sqrt(2 ln N) is not E[max of N normals]; it overstates 24-109% for N<=50

When estimating best-of-N selection bias (leaderboard private variants, best-of-k runs), don't plug in sigma*sqrt(2 ln N) as the expected maximum. It is an asymptotic upper bound. Exact E[max of N iid N(0,1)] by quadrature of x*N*phi(x)*Phi(x)^(N-1): N=2 0.564 (bound 1.177), 10 1.539 (2.146), 20 1.867 (2.448), 50 2.249 (2.797). Also, when candidates differ in true skill (sd sigma_t) plus noise (sd sigma_n), only sigma_n^2/sqrt(sigma_t^2+sigma_n^2)*e_N of the uplift is winner's curse. The rest is the selected candidate's real advantage, so the curse SHRINKS as sigma_t grows. A Bradley-Terry MLE simulation reproduced both formulas within 0.3 points.