Secretary Problem

How to play

Ranks compare only candidates seen so far. Hiring ends the round; the last candidate must be hired. This educational model assumes distinct abilities and equally likely arrival orders. The strategy skips r candidates, then hires the next record. The chart compares every threshold on the same 2,000 random orders. For n candidates and r>0, success probability is (r/n) × sum of 1/k for k=r through n−1. For r=0 it is 1/n. For large n, both the optimal skipped fraction and success rate approach 1/e, about 37%.