This perspective piece explores the transformative potential and associated challenges of large language models (LLMs) in education and how those challenges might be addressed utilizing playful and game-based learning. While providing many opportunities, the stochastic elements incorporated in how present LLMs process text, requires domain expertise for a critical evaluation and responsible use of the generated output. Yet, due to their low opportunity cost, LLMs in education may pose some risk of over-reliance, potentially and unintendedly limiting the development of such expertise. Education is thus faced with the challenge of preserving reliable expertise development while not losing out on emergent opportunities. To address this challenge, we first propose a playful approach focusing on skill practice and human judgment. Drawing from game-based learning research, we then go beyond this playful account by reflecting on the potential of well-designed games to foster a willingness to practice, and thus nurturing domain-specific expertise. We finally give some perspective on how a new pedagogy of learning with AI might utilize LLMs for learning by generating games and gamifying learning materials, leveraging the full potential of human-AI interaction in education.