Back to Scrabble Analysis

Maven Simulation Analysis

Table of Contents

This is a simulation analysis prepared by pams v.2.006 (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

Back to top

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

Initial Conditions

Back to top

Statistics by Play and Turn

Back to top

              heinie L8   veep K5  alive H8 veinal H4 
  Iterations:     42754     42754     42753     42753 
  MyScore[0]:     18.00     18.00      9.00     13.00 
 OppScore[1]:     37.21     34.03     35.01     37.40 
      95% +-       0.21      0.20      0.21      0.22 
        0lp%:      1.39      2.11      1.78      1.48 
        1lp%:      0.00      0.01      0.03      0.01 
        2lp%:      5.48      4.90      0.53      1.68 
        3lp%:     15.71     15.67      9.40     11.03 
        4lp%:     28.02     27.13     26.85     24.29 
        5lp%:     19.03     21.78     28.54     24.65 
        6lp%:     11.45     11.76     15.78     16.67 
        7lp%:     18.92     16.62     17.10     20.19 
  MyScore[1]:     31.04     28.15     35.32     33.80 
      95% +-       0.12      0.15      0.17      0.17 
        0lp%:      0.96      2.80      0.12      1.70 
        1lp%:      0.09      0.00      0.00      0.00 
        2lp%:      6.86      1.48      1.28      2.87 
        3lp%:     28.83     10.58      6.89     14.10 
        4lp%:     38.96     36.81     33.89     35.24 
        5lp%:     17.20     32.31     34.55     26.68 
        6lp%:      5.65     10.24     13.42     11.32 
        7lp%:      1.45      5.78      9.85      8.10 
 OppScore[2]:     37.06     37.79     37.72     39.13 
      95% +-       0.21      0.21      0.20      0.21 
        0lp%:      1.63      1.34      1.28      1.12 
        1lp%:      0.10      0.08      0.07      0.07 
        2lp%:      7.53      4.75      4.70      4.33 
        3lp%:     20.35     16.18     18.56     16.86 
        4lp%:     25.57     27.50     30.52     28.38 
        5lp%:     18.39     23.38     22.14     22.56 
        6lp%:     10.17      9.42      8.43      9.69 
        7lp%:     16.26     17.35     14.30     16.99 
  MyScore[2]:     34.24     35.99     37.54     38.21 
      95% +-       0.18      0.20      0.20      0.20 
        0lp%:      1.56      2.02      1.06      1.53 
        1lp%:      0.23      0.05      0.06      0.07 
        2lp%:      7.94      4.39      4.47      4.52 
        3lp%:     25.01     16.96     17.94     17.32 
        4lp%:     30.89     29.80     30.00     30.49 
        5lp%:     18.88     24.07     23.55     22.56 
        6lp%:      7.73      9.17      9.24      9.16 
        7lp%:      7.78     13.54     13.69     14.35 
 OppScore[3]:     37.29     38.80     38.09     39.84 
      95% +-       0.21      0.21      0.20      0.21 
        0lp%:      1.72      1.29      1.30      0.84 
        1lp%:      0.22      0.14      0.19      0.13 
        2lp%:      7.71      6.01      6.23      5.62 
        3lp%:     20.14     18.90     19.68     18.28 
        4lp%:     25.24     27.05     28.57     28.18 
        5lp%:     19.34     21.15     21.34     21.44 
        6lp%:      9.27      8.53      7.98      8.26 
        7lp%:     16.37     16.92     14.73     17.24 
  MyScore[3]:     36.29     37.61     37.62     39.24 
      95% +-       0.20      0.20      0.20      0.21 
        0lp%:      1.56      1.60      1.24      1.24 
        1lp%:      0.28      0.16      0.19      0.14 
        2lp%:      8.05      6.22      6.03      5.76 
        3lp%:     23.02     19.05     19.78     18.52 
        4lp%:     28.18     27.12     28.13     28.57 
        5lp%:     18.48     22.03     21.90     21.41 
        6lp%:      7.77      8.41      8.27      8.22 
        7lp%:     12.66     15.42     14.46     16.15 
  ResidualEq:      0.88     -0.50     -0.70     -0.26 
      95% +-       0.13      0.13      0.13      0.13 
   NetEquity:      8.90      8.63      7.97      7.61 
      95% +-       0.45      0.46      0.47      0.48 

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

Back to top

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]='heinie L8':

