Let’s prove it by contradiction: Lets say you pick the larger ones and drop the smaller ones every single round, you have lost the probabilistic guarantee of 1/

Let’s prove it by contradiction: Lets say you pick the larger ones and drop the smaller ones every single round, you have lost the probabilistic guarantee of 1/2^k that the authors show because the most frequent words will be the lost frequent in subsequent rounds as well. This is the intuition, the math might be more illuminating.