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Maven Simulation Analysis

Table of Contents

This is a simulation analysis prepared by pams v.2.007 (poslfit's analyser of Maven simulations), a Perl script that runs on Macintosh, Unix, DOS and other platforms and analyses logs generated by Brian Sheppard's Maven program.

Initial Board Diagram

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   A B C D E F G H I J K L M N O
 1 = . . ' . . . = . . . ' . . =
 2 . - . . . " . . . " . . . - .
 3 . . - . . . ' . ' . . . - . .
 4 ' . . - . . . ' . . . - . . '
 5 . . . . - . . . . . - . . . .
 6 . " . . . " . . . " . . . " .
 7 . . ' . . . ' . ' . . . ' . .
 8 = . . ' . . . - . . . ' . . =
 9 . . ' . . . ' . ' . . . ' . .
10 . " . . . " . . . " . . . " .
11 . . . . - . . . . . - . . . .
12 ' . . - . . . ' . . . - . . '
13 . . - . . . ' . ' . . . - . .
14 . - . . . " . . . " . . . - .
15 = . . ' . . . = . . . ' . . =

Initial Conditions

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Statistics by Play and Turn

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                 -yvqh  viny 8G     -yvq    -yvqn shiny 8H 
  Iterations:    30001    30002    30001    30001    30002 
  MyScore[0]:     0.00    20.00     0.00     0.00    30.00 
 OppScore[1]:    29.56    30.94    29.56    29.56    38.00 
      95% +-      0.24     0.26     0.24     0.24     0.29 
        0lp%:     4.84     1.68     4.84     4.84     0.96 
        1lp%:     0.00     0.00     0.00     0.00     0.00 
        2lp%:     0.17     6.39     0.17     0.17     0.45 
        3lp%:     7.25    11.54     7.25     7.25     7.76 
        4lp%:    16.36    27.49    16.36    16.36    30.12 
        5lp%:    37.85    19.96    37.85    37.85    22.32 
        6lp%:    18.72    12.29    18.72    18.72    13.72 
        7lp%:    14.82    20.66    14.82    14.82    24.67 
  MyScore[1]:    48.84    33.15    47.03    42.57    26.50 
      95% +-      0.31     0.17     0.31     0.30     0.13 
        0lp%:     0.31     4.02     0.09     0.65     6.60 
        1lp%:     0.00     0.07     0.00     0.00     0.02 
        2lp%:     1.29     8.12     1.37     3.02     6.87 
        3lp%:     6.29    20.13    11.34    14.86    22.81 
        4lp%:    16.62    36.71    19.81    23.49    39.35 
        5lp%:    16.63    23.32    16.52    17.48    19.38 
        6lp%:     9.88     6.13    11.17    10.20     4.61 
        7lp%:    48.98     1.50    39.70    30.31     0.35 
 OppScore[2]:    39.45    36.98    39.34    38.91    38.06 
      95% +-      0.26     0.24     0.26     0.26     0.26 
        0lp%:     0.81     0.94     0.94     0.94     0.86 
        1lp%:     0.02     0.12     0.05     0.06     0.09 
        2lp%:     3.75     4.56     3.59     3.44     3.39 
        3lp%:    14.15    16.64    14.49    15.00    15.78 
        4lp%:    25.75    27.57    26.72    26.47    27.89 
        5lp%:    21.39    22.42    21.13    21.35    22.48 
        6lp%:    10.81     9.28    10.25    10.27     9.49 
        7lp%:    23.32    18.48    22.83    22.46    20.03 
  MyScore[2]:    41.14    35.89    41.26    41.25    32.46 
      95% +-      0.26     0.22     0.26     0.26     0.20 
        0lp%:     0.75     3.10     0.65     0.86     3.06 
        1lp%:     0.05     0.21     0.05     0.06     0.19 
        2lp%:     3.74     7.20     4.05     4.36     6.86 
        3lp%:    15.27    20.60    15.83    15.73    22.73 
        4lp%:    26.59    32.28    26.20    26.31    34.08 
        5lp%:    21.08    21.73    20.77    20.64    20.68 
        6lp%:     8.81     6.58     9.18     8.81     6.08 
        7lp%:    23.72     8.30    23.27    23.23     6.33 
  ResidualEq:    -0.16    -0.74     0.06     0.27    -1.81 
      95% +-      0.12     0.15     0.12     0.12     0.15 
   NetEquity:    20.82    20.38    19.44    15.62    11.09 
      95% +-      0.49     0.43     0.48     0.48     0.45 

Legend:

Iterations
number of analysed simulation runs (involving this choice)
MyScore[n]
average number of points you score on your nth turn
OppScore[n]
average number of points opponent scores on his/her nth turn
95% +-
95% confidence margin for preceding figure
0lp%, etc.
percentage of runs where 0, 1, 2, ..., 7 tiles get played
ResidualEq
equity unaccounted for by raw scores (final rack leave, etc.)
NetEquity
equity as reported by Maven

Total Expected Square Value Diagrams

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The following tables show for each square the average number of points that plays whose main word covers that square contributes to the final score. Positive values indicate hotspots in our favour, negative values show hotspots in opponent's favour. Values are colour-coded: red (below -10), orange (below -5), light blue (above +5), blue (above +10).