      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  0.2 -0.5  0.2  0.2  0.1  0.9  0.2  0.3  0.4
 2   0.0  0.1  0.1  0.2  0.1  0.2  0.2 -0.6  0.2  0.8  0.7  1.6 -4.1  1.0  0.3
 3   0.0  0.1  0.2  0.2  0.2  0.2  0.2 -0.6  0.1  0.2  0.2  1.2 -6.1  0.4  0.3
 4   0.1  0.1  0.2  0.4  0.2  0.2  0.2 -0.3  0.5  0.8  0.6  2.2 -5.3  0.8  0.5
 5   0.1  0.1  0.2  0.4  0.3  0.2  0.2 -0.7  0.1  0.3 -0.0  0.7 -5.9  0.3 -0.0
 6   0.1  0.2  0.2  0.4  0.4  0.4  0.2 -0.7  0.1  0.4  0.0  0.6 -5.8  0.4  0.1
 7   0.2 -1.2 -1.2 -1.1 -1.0 -1.0 -1.0 -2.2 -0.1 -0.2 -0.5   .  -6.2 -0.0  0.1
 8   0.8  0.6  0.6  0.7  0.4  0.1   .  -1.4 -0.1 -0.2 -0.5   h  -6.2 -0.1  0.1
 9   0.3  0.1  0.3  0.3  0.2   .  -0.0 -1.4 -0.1 -0.2   .   0.0 -1.3 -0.2 -0.1
10   0.1  0.1  0.2  0.2  0.1 -0.0 -0.4 -1.4 -1.7 -2.9 -3.2 -0.7 -1.3  0.5 -0.2
11   0.2  0.3  0.5  0.5 -1.2 -2.6 -4.0 -4.3 -5.6 -5.5 -8.5 -5.4 -4.0 -1.3 -0.8
12   0.4  0.4  0.4  0.6  0.3 -0.1 -1.1  1.4 -1.4 -1.1 -4.2 -1.1 -1.9 -0.3 -0.3
13   0.3  0.4  0.7  0.6  0.1 -2.0 -4.0 -1.4 -5.0 -4.4 -6.4 -4.1 -4.8 -0.4 -0.2
14   0.3  0.3  0.2  0.2 -0.0  0.1 -0.2  2.6 -1.1 -2.1 -3.5 -2.4 -2.8 -1.5 -0.3
15   0.5  0.4  0.3  0.4  0.2  0.4  0.7  3.7  0.3  0.1 -0.2 -0.0  0.2  0.1  0.9

Total Expected Square Values when MyTurn[0]='veep K5':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1   0.2  0.1  0.1  0.2  0.1  0.1  0.2  0.7  0.1  0.1  0.0  0.7  0.2  0.2  0.3
 2   0.1  0.3  0.2  0.2  0.2  0.3  0.2  0.7  0.2  0.3  0.3  1.0 -2.2  0.8  0.3
 3   0.1  0.3  0.3  0.3  0.3  0.2  0.2  0.7  0.2  0.2  0.2  0.9 -3.9  0.6  0.2
 4   0.2  0.3  0.3  0.5  0.3  0.2  0.1  0.7  0.0  0.0   .   1.0 -3.9  0.8  0.4
 5   0.1  0.3  0.4  0.6  0.6  0.2 -0.0  0.4 -0.4 -0.4 -0.4 -0.2 -4.8  0.5  0.0
 6   0.2  0.3  0.2 -0.2 -1.1 -1.7 -2.0 -2.1 -2.9 -5.4 -4.5 -4.4 -7.1 -0.7  0.3
 7   0.2 -0.0  0.1  0.2  0.3  0.0 -0.0 -1.1 -0.2 -1.3 -0.2 -1.1 -5.6  0.3  0.4
 8   0.7  0.6  0.5  0.6  0.5  0.1   .  -1.1 -0.2 -1.1 -0.0 -1.3 -7.3  0.3  0.5
 9   0.3  0.2  0.2  0.3  0.3   .   0.0 -1.1 -0.2 -1.1 -0.0 -1.3 -2.8  0.4  0.5
10   0.1  0.1  0.1 -0.0 -0.2 -2.3 -2.6 -4.7 -5.5 -9.2 -7.3 -6.7 -5.5 -2.2 -0.1
11   0.2  0.4  0.6  0.9  1.2  1.1  1.0  0.5  0.6 -0.1  1.7  0.3 -0.7  1.1  0.2
12   0.4  0.4  0.5  0.6  0.4  0.3  0.2 -0.1  0.1 -0.1  1.0 -0.2 -0.8  0.6  0.3
13   0.3  0.3  0.4  0.4  0.3  0.2  0.1 -0.3  0.0  0.1  1.0  0.4 -0.6  0.6  0.3
14   0.2  0.5  0.5  0.5  0.5  0.6  0.4  0.1  0.2  0.2  0.6 -0.4 -0.5  0.4  0.3
15   0.4  0.3  0.3  0.4  0.4  0.4  0.6  0.4  0.4  0.3  0.1 -0.3  0.2  0.2  0.3

Total Expected Square Values when MyTurn[0]='alive H8':

