true edge +1.0pts over break-even | pool 20 | 300,000 slates per row | seed 12345

growth = mean log wealth change per slate, x 1e-4

  err           full        half     quarter full+3% cap   best
  0.0         115.34       87.26       50.91       88.51   full Kelly, uncapped
  0.5         109.58       86.57       51.08       85.36   full Kelly, uncapped
  1.0          87.25       81.15       49.68       78.84   full Kelly, uncapped
  1.1          84.43       81.25       50.09       75.88   full Kelly, uncapped
  1.2          75.39       78.88       49.38       75.08   half Kelly, uncapped
  1.3          64.23       75.27       48.00       71.18   half Kelly, uncapped
  1.4          61.46       75.92       48.78       71.06   half Kelly, uncapped
  1.5          49.72       72.21       47.39       67.38   half Kelly, uncapped
  2.0           5.62       64.24       46.35       60.64   half Kelly, uncapped
  2.1          -3.07       63.39       46.70       59.55   half Kelly, uncapped
  2.2         -14.96       61.16       46.32       57.95   half Kelly, uncapped
  2.3         -29.35       59.02       46.03       56.70   half Kelly, uncapped
  2.4         -31.55       60.55       47.51       58.86   half Kelly, uncapped
  2.5         -52.47       55.79       45.95       56.58   full Kelly + 3% per-bet cap
  3.0        -146.01       42.33       43.71       51.48   full Kelly + 3% per-bet cap

selection effect on the bets actually taken
  err   taken   believed   true    overstatement
  0.0    14.9       1.64    1.64      1.00x
  0.5    14.7       1.70    1.63      1.04x
  1.0    14.2       1.87    1.60      1.17x
  1.1    14.1       1.91    1.59      1.20x
  1.2    14.0       1.96    1.58      1.24x
  1.3    13.9       2.01    1.58      1.27x
  1.4    13.7       2.06    1.57      1.31x
  1.5    13.6       2.11    1.55      1.36x
  2.0    13.1       2.40    1.51      1.60x
  2.1    13.0       2.47    1.50      1.65x
  2.2    12.9       2.53    1.49      1.71x
  2.3    12.8       2.60    1.48      1.76x
  2.4    12.8       2.66    1.47      1.81x
  2.5    12.7       2.73    1.46      1.87x
  3.0    12.3       3.07    1.42      2.17x

half Kelly minus full Kelly, paired on the same slates (x 1e-4, 95% CI)
  err    gap        95% CI               significant
  0.0    -28.09   [  -30.88,   -25.29]   yes, full ahead
  0.5    -23.01   [  -25.91,   -20.10]   yes, full ahead
  1.0     -6.10   [   -9.28,    -2.92]   yes, full ahead
  1.1     -3.18   [   -6.43,     0.06]   no
  1.2      3.49   [    0.14,     6.83]   yes, half ahead
  1.3     11.04   [    7.60,    14.47]   yes, half ahead
  1.4     14.46   [   10.93,    17.98]   yes, half ahead
  1.5     22.49   [   18.88,    26.11]   yes, half ahead
  2.0     58.62   [   54.24,    62.99]   yes, half ahead
  2.1     66.45   [   62.12,    70.79]   yes, half ahead
  2.2     76.12   [   71.65,    80.59]   yes, half ahead
  2.3     88.37   [   83.07,    93.67]   yes, half ahead
  2.4     92.09   [   87.17,    97.02]   yes, half ahead
  2.5    108.27   [  102.53,   114.00]   yes, half ahead
  3.0    188.34   [  178.85,   197.83]   yes, half ahead

full Kelly stops being the best rule at 1.2pts of error
half Kelly is ahead of full Kelly beyond noise from 1.2pts of error
full Kelly turns negative at 2.1pts of error

wrote estimate-error-sweep.json