Total Expected Square Values when MyTurn[0]='-yvqh':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1   0.1  0.1  0.1  0.4  0.3  0.3  0.3  2.4  0.4  0.3  0.3  0.4  0.3  0.3  0.4
 2   0.1  0.2  0.3  0.6  0.5  0.5  0.4  2.4  1.4  1.5  1.1  0.5  1.0  0.4  0.3
 3   0.1  0.2  0.5  0.8  0.8  0.6  0.6  2.7  2.0  1.7  1.4  0.5  1.5  0.4  0.4
 4   0.3  0.2  0.5  1.1  2.1  0.7  0.5  2.6  1.8  1.9  2.3  0.6  1.4  0.5  0.6
 5   0.2  0.2  0.5  1.5  5.1  0.9  0.8  2.9  2.3  2.5  4.8  0.9  1.6  0.5  0.6
 6   0.2  0.2  0.4  1.8  5.3  1.3  1.0  2.8  2.7  3.2  5.1  0.9  1.6  0.4  0.7
 7   0.3  0.4  1.0  2.7  6.8  2.9  3.0  4.7  4.9  4.9  6.6  1.8  2.4  0.7  0.8
 8   0.4 -1.4 -2.8-13.7-10.7-17.6-22.0-22.5-14.3 -7.9 -0.4 -5.1  0.4 -0.0  1.0
 9   0.3  0.7  1.5  3.8  7.5  3.6  3.8  5.6  4.7  4.5  6.0  1.8  1.9  0.8  0.6
10   0.2  0.4  0.5  2.6  5.7  1.7  1.5  3.5  2.3  2.6  4.5  0.9  1.0  0.5  0.5
11   0.2  0.4  0.6  2.6  5.5  1.4  1.3  3.2  1.9  2.0  4.1  0.8  1.0  0.4  0.4
12   0.3  0.4  0.5  2.2  3.1  1.0  0.9  3.0  1.3  1.3  2.0  0.6  0.8  0.3  0.4
13   0.2  0.5  0.6  1.7  1.1  1.0  1.0  3.1  1.3  1.0  0.9  0.5  0.9  0.3  0.3
14   0.2  0.5  0.4  1.0  0.8  0.7  0.6  2.7  0.9  0.9  0.7  0.4  0.5  0.4  0.2
15   0.3  0.3  0.3  0.8  0.3  0.3  0.4  2.7  0.4  0.3  0.2  0.3  0.2  0.1  0.2

Total Expected Square Values when MyTurn[0]='viny 8G':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1   0.1  0.1  0.1  0.1  0.1  0.2  0.3  1.0  0.2  0.0  0.4  0.7  0.5  0.5  0.7
 2   0.0  0.1  0.1  0.1  0.1  0.3  0.0  0.6 -1.0  0.2  0.4  0.8  0.9  1.1  0.5
 3   0.0  0.0  0.0  0.1  0.0  0.1 -0.4 -0.3 -1.6 -0.3 -0.1  0.9  0.8  0.6  0.6
 4   0.1  0.1  0.1  0.2  0.2  0.2 -0.4  0.2 -1.2 -0.3 -0.5  3.1  0.5  0.7  1.2
 5  -0.0 -0.0  0.0 -0.0  0.1  0.2 -0.6 -1.2 -2.1 -1.6 -4.4  1.7 -0.1  0.3  1.1
 6   0.0  0.0  0.0  0.0  0.0  0.8 -0.5 -0.8 -1.9 -1.4 -4.5  2.6  0.5  0.8  1.1
 7   0.0  0.0  0.1  0.1  0.1  0.1 -2.0 -4.4 -7.6 -8.6-10.5 -0.5 -2.0 -0.6  1.3
 8   0.1  0.1  0.1  0.2  0.1  0.0 -2.4 -3.5 -5.0 -5.8-10.1  3.6  1.0  1.5  2.9
 9   0.0  0.0  0.1  0.1  0.1  0.1 -2.4 -4.6 -6.0 -4.0 -9.1  0.7 -0.6 -0.0  0.9
10   0.0  0.1  0.1  0.1  0.2  1.0 -1.0 -2.1 -1.7  0.1 -5.3  1.9  0.4  0.6  0.6
11   0.0  0.1  0.1  0.2  0.7  0.8 -0.7 -0.9 -1.2  0.8 -3.9  1.7  0.3  0.5  0.4
12   0.1  0.1  0.1  0.3  0.2  0.2 -1.3 -0.2 -0.9  1.0 -0.6  2.6  0.3  0.5  0.4
13   0.0  0.1  0.2  0.1  0.1  0.1 -1.1 -0.6 -1.1  0.5 -0.5  0.7  0.6  0.4  0.2
14   0.0  0.2  0.2  0.3  0.2  0.5 -0.2 -0.1 -0.4  0.6  0.1  0.6  0.5  0.7  0.3
15   0.1  0.1  0.1  0.5  0.6  0.8  0.9  1.0  0.8  0.7  0.6  0.6  0.4  0.3  0.4

Total Expected Square Values when MyTurn[0]='-yvq':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1   0.2  0.1  0.1  0.5  0.2  0.2  0.3  1.9  0.3  0.3  0.2  0.3  0.3  0.3  0.4
 2   0.1  0.2  0.3  0.6  0.4  0.6  0.5  2.1  1.0  1.3  1.0  0.3  0.9  0.5  0.3
 3   0.1  0.2  0.5  0.8  0.7  0.6  0.8  2.4  2.0  1.6  1.5  0.4  1.5  0.5  0.4
 4   0.2  0.2  0.5  1.3  1.6  0.7  0.9  2.3  2.0  1.7  2.1  0.6  1.4  0.4  0.6
 5   0.2  0.2  0.5  1.4  3.5  0.9  1.0  2.8  2.4  2.2  3.6  0.9  1.7  0.6  0.7
 6   0.2  0.1  0.4  1.6  3.7  1.2  1.1  2.7  2.7  3.0  3.7  0.9  1.5  0.6  0.7
 7   0.2  0.3  0.9  2.4  5.3  2.9  4.2  5.5  5.8  5.3  5.6  2.1  2.6  0.8  0.8
 8   0.4 -1.6 -2.7-13.9-12.2-17.7-21.8-23.3-14.3 -8.4 -1.6 -5.1  0.3 -0.1  1.1
 9   0.3  0.5  1.6  3.4  6.1  3.4  4.2  5.5  5.6  4.7  5.1  2.0  2.2  0.8  0.6
10   0.2  0.3  0.6  2.3  4.3  1.4  1.5  2.6  1.9  2.0  2.7  0.8  1.0  0.4  0.5
11   0.2  0.5  0.8  2.6  4.3  1.5  1.6  2.8  1.9  1.8  2.8  0.9  1.0  0.4  0.4
12   0.3  0.4  0.7  2.1  2.4  1.2  1.1  2.5  1.4  1.4  1.6  0.7  0.9  0.3  0.4
13   0.2  0.4  0.7  1.5  1.1  1.0  1.1  2.4  1.2  1.0  0.9  0.5  0.8  0.3  0.2
14   0.2  0.5  0.4  1.0  0.9  0.8  0.7  2.2  0.9  0.9  0.7  0.3  0.6  0.3  0.2
15   0.3  0.2  0.2  0.7  0.3  0.3  0.4  1.9  0.3  0.3  0.2  0.3  0.2  0.2  0.2

