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Maven Simulation Analysis

Table of Contents

This is a simulation analysis prepared by pams v.2.004 (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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              quite 8D quate 8D quiet 8D 
  Iterations:    25005    25004    25004 
  MyScore[0]:    48.00    48.00    48.00 
 OppScore[1]:    34.00    41.42    36.97 
      95% +-      0.29     0.30     0.28 
        0lp%:     1.58     0.85     1.16 
        1lp%:     0.00     0.00     0.00 
        2lp%:     0.66     1.26     2.69 
        3lp%:    11.19    18.33    14.05 
        4lp%:    31.37    26.95    29.98 
        5lp%:    21.24    17.70    19.17 
        6lp%:    11.35    11.95    10.12 
        7lp%:    22.61    22.98    22.84 
  MyScore[1]:    38.81    45.58    39.97 
      95% +-      0.27     0.28     0.27 
        0lp%:     0.19     0.36     0.22 
        1lp%:     0.00     0.00     0.01 
        2lp%:     1.14    11.66     1.85 
        3lp%:     9.89    12.94    14.30 
        4lp%:    28.33    18.40    25.18 
        5lp%:    25.47    19.57    24.33 
        6lp%:    12.74    12.79    13.17 
        7lp%:    22.24    24.28    20.93 
 OppScore[2]:    40.62    42.85    40.50 
      95% +-      0.28     0.28     0.28 
        0lp%:     0.55     0.61     0.72 
        1lp%:     0.03     0.03     0.06 
        2lp%:     2.92     6.95     3.26 
        3lp%:    16.82    16.12    15.41 
        4lp%:    29.00    24.75    27.33 
        5lp%:    21.34    19.78    22.43 
        6lp%:     9.19    10.31    10.55 
        7lp%:    20.14    21.45    20.25 
  MyScore[2]:    40.26    42.13    40.45 
      95% +-      0.27     0.28     0.26 
        0lp%:     0.35     0.81     0.48 
        1lp%:     0.03     0.03     0.08 
        2lp%:     3.21     7.75     3.22 
        3lp%:    16.81    15.70    16.97 
        4lp%:    28.78    25.53    28.21 
        5lp%:    22.25    20.21    22.64 
        6lp%:     9.04    10.28     9.77 
        7lp%:    19.53    19.69    18.64 
  ResidualEq:    -0.76    -1.05    -0.86 
      95% +-      0.14     0.14     0.14 
   NetEquity:    51.69    50.39    50.09 
      95% +-      0.53     0.55     0.52 

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

Square Hit Probabilities

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Square Values are the average number of points scored by plays whose main word covers a particular square. Large values are shaded orange to red.

Square Hit Probabilities for OppTurn[1] when MyTurn[0]='quite 8D':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1    =    .    .    '   0.0  0.0  0.2  2.5   .    .    .    '    .    .    = 
 2    .    -    .    .   0.4  0.3  0.9  3.1   .    "    .    .    .    -    . 
 3    .    .    -   0.0  1.2  1.5  2.0  3.7   '    .    .    .    -    .    . 
 4    '    .    .   0.7  3.9  3.0  2.8  5.7   .    .    .    -    .    .    ' 
 5    .    .    .   1.0  8.6  5.2  4.1  6.1   .    .    -    .    .    .    . 
 6    .    "    .   1.5 10.7 12.1  6.0  6.3   .    "    .    .    .    "    . 
 7    .    .    '   2.5 18.1 27.3 23.2 28.9 20.3 15.1  9.8  5.7  3.8  1.8   . 
 8   2.0  2.1  2.1 13.9 22.0 17.5  9.1  9.7  0.1  0.0   .    '    .    .    = 
 9    .    .    '  11.3 19.0 22.1 16.9 16.4 11.6  7.6  4.6  2.7  1.9  1.1   . 
10    .    "    .  11.3 16.1 12.6  4.3  2.2   .    "    .    .    .    "    . 
11    .    .    .  10.7 14.9  4.7  3.1  1.8   .    .    -    .    .    .    . 
12    '    .    .   9.9  8.2  2.2  2.0  1.5   .    .    .    -    .    .    ' 
13    .    .    -   2.7  4.0  1.2  1.5  1.2   '    .    .    .    -    .    . 
14    .    -    .   0.8  1.5  0.6  0.4  1.0   .    "    .    .    .    -    . 
15    =    .    .   0.1  0.2  0.1  0.2  0.7   .    .    .    '    .    .    = 

