Inspired by the title my two top ideas from theoretical compsci:
1. Move to front lists are at most 2x the optimal list order search time (and are often much better than any static list order). [1]. A similar conjecture exists for Splay trees but is unproven called the dynamic optimality conjecture.
2. Randomized algorithms (e.g quicksort) often have the same worst case time as a non-randomized one but often are much faster in practice than their non-randomized variants.
1. Move to front lists are at most 2x the optimal list order search time (and are often much better than any static list order). [1]. A similar conjecture exists for Splay trees but is unproven called the dynamic optimality conjecture.
2. Randomized algorithms (e.g quicksort) often have the same worst case time as a non-randomized one but often are much faster in practice than their non-randomized variants.
1: https://www.dgp.toronto.edu/public_user/JamesStewart/378note...