Total Expected Square Values when MyTurn[0]='-yvqn':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1   0.1  0.1  0.1  0.3  0.2  0.2  0.2  1.7  0.4  0.4  0.2  0.4  0.3  0.3  0.4
 2   0.1  0.2  0.2  0.3  0.4  0.5  0.4  1.7  0.9  1.2  0.7  0.3  0.8  0.4  0.3
 3   0.1  0.2  0.5  0.6  0.6  0.7  0.7  2.0  1.8  1.5  1.2  0.4  1.5  0.4  0.4
 4   0.2  0.2  0.4  1.0  1.3  0.7  0.6  1.7  1.5  1.5  1.8  0.4  1.2  0.4  0.6
 5   0.2  0.3  0.4  1.2  2.7  1.0  0.8  1.9  2.0  2.0  3.3  0.8  1.5  0.5  0.7
 6   0.2  0.2  0.3  1.2  2.9  1.4  0.8  1.7  2.2  2.8  3.4  0.7  1.3  0.4  0.8
 7   0.2  0.4  0.9  2.0  4.4  3.0  4.1  4.9  5.6  5.3  5.2  1.8  2.3  0.7  0.9
 8   0.3 -1.6 -3.0-14.6-13.3-17.8-22.4-24.8-15.1 -8.7 -2.0 -5.3  0.0 -0.2  1.0
 9   0.3  0.6  1.3  2.9  4.6  3.1  3.6  4.1  4.7  4.1  4.8  1.8  2.0  0.7  0.7
10   0.3  0.4  0.6  2.0  3.2  1.4  1.3  1.9  1.5  1.7  2.6  0.8  0.8  0.3  0.4
11   0.3  0.5  0.8  2.2  3.5  1.5  1.5  2.3  1.7  1.6  2.9  1.1  0.9  0.4  0.4
12   0.4  0.4  0.7  1.9  1.8  1.0  1.0  1.9  1.2  1.1  1.4  0.8  0.8  0.3  0.3
13   0.3  0.4  0.8  1.3  1.0  0.9  1.0  2.0  1.0  0.7  0.7  0.5  0.8  0.3  0.2
14   0.3  0.5  0.5  0.8  0.6  0.6  0.5  1.7  0.6  0.5  0.5  0.3  0.4  0.3  0.2
15   0.3  0.2  0.3  0.7  0.3  0.4  0.4  1.7  0.4  0.3  0.3  0.3  0.2  0.2  0.2

Total Expected Square Values when MyTurn[0]='shiny 8H':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1   0.0 -0.0  0.0  0.1  0.1  0.1  0.1 -8.3 -0.0 -0.0 -0.3 -0.0  0.2  0.2  0.2
 2   0.0  0.0  0.0  0.2  0.1  0.4  0.4 -8.3  0.2  1.1 -0.1  0.4  1.3  0.8  0.2
 3   0.0  0.0  0.1  0.2  0.1  0.1  0.2 -8.6  0.4  0.3 -0.6 -1.2  1.6  0.3  0.1
 4   0.1  0.1  0.2  0.4  0.2  0.2  0.2 -8.3  0.2  0.2 -3.4 -3.4  1.1  0.3  0.0
 5   0.0  0.0  0.1  0.3  0.1 -0.0 -0.1 -9.0  0.0 -0.4 -7.3 -3.6  1.3  0.5 -0.0
 6   0.1  0.2  0.2  0.4  0.5  1.4  0.9 -8.6  0.2  2.3 -8.3 -4.2  0.8  0.6  0.0
 7   0.0 -0.1 -0.7 -0.9 -0.9 -1.1 -2.4-12.2 -4.2 -2.4-12.0 -7.2 -0.6 -0.0  0.1
 8   0.5  0.5  0.5  0.6  0.5  0.5  0.0-12.2 -1.0 -0.0-10.7 -6.7   .   0.1  0.1
 9   0.0 -0.0 -0.1 -0.3 -0.5 -0.5 -1.2 -5.3 -2.7 -1.4-11.0 -2.2 -0.1  0.1  0.0
10   0.0  0.2  0.2  0.1  0.1  0.6  0.4 -3.2 -0.8 -1.1 -8.4 -1.1  0.3  0.2 -0.0
11   0.0  0.1  0.2  0.2  0.0 -0.0 -0.0 -3.4 -0.8 -0.8 -8.2 -1.1  0.3  0.2 -0.0
12   0.1  0.2  0.2  0.3  0.2  0.1  0.1 -2.4 -0.1 -0.3 -2.6 -0.4  0.3  0.2 -0.0
13  -0.0  0.0  0.1  0.1  0.0  0.0  0.1 -2.7 -0.3 -0.3 -0.9 -0.1  0.4  0.2 -0.0
14  -0.0  0.0  0.0  0.1  0.0  0.2  0.2 -2.2 -0.2 -0.1 -0.3  0.2  0.3  0.4  0.0
15   0.1  0.1  0.1  0.1  0.1  0.2  0.2 -2.1  0.0  0.1  0.0  0.1  0.1  0.1  0.1

Equity Distribution

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The tabulated value is the percentage of runs in which the difference in scores has been changed by an amount less than or equal to the value in the first column. Best value is shown in dark blue, second best in light blue.