Square Hit Probabilities for OppTurn[1] when MyTurn[0]='quate 8D':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1    =    .    .    '   0.0  0.1  0.2  1.5   .    .    .    '    .    .    = 
 2    .    -   1.4   .   0.2  0.5  0.7  2.0   .    "    .    .    .    -    . 
 3    .    .   8.9  0.0  0.5  1.0  1.3  2.4   '    .    .    .    -    .    . 
 4    '    .  12.4  0.6  1.6  1.6  1.9  3.4   .    .    .    -    .    .    ' 
 5    .    .  17.9  0.7  4.1  2.7  2.4  3.7   .    .    -    .    .    .    . 
 6    .    "  23.6  1.0  4.9  6.6  3.4  3.8   .    "    .    .    .    "    . 
 7    .    .  39.6  1.6  7.9 13.6  9.5 11.2  6.1  3.5  1.9  1.0  0.6  0.3   . 
 8   8.4  8.4 50.2 16.4 17.0 17.7 12.3 13.2  0.5  0.2  0.1  0.1  0.1  0.0  0.0
 9    .    .  31.6  7.5  9.4 14.3 10.8 10.5  6.6  3.1  1.6  0.9  0.5  0.2   . 
10    .    "  15.5  7.5  7.2  6.5  2.6  1.7   .    "    .    .    .    "    . 
11    .    .   9.2  7.3  6.8  3.0  2.1  1.3   .    .    -    .    .    .    . 
12    '    .   5.9  6.9  3.4  1.9  1.5  1.1   .    .    .    -    .    .    ' 
13    .    .   4.6  2.0  1.7  1.1  1.1  0.8   '    .    .    .    -    .    . 
14    .    -   0.5  0.6  0.8  0.7  0.3  0.7   .    "    .    .    .    -    . 
15    =    .    .   0.1  0.1  0.1  0.2  0.4   .    .    .    '    .    .    = 

Square Hit Probabilities for OppTurn[1] when MyTurn[0]='quiet 8D':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1    =    .    .    '   0.0  0.0  0.2  1.7   .    .    .    '    .    .    = 
 2    .    -    .    .   0.2  0.2  1.1  2.2  1.9   "    .    .    .    -    . 
 3    .    .    -   0.0  0.6  1.2  2.0  2.6  3.6   .    .    .    -    .    . 
 4    '    .    .   0.7  2.2  2.2  2.6  3.4  4.6   .    .    -    .    .    ' 
 5    .    .    .   0.9  5.7  3.5  3.4  3.9  6.2   .    -    .    .    .    . 
 6    .    "    .   1.3  7.0  7.1  4.0  4.6  6.9   "    .    .    .    "    . 
 7    .    .    '   2.1 11.8 16.7 33.0 32.4 33.3 17.8  8.8  3.8  2.3  0.5   . 
 8   1.2  1.3  1.3 11.7 13.4 10.6  7.8  8.0  9.1  0.2  0.1  0.1  0.0   .    = 
 9    .    .    '   9.7 11.6  9.9 21.4 21.4 19.1 11.0  5.5  2.4  1.3  0.2   . 
10    .    "    .   9.7 10.4  7.5  3.0  3.9  2.8   "    .    .    .    "    . 
11    .    .    .   9.3  9.8  3.0  2.0  3.4  2.3   .    -    .    .    .    . 
12    '    .    .   8.9  5.2  1.5  1.4  2.8  1.7   .    .    -    .    .    ' 
13    .    .    -   2.7  2.4  0.9  1.1  2.3  1.3   .    .    .    -    .    . 
14    .    -    .   0.8  1.0  0.5  0.7  1.7  0.8   "    .    .    .    -    . 
15    =    .    .   0.1  0.2  0.1  0.1  1.6   .    .    .    '    .    .    = 

Square Values

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Square Hit Probabilities are the percentage of runs in which the main word played covers a particular square. Large values are shaded orange to red.

Square Values for OppTurn[1] when MyTurn[0]='quite 8D':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1    =    .    .    '   0.0  0.0  0.1  2.1   .    .    .    '    .    .    = 
 2    .    -    .    .   0.2  0.2  0.5  2.5   .    "    .    .    .    -    . 
 3    .    .    -   0.0  0.5  1.0  1.0  2.7   '    .    .    .    -    .    . 
 4    '    .    .   0.3  1.7  1.5  1.3  3.2   .    .    .    -    .    .    ' 
 5    .    .    .   0.4  3.8  2.1  1.7  3.3   .    .    -    .    .    .    . 
 6    .    "    .   0.6  4.5  4.0  2.4  3.4   .    "    .    .    .    "    . 
 7    .    .    '   0.9  6.7  8.0  7.0  9.8  5.8  4.8  3.8  3.1  2.1  1.2   . 
 8   1.3  1.3  1.3  5.1  8.4  6.3  4.0  5.6  0.0  0.0   .    '    .    .    = 
 9    .    .    '   3.6  7.0  6.7  5.3  5.6  3.5  2.6  2.0  1.6  1.2  0.8   . 
10    .    "    .   3.6  6.2  4.2  1.9  1.4   .    "    .    .    .    "    . 
11    .    .    .   3.5  5.8  1.9  1.5  1.2   .    .    -    .    .    .    . 
12    '    .    .   3.3  3.4  1.1  1.1  1.0   .    .    .    -    .    .    ' 
13    .    .    -   1.1  1.7  0.7  0.8  0.9   '    .    .    .    -    .    . 
14    .    -    .   0.4  0.9  0.4  0.2  0.8   .    "    .    .    .    -    . 
15    =    .    .   0.1  0.1  0.0  0.1  0.6   .    .    .    '    .    .    = 

