Probability of Transforming Delver of Secrets — A Pauper Format Case Study in Magic: The Gathering

We study the probability of Delver of Secrets transforming in Magic: The Gathering, modeling the event as a sampling problem over a deck composed of spells and non-spells. We derive exact expressions for the transformation probability under both complete and incomplete information, and analyze the impact of library manipulation through Brainstorm. Within a unified probabilistic framework, we characterize both natural flip and manipulation scenarios, providing practical estimates that can inform strategic decisions for both players and their opponents.