                 -yvqh  viny 8G     -yvq    -yvqn shiny 8H 
        -227:     0.00     0.00     0.00     0.00     0.00 
        -226:     0.00     0.00     0.00     0.00     0.00 
        -225:     0.00     0.00     0.00     0.00     0.00 
        -224:     0.00     0.00     0.00     0.00     0.00 
        -223:     0.00     0.00     0.00     0.00     0.00 
        -222:     0.00     0.00     0.00     0.00     0.00 
        -221:     0.00     0.00     0.00     0.00     0.00 
        -220:     0.00     0.00     0.00     0.00     0.00 
        -219:     0.00     0.00     0.00     0.00     0.00 
        -218:     0.00     0.00     0.00     0.00     0.00 
        -217:     0.00     0.00     0.00     0.00     0.00 
        -216:     0.00     0.00     0.00     0.00     0.00 
        -215:     0.00     0.00     0.00     0.00     0.00 
        -214:     0.00     0.00     0.00     0.00     0.00 
        -213:     0.00     0.00     0.00     0.00     0.00 
        -212:     0.00     0.00     0.00     0.00     0.00 
        -211:     0.00     0.00     0.00     0.00     0.00 
        -210:     0.00     0.00     0.00     0.00     0.00 
        -209:     0.00     0.00     0.00     0.00     0.00 
        -208:     0.00     0.00     0.00     0.00     0.00 
        -207:     0.00     0.00     0.00     0.00     0.00 
        -206:     0.00     0.00     0.00     0.00     0.00 
        -205:     0.00     0.00     0.00     0.00     0.00 
        -204:     0.00     0.00     0.00     0.00     0.00 
        -203:     0.00     0.00     0.00     0.00     0.00 
        -202:     0.00     0.00     0.00     0.00     0.00 
        -201:     0.00     0.00     0.00     0.00     0.00 
        -200:     0.00     0.00     0.00     0.00     0.00 
        -199:     0.00     0.00     0.00     0.00     0.00 
        -198:     0.00     0.00     0.00     0.00     0.00 
        -197:     0.00     0.00     0.00     0.00     0.00 
        -196:     0.00     0.00     0.00     0.00     0.00 
        -195:     0.00     0.00     0.00     0.00     0.00 
        -194:     0.00     0.00     0.00     0.00     0.00 
        -193:     0.00     0.00     0.00     0.00     0.00 
        -192:     0.00     0.00     0.00     0.00     0.00 
        -191:     0.00     0.00     0.00     0.00     0.00 
        -190:     0.00     0.00     0.00     0.00     0.00 
        -189:     0.00     0.00     0.00     0.00     0.00 
        -188:     0.00     0.00     0.00     0.00     0.00 
        -187:     0.00     0.00     0.00     0.00     0.00 
        -186:     0.00     0.00     0.00     0.00     0.00 
        -185:     0.00     0.00     0.00     0.00     0.00 
        -184:     0.00     0.00     0.00     0.00     0.00 
        -183:     0.00     0.00     0.00     0.00     0.00 
        -182:     0.00     0.00     0.00     0.00     0.00 
        -181:     0.00     0.00     0.00     0.00     0.00 
        -180:     0.00     0.00     0.00     0.00     0.00 
        -179:     0.00     0.00     0.00     0.00     0.00 
        -178:     0.00     0.00     0.00     0.00     0.00 
        -177:     0.00     0.00     0.00     0.00     0.00 
        -176:     0.00     0.00     0.00     0.00     0.00 
        -175:     0.00     0.00     0.00     0.00     0.00 
        -174:     0.00     0.00     0.00     0.00     0.00 
        -173:     0.00     0.00     0.00     0.00     0.00 
        -172:     0.00     0.00     0.00     0.00     0.00 
        -171:     0.00     0.00     0.00     0.00     0.00 
        -170:     0.00     0.00     0.00     0.00     0.00 
        -169:     0.00     0.00     0.00     0.00     0.00 
        -168:     0.00     0.00     0.00     0.00     0.00 
        -167:     0.00     0.00     0.00     0.00     0.00 
        -166:     0.00     0.00     0.00     0.00     0.00 
        -165:     0.00     0.00     0.00     0.00     0.00 
        -164:     0.00     0.00     0.00     0.00     0.00 
        -163:     0.00     0.00     0.00     0.00     0.00 
        -162:     0.00     0.00     0.00     0.00     0.00 
        -161:     0.00     0.00     0.00     0.00     0.00 
        -160:     0.00     0.00     0.00     0.00     0.00 
        -159:     0.00     0.00     0.00     0.00     0.00 
        -158:     0.00     0.00     0.00     0.00     0.00 
        -157:     0.00     0.00     0.00     0.00     0.00 
        -156:     0.00     0.00     0.00     0.00     0.00 
        -155:     0.00     0.00     0.00     0.00     0.00 
        -154:     0.00     0.00     0.00     0.00     0.01 
        -153:     0.00     0.00     0.00     0.00     0.01 
        -152:     0.00     0.00     0.00     0.00     0.01 
        -151:     0.00     0.00     0.00     0.00     0.01 
        -150:     0.00     0.00     0.00     0.00     0.01 
        -149:     0.00     0.00     0.00     0.00     0.01 
        -148:     0.00     0.00     0.00     0.00     0.01 
        -147:     0.00     0.00     0.00     0.00     0.01 
        -146:     0.00     0.00     0.00     0.00     0.01 
        -145:     0.00     0.00     0.00     0.00     0.01 
        -144:     0.00     0.00     0.00     0.00     0.01 
        -143:     0.00     0.00     0.01     0.00     0.02 
        -142:     0.00     0.00     0.01     0.00     0.02 
        -141:     0.00     0.00     0.01     0.00     0.02 
        -140:     0.00     0.00     0.01     0.00     0.02 
        -139:     0.01     0.00     0.01     0.01     0.03 