Square Values for OppTurn[1] when MyTurn[0]='quate 8D':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1    =    .    .    '   0.0  0.0  0.1  1.3   .    .    .    '    .    .    = 
 2    .    -   1.3   .   0.1  0.3  0.4  1.6   .    "    .    .    .    -    . 
 3    .    .   5.9  0.0  0.3  0.5  0.8  1.8   '    .    .    .    -    .    . 
 4    '    .   7.2  0.2  0.9  0.8  1.1  2.1   .    .    .    -    .    .    ' 
 5    .    .   9.0  0.3  2.1  1.2  1.3  2.2   .    .    -    .    .    .    . 
 6    .    "  10.7  0.4  2.4  2.4  1.8  2.3   .    "    .    .    .    "    . 
 7    .    .  17.6  0.7  3.5  4.2  3.3  4.2  1.6  1.0  0.7  0.5  0.3  0.2   . 
 8   4.5  4.5 23.1  7.2  8.2  7.8  6.6  7.4  0.3  0.1  0.1  0.1  0.1  0.1  0.1
 9    .    .  14.6  2.5  3.9  4.5  3.8  3.6  1.8  1.1  0.7  0.6  0.3  0.2   . 
10    .    "   7.5  2.5  3.3  2.4  1.5  1.1   .    "    .    .    .    "    . 
11    .    .   5.3  2.5  3.1  1.5  1.2  0.9   .    .    -    .    .    .    . 
12    '    .   4.2  2.4  1.8  1.1  0.9  0.8   .    .    .    -    .    .    ' 
13    .    .   3.7  0.8  0.9  0.7  0.7  0.6   '    .    .    .    -    .    . 
14    .    -   0.4  0.3  0.6  0.4  0.2  0.5   .    "    .    .    .    -    . 
15    =    .    .   0.1  0.1  0.1  0.1  0.3   .    .    .    '    .    .    = 

Square Values for OppTurn[1] when MyTurn[0]='quiet 8D':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1    =    .    .    '   0.0  0.0  0.2  1.5   .    .    .    '    .    .    = 
 2    .    -    .    .   0.2  0.2  0.7  1.8  1.5   "    .    .    .    -    . 
 3    .    .    -   0.0  0.3  0.8  1.0  2.0  2.3   .    .    .    -    .    . 
 4    '    .    .   0.3  1.3  1.2  1.2  2.4  2.6   .    .    -    .    .    ' 
 5    .    .    .   0.4  3.1  1.6  1.5  2.6  3.2   .    -    .    .    .    . 
 6    .    "    .   0.5  3.5  2.7  1.7  3.0  3.5   "    .    .    .    "    . 
 7    .    .    '   0.9  5.0  5.4 10.0 11.0 11.2  5.5  3.3  2.1  1.6  0.4   . 
 8   0.7  0.7  0.7  4.1  5.8  4.2  3.2  5.1  4.5  0.1  0.0  0.0  0.0   .    = 
 9    .    .    '   3.2  5.0  3.7  7.0  7.9  6.5  3.3  1.9  1.2  0.9  0.1   . 
10    .    "    .   3.2  4.7  2.9  1.4  2.6  1.5   "    .    .    .    "    . 
11    .    .    .   3.1  4.4  1.5  1.0  2.4  1.3   .    -    .    .    .    . 
12    '    .    .   3.0  2.5  0.9  0.8  2.0  1.0   .    .    -    .    .    ' 
13    .    .    -   1.1  1.1  0.6  0.6  1.8  0.8   .    .    .    -    .    . 
14    .    -    .   0.4  0.7  0.3  0.4  1.4  0.6   "    .    .    .    -    . 
15    =    .    .   0.1  0.1  0.0  0.0  1.4   .    .    .    '    .    .    = 

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]='quite 8D':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1   0.2  0.2  0.3  0.5  0.3  0.2  0.2 -0.0  0.2  0.2  0.2  0.4  0.3  0.2  0.4
 2   0.1  0.2  0.3  0.5  0.2  0.3 -0.0 -0.1  0.3  0.5  0.4  0.5  0.4  0.4  0.3
 3   0.2  0.2  0.6  0.6  0.2 -0.2 -0.1 -0.1  0.4  0.6  0.5  0.7  0.4  0.3  0.3
 4   0.4  0.4  0.8  1.0 -0.3  0.1  0.1  0.1  0.8  1.1  0.9  1.1  0.6  0.5  0.4
 5   0.3  0.2  0.5  0.6 -1.5  0.2  0.3  0.2  1.3  1.6  1.7  0.9  0.3  0.3  0.3
 6   0.4  0.6  0.9  0.5 -2.4 -1.5  0.2  0.7  2.1  2.8  2.4  1.7  1.0  0.7  0.3
 7   0.3  0.3  0.4 -0.6 -5.6 -6.4 -5.2 -5.3 -3.4 -1.8 -0.9 -0.6 -0.2  0.2  0.3
 8  -1.0 -1.2 -1.2 -3.4 -7.3 -5.4 -3.4 -3.3  0.1  1.5  2.2  2.3  2.0  1.9  2.1
 9   0.4  0.3  0.3 -1.9 -5.7 -5.0 -3.5 -2.8 -1.9 -0.6 -0.1 -0.2 -0.2 -0.1  0.3
10   0.4  0.6  1.1 -0.7 -3.4 -2.1 -0.3  0.4  1.3  1.8  1.6  1.1  0.7  0.5  0.3
11   0.4  0.5  1.0 -0.0 -2.4  0.2  0.1  0.9  1.2  1.4  1.5  0.7  0.4  0.3  0.2
12   0.7  0.8  1.4  0.4 -0.7  0.6  0.1  0.8  0.7  0.8  0.7  0.6  0.4  0.3  0.2
13   0.4  0.8  1.5  1.7  0.5  0.7  0.3  0.6  0.6  0.6  0.4  0.5  0.4  0.2  0.2
14   0.3  0.5  0.6  1.0  0.2  0.3  0.0  0.3  0.3  0.4  0.4  0.4  0.4  0.3  0.2
15   0.4  0.3  0.3  0.8  0.4  0.4  0.4  0.7  0.4  0.4  0.3  0.4  0.2  0.2  0.2

