The 1/e Law of Best Choice

In the classic secretary problem with n candidates (relative ranks only, irrevocable choices), the look-then-leap rule observes the first r candidates without choosing and then accepts the first later candidate who beats all seen so far. For large n, write r = t*n and derive the limiting win probability as a function of the skip fraction t in (0,1). Then find the t that maximizes it and the resulting optimal asymptotic probability of selecting the single best candidate.