        -138:     0.01     0.01     0.01     0.01     0.03 
        -137:     0.01     0.01     0.01     0.01     0.03 
        -136:     0.01     0.01     0.01     0.01     0.03 
        -135:     0.01     0.01     0.01     0.01     0.03 
        -134:     0.01     0.01     0.02     0.01     0.03 
        -133:     0.02     0.01     0.02     0.01     0.04 
        -132:     0.02     0.01     0.02     0.02     0.04 
        -131:     0.02     0.02     0.02     0.02     0.04 
        -130:     0.02     0.02     0.02     0.03     0.05 
        -129:     0.03     0.02     0.03     0.03     0.06 
        -128:     0.03     0.02     0.03     0.03     0.06 
        -127:     0.04     0.02     0.04     0.03     0.06 
        -126:     0.05     0.02     0.04     0.03     0.06 
        -125:     0.05     0.02     0.04     0.03     0.06 
        -124:     0.05     0.02     0.04     0.04     0.07 
        -123:     0.05     0.02     0.05     0.04     0.07 
        -122:     0.06     0.02     0.05     0.04     0.07 
        -121:     0.08     0.03     0.05     0.06     0.07 
        -120:     0.08     0.03     0.05     0.06     0.07 
        -119:     0.09     0.03     0.06     0.07     0.08 
        -118:     0.09     0.04     0.06     0.07     0.09 
        -117:     0.10     0.04     0.06     0.07     0.09 
        -116:     0.11     0.05     0.06     0.08     0.09 
        -115:     0.12     0.05     0.07     0.10     0.11 
        -114:     0.12     0.05     0.08     0.11     0.14 
        -113:     0.14     0.05     0.08     0.12     0.15 
        -112:     0.16     0.05     0.08     0.13     0.16 
        -111:     0.18     0.06     0.10     0.14     0.17 
        -110:     0.18     0.06     0.10     0.15     0.18 
        -109:     0.20     0.06     0.13     0.16     0.21 
        -108:     0.21     0.07     0.13     0.17     0.23 
        -107:     0.22     0.08     0.15     0.21     0.25 
        -106:     0.24     0.08     0.17     0.23     0.28 
        -105:     0.25     0.08     0.19     0.25     0.30 
        -104:     0.27     0.09     0.21     0.27     0.33 
        -103:     0.28     0.10     0.24     0.29     0.38 
        -102:     0.29     0.11     0.24     0.31     0.43 
        -101:     0.31     0.12     0.26     0.35     0.46 
        -100:     0.34     0.13     0.28     0.37     0.49 
         -99:     0.38     0.14     0.31     0.39     0.53 
         -98:     0.41     0.15     0.34     0.42     0.58 
         -97:     0.41     0.16     0.35     0.45     0.62 
         -96:     0.44     0.17     0.39     0.47     0.68 
         -95:     0.48     0.17     0.42     0.50     0.71 
         -94:     0.49     0.19     0.44     0.54     0.76 
         -93:     0.52     0.21     0.48     0.58     0.80 
         -92:     0.53     0.23     0.51     0.60     0.85 
         -91:     0.55     0.24     0.54     0.63     0.90 
         -90:     0.57     0.26     0.56     0.68     0.95 
         -89:     0.60     0.28     0.60     0.72     1.03 
         -88:     0.64     0.30     0.64     0.75     1.10 
         -87:     0.69     0.33     0.70     0.80     1.17 
         -86:     0.72     0.36     0.74     0.84     1.27 
         -85:     0.77     0.38     0.78     0.87     1.35 
         -84:     0.83     0.41     0.82     0.93     1.42 
         -83:     0.88     0.46     0.88     1.01     1.50 
         -82:     0.94     0.52     0.92     1.07     1.59 
         -81:     0.98     0.57     0.97     1.13     1.67 
         -80:     1.05     0.62     1.01     1.20     1.79 
         -79:     1.09     0.65     1.09     1.28     1.88 
         -78:     1.16     0.70     1.14     1.35     1.96 
         -77:     1.22     0.77     1.22     1.44     2.07 
         -76:     1.27     0.82     1.33     1.52     2.21 
         -75:     1.35     0.89     1.41     1.62     2.32 
         -74:     1.44     0.94     1.49     1.69     2.43 
         -73:     1.52     1.00     1.59     1.77     2.53 
         -72:     1.63     1.06     1.66     1.88     2.62 
         -71:     1.75     1.17     1.74     2.01     2.74 
         -70:     1.84     1.26     1.80     2.10     2.87 
         -69:     1.95     1.34     1.90     2.21     2.98 
         -68:     2.08     1.38     1.99     2.32     3.17 
         -67:     2.18     1.48     2.08     2.47     3.33 
         -66:     2.30     1.59     2.22     2.61     3.49 
         -65:     2.43     1.66     2.34     2.75     3.64 
         -64:     2.57     1.72     2.50     2.91     3.86 
         -63:     2.72     1.81     2.65     3.07     4.01 
         -62:     2.89     1.93     2.76     3.22     4.21 
         -61:     3.06     2.03     2.94     3.42     4.39 
         -60:     3.21     2.17     3.12     3.59     4.59 
         -59:     3.38     2.28     3.31     3.81     4.77 
         -58:     3.53     2.43     3.50     3.99     4.98 
         -57:     3.70     2.55     3.73     4.22     5.20 
         -56:     3.91     2.70     3.93     4.46     5.49 
         -55:     4.12     2.84     4.15     4.76     5.70 
         -54:     4.33     2.99     4.35     5.01     5.96 
         -53:     4.56     3.18     4.57     5.29     6.20 
         -52:     4.77     3.33     4.79     5.53     6.47 
         -51:     5.03     3.51     5.03     5.87     6.71 
         -50:     5.28     3.66     5.27     6.16     7.00 
         -49:     5.55     3.87     5.59     6.45     7.26 
