the Yao lemma

Yao's Lemma is a principle in computational complexity that helps analyze the difficulty of decision problems. It states that the best performance of any randomized algorithm (one that uses chance) can be bounded by the performance of the best deterministic algorithm (one that follows a fixed procedure) on a carefully chosen probability distribution of problem instances. In essence, to understand the limits of randomized algorithms, it suffices to examine deterministic algorithms against specific distributions, simplifying the task of proving lower bounds on problem-solving complexity.