certificate A: gamma = 0.666667, bound kappa = 2 sqrt(1+gamma) = 2.5819888975
  n=1: max ratio random (3000 configs) = 1.8979914712; after adversarial search = 1.8979914712  (kappa - max = 6.840e-01) at ['0.500000']
  n=2: max ratio random (3000 configs) = 2.1395660628; after adversarial search = 2.1395664414  (kappa - max = 4.424e-01) at ['0.500000', '0.500000']
  n=3: max ratio random (3000 configs) = 2.2447417702; after adversarial search = 2.2447527484  (kappa - max = 3.372e-01) at ['0.440871', '0.500000', '0.559129']
  n=4: max ratio random (3000 configs) = 2.3374962731; after adversarial search = 2.3380760400  (kappa - max = 2.439e-01) at ['0.313487', '0.500000', '0.500000', '0.686513']
  n=5: max ratio random (3000 configs) = 2.4258575406; after adversarial search = 2.4278448425  (kappa - max = 1.541e-01) at ['0.160632', '0.499999', '0.499999', '0.499999', '0.839365']
  n=6: max ratio random (3000 configs) = 2.4920443949; after adversarial search = 2.4958230624  (kappa - max = 8.617e-02) at ['0.000000', '0.497958', '0.497958', '0.497958', '0.497958', '0.969833']
  n=8: max ratio over 60 configurations (30 clustered at 1/2, 30 uniform) = 2.5056138754  (kappa - max = 7.638e-02)
  n=12: max ratio over 60 configurations (30 clustered at 1/2, 30 uniform) = 2.5503720106  (kappa - max = 3.162e-02)
  n=20: max ratio over 60 configurations (30 clustered at 1/2, 30 uniform) = 2.5709402224  (kappa - max = 1.105e-02)
  n=40: max ratio over 60 configurations (30 clustered at 1/2, 30 uniform) = 2.5752649245  (kappa - max = 6.724e-03)
  certificate A: largest ratio found 2.5752649245 < kappa = 2.5819888975
  n=1 ratios at t = 0, 0.25, 0.5, 0.75, 1: ['1.632993', '1.838181', '1.897991', '1.838181', '1.632993']
certificate B: gamma = 0.500000, bound kappa = 2 sqrt(1+gamma) = 2.4494897428
  n=1: max ratio random (3000 configs) = 2.2513540450; after adversarial search = 2.2513540450  (kappa - max = 1.981e-01) at ['0.500000']
  n=2: max ratio random (3000 configs) = 2.1947348019; after adversarial search = 2.1947544677  (kappa - max = 2.547e-01) at ['0.468059', '0.531941']
  n=3: max ratio random (3000 configs) = 2.2226975927; after adversarial search = 2.2230147912  (kappa - max = 2.265e-01) at ['0.421416', '0.500000', '0.578584']
  n=4: max ratio random (3000 configs) = 2.2734449988; after adversarial search = 2.2738452047  (kappa - max = 1.756e-01) at ['0.355131', '0.500000', '0.500000', '0.644869']
  n=5: max ratio random (3000 configs) = 2.3274750067; after adversarial search = 2.3291125717  (kappa - max = 1.204e-01) at ['0.278660', '0.500000', '0.500000', '0.500000', '0.721340']
  n=6: max ratio random (3000 configs) = 2.3723797262; after adversarial search = 2.3756243873  (kappa - max = 7.387e-02) at ['0.199948', '0.499989', '0.499989', '0.499989', '0.499989', '0.800141']
  n=8: max ratio over 60 configurations (30 clustered at 1/2, 30 uniform) = 2.3542493069  (kappa - max = 9.524e-02)
  n=12: max ratio over 60 configurations (30 clustered at 1/2, 30 uniform) = 2.4037852177  (kappa - max = 4.570e-02)
  n=20: max ratio over 60 configurations (30 clustered at 1/2, 30 uniform) = 2.4349210863  (kappa - max = 1.457e-02)
  n=40: max ratio over 60 configurations (30 clustered at 1/2, 30 uniform) = 2.4450955528  (kappa - max = 4.394e-03)
  certificate B: largest ratio found 2.4450955528 < kappa = 2.4494897428
  n=1 ratios at t = 0, 0.25, 0.5, 0.75, 1: ['1.535932', '2.035401', '2.251354', '2.035401', '1.535932']
done