         -48:     5.80     4.05     5.84     6.75     7.55 
         -47:     6.11     4.21     6.07     7.12     7.85 
         -46:     6.36     4.47     6.36     7.43     8.13 
         -45:     6.62     4.73     6.63     7.82     8.51 
         -44:     6.92     4.95     6.94     8.23     8.89 
         -43:     7.27     5.23     7.30     8.62     9.21 
         -42:     7.59     5.51     7.66     9.03     9.61 
         -41:     7.90     5.75     8.02     9.38     9.96 
         -40:     8.25     6.02     8.43     9.77    10.34 
         -39:     8.57     6.27     8.81    10.15    10.74 
         -38:     8.88     6.58     9.21    10.71    11.24 
         -37:     9.20     6.91     9.62    11.12    11.73 
         -36:     9.70     7.25    10.07    11.50    12.18 
         -35:    10.10     7.61    10.50    11.97    12.56 
         -34:    10.51     7.93    10.86    12.39    13.12 
         -33:    10.88     8.25    11.23    12.82    13.70 
         -32:    11.27     8.58    11.70    13.34    14.29 
         -31:    11.69     8.91    12.18    13.87    14.83 
         -30:    12.08     9.33    12.69    14.39    15.38 
         -29:    12.50     9.76    13.09    14.91    15.99 
         -28:    12.90    10.19    13.55    15.35    16.63 
         -27:    13.32    10.67    13.93    15.85    17.26 
         -26:    13.79    11.19    14.40    16.42    17.85 
         -25:    14.22    11.65    14.93    16.95    18.52 
         -24:    14.69    12.13    15.49    17.45    19.11 
         -23:    15.16    12.69    16.03    17.92    19.72 
         -22:    15.73    13.27    16.55    18.49    20.33 
         -21:    16.33    13.84    17.06    19.03    20.94 
         -20:    16.94    14.36    17.58    19.72    21.58 
         -19:    17.54    14.89    18.17    20.34    22.25 
         -18:    18.12    15.42    18.65    20.93    22.98 
         -17:    18.66    16.01    19.23    21.62    23.68 
         -16:    19.27    16.64    19.83    22.23    24.43 
         -15:    19.92    17.25    20.47    22.89    25.17 
         -14:    20.58    17.86    21.02    23.57    25.94 
         -13:    21.17    18.44    21.62    24.20    26.64 
         -12:    21.87    19.04    22.35    24.91    27.32 
         -11:    22.53    19.76    23.09    25.57    28.05 
         -10:    23.21    20.45    23.75    26.34    28.77 
          -9:    24.00    21.18    24.56    27.14    29.43 
          -8:    24.68    21.80    25.19    28.00    30.05 
          -7:    25.36    22.54    25.96    28.76    30.88 
          -6:    26.09    23.29    26.73    29.57    31.60 
          -5:    26.88    24.14    27.52    30.43    32.38 
          -4:    27.71    24.86    28.38    31.36    33.15 
          -3:    28.56    25.61    29.21    32.25    33.95 
          -2:    29.40    26.36    30.04    33.22    34.67 
          -1:    30.28    27.14    30.77    34.19    35.51 
           0:    32.05    28.81    32.66    36.16    37.17 
           1:    32.95    29.69    33.65    37.27    37.95 
           2:    33.97    30.45    34.77    38.25    38.79 
           3:    34.82    31.36    35.70    39.24    39.55 
           4:    35.92    32.24    36.62    40.26    40.35 
           5:    36.90    33.14    37.63    41.34    41.23 
           6:    37.77    33.92    38.52    42.38    42.20 
           7:    38.74    34.80    39.61    43.57    43.03 
           8:    39.63    35.79    40.62    44.50    43.88 
           9:    40.49    36.79    41.77    45.38    44.81 
          10:    41.43    37.79    42.83    46.52    45.75 
          11:    42.37    38.87    43.84    47.46    46.76 
          12:    43.26    39.93    44.93    48.54    47.85 
          13:    44.13    41.02    45.92    49.52    48.83 
          14:    45.06    41.98    46.93    50.53    49.78 
          15:    46.10    42.99    47.85    51.65    50.81 
          16:    47.04    44.06    48.81    52.59    51.88 
          17:    47.96    45.24    49.78    53.58    52.92 
          18:    48.83    46.40    50.79    54.57    53.98 
          19:    49.74    47.49    51.82    55.36    55.11 
          20:    50.57    48.66    52.64    56.21    56.29 
          21:    51.47    49.73    53.63    57.04    57.41 
          22:    52.36    50.84    54.59    57.93    58.53 
          23:    53.14    51.93    55.47    58.86    59.73 
          24:    53.92    53.03    56.35    59.81    60.91 
          25:    54.66    54.17    57.13    60.67    61.92 
          26:    55.52    55.35    58.01    61.52    63.05 
          27:    56.33    56.56    58.84    62.35    64.09 
          28:    57.08    57.66    59.73    63.16    65.21 
          29:    57.87    58.95    60.50    63.92    66.29 
          30:    58.60    60.03    61.27    64.66    67.43 
          31:    59.34    61.24    62.05    65.52    68.54 
          32:    60.16    62.40    62.83    66.36    69.59 
          33:    60.88    63.52    63.57    67.14    70.78 
          34:    61.63    64.67    64.32    67.79    71.80 
          35:    62.51    65.83    65.06    68.60    72.83 
          36:    63.35    66.81    65.74    69.31    73.89 
          37:    64.10    67.83    66.45    70.07    74.90 
          38:    64.93    68.91    67.17    70.80    75.83 
          39:    65.75    70.07    67.92    71.51    76.77 
          40:    66.67    71.14    68.66    72.22    77.69 
          41:    67.47    72.14    69.43    72.95    78.64 
          42:    68.29    73.06    70.19    73.62    79.66 