Total Expected Square Values when MyTurn[0]='quate 8D':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1   0.7  0.2  0.3  0.7  0.4  0.3  0.3  0.4  0.3  0.2  0.2  0.2  0.1  0.1  0.2
 2   0.5  0.4 -0.6  0.5  0.2  0.3 -0.0  0.5  1.3  0.2  0.2  0.2  0.2  0.2  0.1
 3   0.6  0.4 -2.5  0.5  0.2  0.1 -0.0  0.5  2.2  0.3  0.3  0.3  0.3  0.2  0.1
 4   0.8  0.5 -3.2  0.7 -0.0  0.2 -0.0  0.6  2.7  0.3  0.4  0.3  0.2  0.2  0.2
 5   0.7  0.3 -4.7  0.2 -0.8 -0.2 -0.3  0.5  4.1  0.4  0.7  0.4  0.1  0.1  0.1
 6   0.6  0.5 -6.3  0.1 -1.1 -1.3 -0.5  0.5  5.7  0.7  0.9  0.5  0.3  0.2  0.2
 7   0.7  0.1-12.5 -0.5 -2.5 -3.1 -2.1 -1.2  4.6 -0.2  0.3  0.0  0.0  0.1  0.2
 8   6.3  5.6 -7.7  3.7  2.9  3.1  4.3  5.2  8.1  0.4  0.7  0.5  0.4  0.3  0.4
 9   0.7  0.3-10.4 -1.6 -2.7 -3.3 -2.4 -1.3  3.6 -0.3  0.2 -0.0  0.1  0.1  0.2
10   0.6  0.7 -5.4 -1.1 -1.4 -0.9 -0.3  0.4  4.2  0.7  0.9  0.4  0.2  0.1  0.1
11   0.6  0.7 -3.4 -0.8 -1.0  0.1  0.1  0.8  3.4  0.7  1.0  0.4  0.2  0.1  0.1
12   0.8  0.7 -2.4 -0.8 -0.3 -0.0 -0.1  0.4  1.9  0.4  0.4  0.3  0.2  0.1  0.1
13   0.7  0.9 -1.7  0.7  0.4  0.4  0.4  0.6  1.6  0.3  0.2  0.2  0.2  0.1  0.1
14   0.6  0.6  0.1  0.4  0.1  0.2  0.1  0.3  1.0  0.2  0.1  0.1  0.1  0.1  0.1
15   0.8  0.5  0.4  0.6  0.5  0.5  0.4  0.6  0.3  0.2  0.2  0.1  0.1  0.0  0.1

Total Expected Square Values when MyTurn[0]='quiet 8D':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1   0.2  0.1  0.2  0.3  0.2  0.2  0.1 -0.1  0.3  0.3  0.3  0.5  0.3  0.3  0.3
 2   0.1  0.2  0.3  0.4  0.3  0.3  0.1 -0.3 -0.6  0.6  0.4  0.6  0.5  0.4  0.3
 3   0.1  0.2  0.4  0.4  0.2 -0.2 -0.1 -0.3 -1.3  0.8  0.6  0.7  0.6  0.3  0.3
 4   0.4  0.4  0.6  0.8  0.1  0.0  0.3 -0.1 -1.1  1.4  1.1  1.2  0.8  0.5  0.5
 5   0.2  0.2  0.4  0.4 -1.0 -0.1  0.3 -0.6 -1.7  1.5  1.4  0.7  0.4  0.2  0.3
 6   0.3  0.6  0.8  0.6 -0.9 -0.1  1.3  0.7 -0.2  3.6  2.8  1.8  1.2  0.8  0.4
 7   0.2  0.1  0.2 -0.5 -3.2 -4.2 -7.6 -8.8 -9.1 -3.1 -1.2 -0.8 -0.4 -0.0  0.3
 8   2.5  2.4  2.3  0.6 -1.0 -0.4  0.9 -0.9 -3.3  2.0  2.9  2.6  2.6  2.3  2.6
 9   0.1  0.1  0.1 -1.7 -3.2 -2.7 -4.6 -5.5 -4.8 -1.1 -0.0 -0.2 -0.0  0.1  0.3
10   0.2  0.4  0.7 -1.0 -2.0 -1.1 -0.1 -0.4 -0.0  2.3  1.9  1.0  0.7  0.4  0.3
11   0.2  0.4  0.8 -0.5 -1.2  0.5  0.6 -0.3 -0.2  1.5  1.5  0.5  0.3  0.1  0.2
12   0.4  0.5  1.0 -0.4 -0.4  0.6  0.4 -0.0 -0.1  1.2  1.1  0.8  0.6  0.3  0.3
13   0.3  0.7  1.4  1.3  1.0  1.0  0.6 -0.0 -0.1  0.7  0.5  0.5  0.4  0.2  0.2
14   0.2  0.4  0.6  0.6  0.4  0.4  0.1 -0.2 -0.3  0.5  0.3  0.3  0.3  0.2  0.2
15   0.3  0.2  0.3  0.4  0.3  0.2  0.2 -0.1  0.3  0.3  0.2  0.3  0.2  0.1  0.2

