(a) KL of best-of-N against log N - (N-1)/N, Gaussian proxy, 100000 trials, KL = E_BoN[log(N F(r))] ...
    N   formula  simulated
    2    0.1931     0.1955
    4    0.6363     0.6407
   16    1.8351     1.8275
   64    3.1745     3.1707

(b) Gaussian proxy noise s = 1: E[gold of the selected response]
    N   formula  simulated
    1    0.0000     0.0083
    4    0.7279     0.7308
   16    1.2487     1.2450
   64    1.6573     1.6653
  256    1.9989     2.0055
    (the formula uses E[max P] = sqrt(1+s^2) m_N since P ~ N(0, 1+s^2))

(c) rare exploitable class: q = 0.01, hack gold -h = -1
    N   formula  simulated
    1   -0.0100    -0.0062
    4    0.9494     0.9503
   16    1.3551     1.3590
   64    0.7575     0.7340
  256   -0.7080    -0.7068
 1024   -0.9999    -1.0000