          43:    69.13    74.03    70.90    74.28    80.53 
          44:    69.88    74.96    71.67    74.96    81.43 
          45:    70.69    75.94    72.45    75.67    82.18 
          46:    71.56    76.85    73.24    76.42    83.00 
          47:    72.34    77.64    73.97    77.07    83.82 
          48:    73.09    78.58    74.70    77.83    84.62 
          49:    73.82    79.47    75.53    78.46    85.39 
          50:    74.71    80.30    76.21    79.07    86.10 
          51:    75.42    81.10    76.93    79.73    86.78 
          52:    76.25    81.87    77.61    80.38    87.37 
          53:    76.97    82.74    78.31    81.04    88.09 
          54:    77.75    83.49    79.03    81.70    88.69 
          55:    78.47    84.14    79.69    82.34    89.31 
          56:    79.21    84.77    80.31    82.89    89.86 
          57:    79.87    85.40    80.97    83.63    90.27 
          58:    80.67    86.06    81.71    84.23    90.83 
          59:    81.38    86.62    82.36    84.75    91.31 
          60:    82.03    87.16    82.96    85.28    91.79 
          61:    82.71    87.75    83.58    85.85    92.22 
          62:    83.45    88.33    84.15    86.34    92.61 
          63:    84.06    88.86    84.70    86.82    92.96 
          64:    84.65    89.35    85.31    87.32    93.33 
          65:    85.15    89.81    85.85    87.85    93.65 
          66:    85.73    90.26    86.37    88.36    93.99 
          67:    86.19    90.71    86.88    88.83    94.28 
          68:    86.73    91.15    87.39    89.27    94.58 
          69:    87.25    91.52    87.92    89.76    94.85 
          70:    87.79    91.96    88.36    90.24    95.04 
          71:    88.29    92.36    88.79    90.63    95.31 
          72:    88.73    92.64    89.21    91.00    95.55 
          73:    89.20    93.01    89.67    91.36    95.76 
          74:    89.63    93.36    90.15    91.77    95.96 
          75:    90.05    93.66    90.65    92.08    96.15 
          76:    90.43    93.92    91.00    92.38    96.36 
          77:    90.86    94.23    91.40    92.72    96.54 
          78:    91.21    94.51    91.79    93.07    96.67 
          79:    91.52    94.74    92.10    93.39    96.85 
          80:    91.88    94.97    92.43    93.70    97.02 
          81:    92.24    95.24    92.73    93.96    97.15 
          82:    92.55    95.47    93.03    94.22    97.29 
          83:    92.90    95.66    93.31    94.52    97.41 
          84:    93.17    95.83    93.60    94.77    97.54 
          85:    93.45    95.99    93.91    94.99    97.69 
          86:    93.70    96.15    94.12    95.22    97.81 
          87:    93.97    96.34    94.38    95.45    97.89 
          88:    94.26    96.50    94.66    95.60    98.00 
          89:    94.52    96.66    94.85    95.75    98.07 
          90:    94.77    96.81    95.05    95.93    98.16 
          91:    95.01    96.97    95.30    96.13    98.25 
          92:    95.23    97.13    95.47    96.36    98.34 
          93:    95.46    97.25    95.62    96.54    98.41 
          94:    95.71    97.40    95.81    96.71    98.46 
          95:    95.92    97.52    95.98    96.84    98.53 
          96:    96.15    97.66    96.16    97.01    98.61 
          97:    96.36    97.82    96.33    97.13    98.68 
          98:    96.55    97.92    96.51    97.26    98.76 
          99:    96.72    98.03    96.65    97.35    98.83 
         100:    96.93    98.12    96.86    97.49    98.89 
         101:    97.08    98.20    97.01    97.65    98.95 
         102:    97.26    98.31    97.14    97.77    99.01 
         103:    97.40    98.40    97.29    97.86    99.06 
         104:    97.53    98.50    97.38    98.02    99.12 
         105:    97.65    98.58    97.54    98.11    99.18 
         106:    97.80    98.72    97.67    98.19    99.26 
         107:    97.92    98.77    97.79    98.29    99.31 
         108:    98.04    98.85    97.93    98.38    99.35 
         109:    98.18    98.93    98.05    98.46    99.38 
         110:    98.32    99.00    98.17    98.54    99.43 
         111:    98.44    99.04    98.28    98.62    99.46 
         112:    98.56    99.08    98.37    98.71    99.51 
         113:    98.66    99.14    98.49    98.79    99.54 
         114:    98.77    99.18    98.58    98.88    99.57 
         115:    98.86    99.23    98.65    98.94    99.60 
         116:    98.92    99.29    98.71    98.98    99.63 
         117:    98.99    99.31    98.83    99.03    99.64 
         118:    99.08    99.35    98.91    99.10    99.66 
         119:    99.18    99.40    98.98    99.14    99.70 
         120:    99.25    99.43    99.02    99.18    99.71 
         121:    99.29    99.46    99.10    99.22    99.72 
         122:    99.35    99.50    99.15    99.29    99.74 
         123:    99.42    99.53    99.20    99.33    99.75 
         124:    99.47    99.54    99.25    99.36    99.77 
         125:    99.51    99.57    99.30    99.41    99.78 
         126:    99.54    99.60    99.35    99.45    99.80 
         127:    99.57    99.61    99.41    99.48    99.81 
         128:    99.60    99.63    99.47    99.52    99.82 
         129:    99.63    99.66    99.50    99.57    99.83 
         130:    99.65    99.68    99.54    99.62    99.85 
         131:    99.67    99.68    99.58    99.66    99.87 
         132:    99.69    99.69    99.61    99.69    99.87 