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.

              quite 8D quate 8D quiet 8D 
        -211:     0.00     0.00     0.00 
        -210:     0.00     0.00     0.00 
        -209:     0.00     0.00     0.00 
        -208:     0.00     0.00     0.00 
        -207:     0.00     0.00     0.00 
        -206:     0.00     0.00     0.00 
        -205:     0.00     0.00     0.00 
        -204:     0.00     0.00     0.00 
        -203:     0.00     0.00     0.00 
        -202:     0.00     0.00     0.00 
        -201:     0.00     0.00     0.00 
        -200:     0.00     0.00     0.00 
        -199:     0.00     0.00     0.00 
        -198:     0.00     0.00     0.00 
        -197:     0.00     0.00     0.00 
        -196:     0.00     0.00     0.00 
        -195:     0.00     0.00     0.00 
        -194:     0.00     0.00     0.00 
        -193:     0.00     0.00     0.00 
        -192:     0.00     0.00     0.00 
        -191:     0.00     0.00     0.00 
        -190:     0.00     0.00     0.00 
        -189:     0.00     0.00     0.00 
        -188:     0.00     0.00     0.00 
        -187:     0.00     0.00     0.00 
        -186:     0.00     0.00     0.00 
        -185:     0.00     0.00     0.00 
        -184:     0.00     0.00     0.00 
        -183:     0.00     0.00     0.00 
        -182:     0.00     0.00     0.00 
        -181:     0.00     0.00     0.00 
        -180:     0.00     0.00     0.00 
        -179:     0.00     0.00     0.00 
        -178:     0.00     0.00     0.00 
        -177:     0.00     0.00     0.00 
        -176:     0.00     0.00     0.00 
        -175:     0.00     0.00     0.00 
        -174:     0.00     0.00     0.00 
        -173:     0.00     0.00     0.00 
        -172:     0.00     0.00     0.00 
        -171:     0.00     0.00     0.00 
        -170:     0.00     0.00     0.00 
        -169:     0.00     0.00     0.00 
        -168:     0.00     0.00     0.00 
        -167:     0.00     0.00     0.00 
        -166:     0.00     0.00     0.00 
        -165:     0.00     0.00     0.00 
        -164:     0.00     0.00     0.00 
        -163:     0.00     0.00     0.00 
        -162:     0.00     0.00     0.01 
        -161:     0.00     0.00     0.01 
        -160:     0.00     0.00     0.01 
        -159:     0.00     0.00     0.01 
        -158:     0.00     0.00     0.01 
        -157:     0.00     0.00     0.01 
        -156:     0.00     0.00     0.01 
        -155:     0.00     0.00     0.01 
        -154:     0.00     0.00     0.01 
        -153:     0.00     0.00     0.01 
        -152:     0.00     0.00     0.01 
        -151:     0.00     0.00     0.01 
        -150:     0.00     0.00     0.01 
        -149:     0.00     0.00     0.01 
        -148:     0.00     0.00     0.01 
        -147:     0.00     0.00     0.01 
        -146:     0.00     0.00     0.01 
        -145:     0.00     0.00     0.01 
        -144:     0.00     0.00     0.01 
        -143:     0.00     0.00     0.01 
        -142:     0.00     0.00     0.01 
        -141:     0.00     0.00     0.01 
        -140:     0.00     0.00     0.01 
        -139:     0.00     0.00     0.01 
        -138:     0.00     0.00     0.01 
        -137:     0.00     0.00     0.01 
        -136:     0.00     0.00     0.01 
        -135:     0.00     0.00     0.01 
        -134:     0.00     0.00     0.01 
        -133:     0.00     0.00     0.01 
        -132:     0.00     0.00     0.01 
        -131:     0.00     0.00     0.01 
        -130:     0.00     0.00     0.01 
        -129:     0.00     0.00     0.01 
        -128:     0.00     0.00     0.01 
        -127:     0.00     0.00     0.01 
        -126:     0.00     0.00     0.01 
        -125:     0.00     0.00     0.01 
        -124:     0.00     0.00     0.01 
        -123:     0.00     0.00     0.01 
        -122:     0.00     0.00     0.01 
        -121:     0.00     0.00     0.01 
        -120:     0.00     0.00     0.01 
        -119:     0.00     0.00     0.01 
        -118:     0.01     0.00     0.01 
        -117:     0.01     0.00     0.01 
        -116:     0.01     0.00     0.01 
        -115:     0.01     0.00     0.01 
        -114:     0.01     0.01     0.01 
        -113:     0.01     0.02     0.01 
        -112:     0.01     0.02     0.02 
        -111:     0.01     0.02     0.02 
        -110:     0.01     0.02     0.02 
        -109:     0.01     0.02     0.02 
        -108:     0.01     0.02     0.02 
        -107:     0.01     0.02     0.02 
        -106:     0.01     0.02     0.02 
        -105:     0.02     0.02     0.02 
        -104:     0.02     0.03     0.02 
        -103:     0.02     0.04     0.02 
        -102:     0.02     0.04     0.02 
        -101:     0.02     0.04     0.03 
        -100:     0.02     0.04     0.03 
         -99:     0.03     0.04     0.03 
         -98:     0.03     0.04     0.04 
         -97:     0.03     0.05     0.04 
         -96:     0.03     0.05     0.04 
         -95:     0.03     0.06     0.05 
