes struggle with a fundamental aspect of communication: asking good questions. Think of playing 20 Questions—while an LLM might eventually guess the answer, its questions are often inefficient, taking far longer than a human would. This research explores a novel way to make LLMs better question-askers by focusing on what’s called 'Expected Information Gain,' or EIG. Essentially, EIG measures how much a question helps narrow down the possibilities. This work uses a clever three-step method: First, it has the LLM itself generate multiple questions. Then, it uses EIG to identify the most informative questions, effectively having the LLM grade its own work! Finally, it uses these self-graded questions to fine-tune the model using a technique called Direct Preference Optimization (DPO), where it rewards better questions. The results are intriguing. The trained model consistently asks significantly better questions, leading to quicker solutions in the 20 Questions game. More surprisingly, this improvement also works in topics the model wasn’t specifically trained on, suggesting a more fundamental improvement in its ability to formulate questions. This research opens up interesting possibilities. Imagine an AI assistant that not only understands your requests but also asks clarifying questions to pinpoint your exact needs. Or think of customer service chatbots that efficiently gather information to resolve issues faster. The challenge now is scaling this approach beyond the relatively simple world of 20 Questions. While calculating EIG becomes more complex with open-ended scenarios, this initial step shows a lot of promise for training AIs to ask effective questions and efficiently gather information in real-world situations.