         133:    99.70    99.71    99.64    99.70    99.87 
         134:    99.71    99.72    99.67    99.71    99.88 
         135:    99.74    99.73    99.70    99.73    99.88 
         136:    99.76    99.75    99.73    99.77    99.89 
         137:    99.77    99.76    99.74    99.78    99.90 
         138:    99.80    99.76    99.76    99.80    99.92 
         139:    99.81    99.78    99.78    99.81    99.93 
         140:    99.83    99.79    99.80    99.82    99.93 
         141:    99.84    99.79    99.81    99.84    99.94 
         142:    99.85    99.80    99.82    99.85    99.94 
         143:    99.86    99.81    99.83    99.87    99.95 
         144:    99.87    99.82    99.84    99.88    99.95 
         145:    99.88    99.83    99.85    99.88    99.95 
         146:    99.89    99.85    99.85    99.89    99.95 
         147:    99.89    99.85    99.86    99.90    99.95 
         148:    99.90    99.86    99.88    99.90    99.96 
         149:    99.91    99.86    99.90    99.91    99.96 
         150:    99.92    99.87    99.90    99.91    99.96 
         151:    99.92    99.88    99.92    99.92    99.96 
         152:    99.93    99.88    99.92    99.92    99.97 
         153:    99.93    99.89    99.93    99.93    99.97 
         154:    99.94    99.89    99.93    99.94    99.97 
         155:    99.94    99.90    99.93    99.94    99.97 
         156:    99.94    99.91    99.94    99.94    99.98 
         157:    99.94    99.92    99.94    99.94    99.98 
         158:    99.95    99.92    99.94    99.94    99.98 
         159:    99.95    99.92    99.94    99.94    99.98 
         160:    99.95    99.93    99.94    99.95    99.99 
         161:    99.95    99.93    99.96    99.95    99.99 
         162:    99.96    99.93    99.96    99.96    99.99 
         163:    99.96    99.94    99.96    99.96    99.99 
         164:    99.96    99.94    99.96    99.96    99.99 
         165:    99.96    99.94    99.96    99.97    99.99 
         166:    99.96    99.94    99.96    99.97    99.99 
         167:    99.96    99.94    99.97    99.97    99.99 
         168:    99.96    99.94    99.97    99.97   100.00 
         169:    99.96    99.94    99.97    99.97   100.00 
         170:    99.96    99.95    99.97    99.98   100.00 
         171:    99.97    99.95    99.97    99.98   100.00 
         172:    99.97    99.95    99.97    99.98   100.00 
         173:    99.97    99.95    99.98    99.98   100.00 
         174:    99.97    99.96    99.98    99.98   100.00 
         175:    99.97    99.96    99.98    99.98   100.00 
         176:    99.97    99.96    99.98    99.98   100.00 
         177:    99.98    99.96    99.98    99.98   100.00 
         178:    99.98    99.97    99.99    99.98   100.00 
         179:    99.98    99.97    99.99    99.98   100.00 
         180:    99.98    99.97    99.99    99.98   100.00 
         181:    99.99    99.97    99.99    99.98   100.00 
         182:    99.99    99.97    99.99    99.98   100.00 
         183:    99.99    99.97    99.99    99.98   100.00 
         184:    99.99    99.97    99.99    99.98   100.00 
         185:    99.99    99.97    99.99    99.98   100.00 
         186:    99.99    99.98    99.99    99.98   100.00 
         187:    99.99    99.98    99.99    99.98   100.00 
         188:    99.99    99.98    99.99    99.98   100.00 
         189:   100.00    99.98    99.99    99.98   100.00 
         190:   100.00    99.98    99.99    99.98   100.00 
         191:   100.00    99.98    99.99    99.99   100.00 
         192:   100.00    99.98    99.99    99.99   100.00 
         193:   100.00    99.98    99.99    99.99   100.00 
         194:   100.00    99.98    99.99    99.99   100.00 
         195:   100.00    99.98    99.99    99.99   100.00 
         196:   100.00    99.98    99.99    99.99   100.00 
         197:   100.00    99.99    99.99    99.99   100.00 
         198:   100.00    99.99    99.99    99.99   100.00 
         199:   100.00    99.99    99.99    99.99   100.00 
         200:   100.00    99.99    99.99    99.99   100.00 
         201:   100.00    99.99    99.99    99.99   100.00 
         202:   100.00    99.99    99.99    99.99   100.00 
         203:   100.00    99.99    99.99    99.99   100.00 
         204:   100.00    99.99   100.00    99.99   100.00 
         205:   100.00    99.99   100.00    99.99   100.00 
         206:   100.00    99.99   100.00    99.99   100.00 
         207:   100.00    99.99   100.00    99.99   100.00 
         208:   100.00    99.99   100.00   100.00   100.00 
         209:   100.00    99.99   100.00   100.00   100.00 
         210:   100.00    99.99   100.00   100.00   100.00 
         211:   100.00    99.99   100.00   100.00   100.00 
         212:   100.00    99.99   100.00   100.00   100.00 
         213:   100.00    99.99   100.00   100.00   100.00 
         214:   100.00    99.99   100.00   100.00   100.00 
         215:   100.00    99.99   100.00   100.00   100.00 
         216:   100.00   100.00   100.00   100.00   100.00 
         217:   100.00   100.00   100.00   100.00   100.00 
         218:   100.00   100.00   100.00   100.00   100.00 
         219:   100.00   100.00   100.00   100.00   100.00 
         220:   100.00   100.00   100.00   100.00   100.00 
         221:   100.00   100.00   100.00   100.00   100.00 
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