         -94:     0.04     0.06     0.05 
         -93:     0.04     0.06     0.05 
         -92:     0.06     0.06     0.05 
         -91:     0.06     0.07     0.05 
         -90:     0.06     0.08     0.06 
         -89:     0.06     0.10     0.06 
         -88:     0.07     0.11     0.06 
         -87:     0.07     0.12     0.07 
         -86:     0.08     0.12     0.08 
         -85:     0.09     0.13     0.09 
         -84:     0.10     0.14     0.10 
         -83:     0.11     0.15     0.11 
         -82:     0.12     0.17     0.11 
         -81:     0.12     0.17     0.12 
         -80:     0.12     0.19     0.12 
         -79:     0.13     0.20     0.15 
         -78:     0.16     0.21     0.16 
         -77:     0.16     0.23     0.16 
         -76:     0.18     0.24     0.17 
         -75:     0.19     0.27     0.20 
         -74:     0.19     0.28     0.22 
         -73:     0.21     0.30     0.23 
         -72:     0.22     0.32     0.25 
         -71:     0.23     0.35     0.26 
         -70:     0.24     0.37     0.28 
         -69:     0.27     0.38     0.30 
         -68:     0.29     0.41     0.31 
         -67:     0.30     0.43     0.32 
         -66:     0.32     0.47     0.34 
         -65:     0.36     0.52     0.35 
         -64:     0.38     0.57     0.41 
         -63:     0.42     0.63     0.43 
         -62:     0.45     0.66     0.48 
         -61:     0.48     0.71     0.52 
         -60:     0.50     0.73     0.54 
         -59:     0.55     0.78     0.56 
         -58:     0.59     0.82     0.60 
         -57:     0.64     0.86     0.66 
         -56:     0.70     0.91     0.69 
         -55:     0.74     0.97     0.72 
         -54:     0.77     1.04     0.76 
         -53:     0.83     1.10     0.78 
         -52:     0.88     1.18     0.83 
         -51:     0.95     1.26     0.88 
         -50:     1.03     1.34     0.94 
         -49:     1.08     1.42     1.00 
         -48:     1.15     1.50     1.04 
         -47:     1.21     1.58     1.13 
         -46:     1.28     1.70     1.22 
         -45:     1.35     1.80     1.27 
         -44:     1.42     1.90     1.36 
         -43:     1.50     2.00     1.44 
         -42:     1.58     2.11     1.53 
         -41:     1.66     2.24     1.62 
         -40:     1.80     2.36     1.71 
         -39:     1.88     2.47     1.81 
         -38:     1.97     2.58     1.94 
         -37:     2.09     2.70     2.02 
         -36:     2.22     2.81     2.12 
         -35:     2.34     2.95     2.24 
         -34:     2.46     3.08     2.34 
         -33:     2.60     3.20     2.45 
         -32:     2.73     3.38     2.56 
         -31:     2.86     3.53     2.64 
         -30:     3.07     3.70     2.81 
         -29:     3.20     3.85     2.90 
         -28:     3.35     4.04     3.05 
         -27:     3.48     4.23     3.22 
         -26:     3.61     4.39     3.36 
         -25:     3.76     4.56     3.56 
         -24:     3.88     4.77     3.72 
         -23:     4.09     4.98     3.95 
         -22:     4.29     5.18     4.18 
         -21:     4.46     5.44     4.38 
         -20:     4.70     5.69     4.64 
         -19:     4.88     5.96     4.92 
         -18:     5.10     6.15     5.21 
         -17:     5.36     6.48     5.42 
         -16:     5.63     6.73     5.70 
         -15:     5.89     7.01     5.96 
         -14:     6.15     7.32     6.25 
         -13:     6.45     7.66     6.55 
         -12:     6.73     7.91     6.93 
         -11:     7.09     8.19     7.26 
         -10:     7.41     8.49     7.64 
          -9:     7.73     8.78     7.97 
          -8:     8.05     9.09     8.34 
          -7:     8.46     9.42     8.69 
          -6:     8.90     9.80     9.15 
          -5:     9.32    10.20     9.54 
          -4:     9.69    10.59     9.98 
          -3:    10.15    11.01    10.40 
          -2:    10.52    11.47    10.77 
          -1:    10.94    11.85    11.24 
           0:    11.36    12.28    11.68 
           1:    11.79    12.83    12.07 
           2:    12.28    13.31    12.60 
           3:    12.82    13.86    13.09 
           4:    13.27    14.30    13.61 
           5:    13.74    14.77    14.12 
           6:    14.26    15.33    14.62 
           7:    14.83    15.93    15.12 
           8:    15.42    16.52    15.64 
           9:    15.96    17.05    16.25 
          10:    16.54    17.61    16.78 
          11:    17.01    18.23    17.31 
          12:    17.60    18.77    17.89 
          13:    18.18    19.30    18.45 
          14:    18.79    19.94    19.01 
          15:    19.34    20.63    19.66 
          16:    20.00    21.26    20.28 
          17:    20.60    22.02    20.88 
          18:    21.36    22.68    21.46 
          19:    21.98    23.39    22.06 
          20:    22.64    24.12    22.72 
          21:    23.24    24.83    23.40 
          22:    23.92    25.66    24.06 
          23:    24.47    26.41    24.73 
          24:    25.10    27.12    25.45 
