mean true reward of the best-of-N candidate (standard error in brackets)
      N            gaussian           student-3              cauchy
      1        -0.036 (0.026)         0.024 (0.026)        -0.011 (0.026)
      4         0.751 (0.022)         0.632 (0.024)         0.410 (0.026)
     16         1.237 (0.021)         0.867 (0.026)         0.340 (0.027)
     64         1.621 (0.020)         0.798 (0.027)         0.076 (0.026)
    256         2.008 (0.020)         0.603 (0.027)         0.001 (0.026)
   1024         2.285 (0.020)         0.359 (0.027)        -0.000 (0.026)
   4096         2.556 (0.019)         0.186 (0.026)         0.012 (0.025)
  16384         2.849 (0.019)         0.182 (0.026)         0.038 (0.026)

E[r | s = t]  (r ~ N(0,1), s = r + e)
     t   gaussian (t/2)   student-3    cauchy
     1           0.5000      0.4621    0.4458
     3           1.5000      1.0048    0.7149
    10           5.0000      0.4078    0.2042
    30          15.0000      0.1336    0.0668
   100          50.0000      0.0400    0.0200
   300         150.0000      0.0133    0.0067