          25:    25.79    27.98    26.12 
          26:    26.43    28.69    26.90 
          27:    27.08    29.53    27.52 
          28:    27.76    30.35    28.19 
          29:    28.40    31.11    28.94 
          30:    29.09    31.88    29.74 
          31:    29.80    32.69    30.58 
          32:    30.50    33.46    31.38 
          33:    31.23    34.27    32.21 
          34:    32.03    35.10    33.01 
          35:    32.82    35.96    33.89 
          36:    33.71    36.78    34.74 
          37:    34.59    37.59    35.71 
          38:    35.49    38.43    36.68 
          39:    36.36    39.26    37.65 
          40:    37.35    40.07    38.69 
          41:    38.29    40.92    39.75 
          42:    39.29    41.65    40.84 
          43:    40.34    42.47    42.02 
          44:    41.34    43.33    43.19 
          45:    42.44    44.13    44.29 
          46:    43.41    45.00    45.36 
          47:    44.53    45.86    46.42 
          48:    45.58    46.70    47.64 
          49:    46.85    47.59    48.76 
          50:    48.01    48.54    49.80 
          51:    49.13    49.46    50.80 
          52:    50.25    50.40    51.88 
          53:    51.31    51.26    53.07 
          54:    52.39    52.08    54.18 
          55:    53.38    52.90    55.23 
          56:    54.41    53.78    56.19 
          57:    55.44    54.73    57.17 
          58:    56.46    55.64    58.27 
          59:    57.55    56.53    59.19 
          60:    58.66    57.43    60.18 
          61:    59.58    58.25    61.19 
          62:    60.56    59.19    62.13 
          63:    61.52    60.09    63.04 
          64:    62.57    60.90    64.00 
          65:    63.65    61.69    64.93 
          66:    64.58    62.63    65.85 
          67:    65.53    63.56    66.69 
          68:    66.33    64.47    67.48 
          69:    67.19    65.44    68.35 
          70:    68.01    66.29    69.11 
          71:    68.88    67.20    69.87 
          72:    69.65    67.96    70.68 
          73:    70.42    68.84    71.49 
          74:    71.15    69.69    72.24 
          75:    71.87    70.42    72.99 
          76:    72.61    71.20    73.72 
          77:    73.40    72.03    74.49 
          78:    74.07    72.91    75.19 
          79:    74.71    73.73    75.90 
          80:    75.36    74.45    76.60 
          81:    76.02    75.18    77.24 
          82:    76.56    75.99    77.88 
          83:    77.14    76.70    78.52 
          84:    77.73    77.38    79.09 
          85:    78.33    78.08    79.72 
          86:    78.94    78.73    80.31 
          87:    79.46    79.38    80.87 
          88:    80.06    80.03    81.45 
          89:    80.67    80.64    82.03 
          90:    81.34    81.29    82.61 
          91:    81.89    81.97    83.15 
          92:    82.38    82.50    83.68 
          93:    82.88    83.21    84.35 
          94:    83.41    83.85    84.90 
          95:    83.97    84.40    85.45 
          96:    84.58    84.93    86.01 
          97:    85.08    85.42    86.60 
          98:    85.59    85.92    87.09 
          99:    86.07    86.45    87.60 
         100:    86.58    86.98    88.08 
         101:    87.06    87.46    88.48 
         102:    87.54    87.91    88.94 
         103:    88.04    88.31    89.38 
         104:    88.51    88.71    89.86 
         105:    88.91    89.08    90.33 
         106:    89.42    89.45    90.73 
         107:    89.91    89.87    91.13 
         108:    90.36    90.25    91.53 
         109:    90.74    90.60    91.92 
         110:    91.13    90.99    92.25 
         111:    91.47    91.34    92.57 
         112:    91.95    91.67    92.83 
         113:    92.29    91.99    93.13 
         114:    92.64    92.35    93.50 
         115:    92.99    92.71    93.84 
         116:    93.28    92.99    94.17 
         117:    93.57    93.27    94.42 
         118:    93.93    93.55    94.68 
         119:    94.22    93.80    94.92 
         120:    94.47    94.02    95.17 
         121:    94.73    94.30    95.39 
         122:    95.01    94.58    95.60 
         123:    95.18    94.82    95.77 
         124:    95.39    95.04    95.97 
         125:    95.58    95.28    96.17 
         126:    95.84    95.48    96.34 
         127:    96.02    95.72    96.51 
         128:    96.20    95.93    96.68 
         129:    96.38    96.11    96.81 
         130:    96.52    96.29    96.99 
         131:    96.64    96.46    97.14 
         132:    96.81    96.61    97.32 
         133:    96.92    96.77    97.40 
         134:    97.07    96.91    97.54 
         135:    97.16    97.09    97.67 
         136:    97.29    97.24    97.81 
         137:    97.39    97.44    97.94 
         138:    97.50    97.56    98.04 
         139:    97.61    97.71    98.14 
         140:    97.70    97.84    98.24 
         141:    97.80    97.99    98.31 
         142:    97.88    98.09    98.42 
         143:    97.98    98.21    98.49 
         144:    98.08    98.33    98.56 
         145:    98.17    98.41    98.66 
         146:    98.28    98.47    98.75 
         147:    98.35    98.55    98.80 
         148:    98.45    98.64    98.89 
         149:    98.55    98.71    98.98 
         150:    98.66    98.79    99.04 
         151:    98.75    98.86    99.08 
         152:    98.83    98.92    99.14 
         153:    98.90    98.97    99.19 
         154:    98.98    99.03    99.25 
         155:    99.05    99.10    99.29 
         156:    99.10    99.17    99.34 
         157:    99.18    99.22    99.38 
         158:    99.22    99.30    99.42 
         159:    99.24    99.34    99.45 
         160:    99.27    99.38    99.51 
         161:    99.34    99.45    99.52 
         162:    99.38    99.46    99.55 
         163:    99.40    99.49    99.58 
         164:    99.41    99.52    99.62 
         165:    99.44    99.57    99.64 
         166:    99.47    99.60    99.67 
         167:    99.50    99.62    99.72 
         168:    99.54    99.63    99.72 
         169:    99.56    99.68    99.73 
         170:    99.58    99.70    99.75 
         171:    99.62    99.72    99.78 
         172:    99.66    99.74    99.79 
         173:    99.68    99.75    99.80 
         174:    99.72    99.76    99.80 
         175:    99.73    99.78    99.83 
         176:    99.74    99.81    99.84 
         177:    99.76    99.84    99.85 
         178:    99.78    99.87    99.86 
         179:    99.80    99.88    99.86 
         180:    99.81    99.89    99.88 
         181:    99.81    99.90    99.90 
         182:    99.83    99.90    99.90 
         183:    99.83    99.92    99.91 
         184:    99.85    99.93    99.91 
         185:    99.86    99.94    99.92 
         186:    99.88    99.94    99.93 
         187:    99.90    99.94    99.93 
         188:    99.91    99.94    99.94 
         189:    99.91    99.94    99.94 
         190:    99.91    99.94    99.94 
         191:    99.92    99.95    99.94 
         192:    99.92    99.95    99.94 
         193:    99.92    99.95    99.94 
         194:    99.92    99.95    99.94 
         195:    99.94    99.96    99.94 
         196:    99.96    99.96    99.96 
         197:    99.96    99.96    99.96 
         198:    99.96    99.96    99.96 
         199:    99.96    99.96    99.97 
         200:    99.97    99.96    99.97 
         201:    99.98    99.97    99.97 
         202:    99.98    99.97    99.97 
         203:    99.98    99.97    99.97 
         204:    99.98    99.98    99.97 
         205:    99.98    99.99    99.97 
         206:    99.98    99.99    99.98 
         207:    99.98    99.99    99.98 
         208:    99.98    99.99    99.98 
         209:    99.98    99.99    99.98 
         210:    99.98    99.99    99.98 
         211:    99.98    99.99    99.98 
         212:    99.98    99.99    99.98 
         213:    99.98    99.99    99.98 
         214:    99.98    99.99    99.98 
         215:    99.98    99.99    99.98 
         216:    99.98   100.00    99.98 
         217:    99.98   100.00    99.99 
         218:    99.98   100.00    99.99 
         219:    99.98   100.00    99.99 
         220:    99.98   100.00    99.99 
         221:    99.98   100.00    99.99 
         222:    99.99   100.00    99.99 
         223:    99.99   100.00    99.99 
         224:    99.99   100.00    99.99 
         225:    99.99   100.00    99.99 
         226:    99.99   100.00    99.99 
         227:    99.99   100.00    99.99 
         228:    99.99   100.00    99.99 
         229:    99.99   100.00    99.99 
         230:    99.99   100.00    99.99 
         231:    99.99   100.00    99.99 
         232:    99.99   100.00    99.99 
         233:    99.99   100.00    99.99 
         234:    99.99   100.00    99.99 
         235:    99.99   100.00    99.99 
         236:    99.99   100.00    99.99 
         237:    99.99   100.00    99.99 
         238:   100.00   100.00    99.99 
         239:   100.00   100.00    99.99 
         240:   100.00   100.00    99.99 
         241:   100.00   100.00   100.00 
         242:   100.00   100.00   100.00 
         243:   100.00   100.00   100.00 
         244:   100.00   100.00   100.00 
         245:   100.00   100.00   100.00 
         246:   100.00   100.00   100.00 
         247:   100.00   100.00   100.00 
         248:   100.00   100.00   100.00 
         249:   100.00   100.00   100.00 
         250:   100.00   100.00   100.00 
         251:   100.00   100.00   100.00 
         252:   100.00   100.00   100.00 
         253:   100.00   100.00   100.00 
         254:   100.00   100.00   100.00 
         255:   100.00   100.00   100.00 
         256:   100.00   100.00   100.00 
         257:   100.00   100.00   100.00 
         258:   100.00   100.00   100.00 
         259:   100.00   100.00   100.00 
         260:   100.00   100.00   100.00 
         261:   100.00   100.00   100.00 
         262:   100.00   100.00   100.00 
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