      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  0.2  0.3  0.1  0.1  0.1  0.7  0.2  0.4  0.4
 2   0.1  0.1  0.1  0.2  0.1  0.2  0.2  0.3  0.2  0.6  0.5  1.1 -1.0  1.1  0.5
 3   0.1  0.1  0.2  0.3  0.2  0.2  0.3  0.4  0.4  0.5  0.6  0.6 -2.0  1.0  0.6
 4   0.2  0.2  0.2  0.4  0.3  0.4  0.4  0.9  0.8  0.8  0.8 -0.5 -1.7  1.3  0.9
 5   0.2  0.2  0.2  0.5  0.7  0.5  0.6  0.8  0.7  0.6 -0.2 -1.7 -2.4  1.1  0.8
 6   0.2  0.2  0.2  0.4  0.5  0.4  0.4  0.6  0.5  0.5 -0.3 -2.0 -2.5  1.4  1.1
 7   0.2  0.2  0.2  0.4  0.5  0.0  0.0   .  -0.0 -1.1 -2.2 -4.5 -4.5  0.5  1.0
 8   0.5  0.4  0.5  0.7  0.7  0.1   .  -0.0 -0.0 -0.3 -1.3 -3.9 -4.5  0.5  1.1
 9   0.2  0.3  0.5  0.4  0.5  0.0  0.0  0.0 -0.0 -0.3 -1.0 -2.5 -0.6  0.6  0.9
10   0.2  0.6  0.7  0.6  0.7  0.0 -0.2 -0.2 -0.3 -4.5 -4.1 -5.7 -2.2 -0.7  0.7
11   0.2  0.5  0.5  0.0 -0.8 -1.4 -2.3 -3.3 -3.3 -3.4 -2.3 -2.9 -0.2  0.6  0.4
12   0.9  0.1 -0.5 -1.6 -1.8 -2.9 -4.1 -4.3 -3.8 -2.1 -0.5 -0.9  0.8  1.1  1.3
13   0.5  0.8  1.2  1.0  0.9  0.6  0.3   .   0.3  0.3  1.0  1.1  1.1  1.0  0.6
14   0.4  0.7  0.7  0.7  0.7  0.7  0.5  0.3  0.2  0.2  0.5  0.2  0.5  0.6  0.5
15   0.5  0.4  0.5  0.7  0.8  0.8  0.9  1.0  0.8  0.5  0.3  0.2  0.3  0.3  0.4

Total Expected Square Values when MyTurn[0]='veinal H4':

      A    B    C    D    E    F    G    H    I    J    K    L    M    N    O
 1   0.0  0.2  0.2  0.4  0.3  0.4  0.4  0.5  0.3  0.2  0.3  0.9  0.4  0.4  0.6
 2   0.0  0.4  0.4  0.6  0.3  0.5  0.2  0.2  0.2  0.7  0.6  1.2 -1.3  0.8  0.4
 3   0.0  0.4  0.7  0.9  0.5  0.5  0.2   .   0.4  0.8  1.0  1.2 -1.8  0.9  0.5
 4   0.9  1.0  1.1  1.5  0.3 -0.2 -1.2 -1.9 -1.9 -1.1 -0.8 -1.6 -3.1  0.4  0.7
 5   0.1 -0.8 -1.3 -3.0 -7.6 -8.3 -9.7 -9.9 -9.4 -7.1 -6.9 -4.6 -3.4  0.2  0.6
 6   0.5  0.4 -0.2 -0.1 -0.7 -2.6 -3.7 -3.8 -3.8 -2.6 -1.7 -2.7 -3.3  0.6  0.8
 7   0.3  0.1  0.3  0.8  0.6  0.1 -0.1 -0.1  0.0 -0.8 -1.6 -3.2 -4.0  0.3  1.2
 8   0.7  0.4  0.5  1.0  0.8  0.1   .  -0.0 -0.0 -0.2 -1.0 -0.7 -4.4  0.4  1.4
 9   0.5  0.3  0.3  0.6  0.6  0.0  0.0  0.0  0.0 -0.1 -0.9  0.4 -0.7  0.5  1.3
10   0.3  0.2  0.2  0.2  0.1 -0.6 -0.7   .  -1.5 -4.5 -4.3 -2.7 -2.9 -1.1  1.0
11   0.3  0.3  0.4  0.7  1.1  0.6  0.5  0.9  0.5  0.1  0.5  1.8  0.3  0.9  0.8
12   0.4  0.4  0.4  0.7  0.6  0.4  0.3  0.8  0.3  0.1  0.5  2.0  0.3  0.6  0.7
13   0.2  0.3  0.3  0.3  0.3  0.1  0.1  0.6  0.0 -0.0  0.4  1.6  0.3  0.6  0.6
14   0.2  0.3  0.3  0.3  0.3  0.3  0.3  0.7  0.2  0.3  0.5  0.8  0.2  0.7  0.6
15   0.3  0.2  0.2  0.3  0.4  0.5  0.6  1.2  0.6  0.4  0.4  0.3  0.3  0.4  0.6

Equity Distribution

Back to top

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.

              heinie L8   veep K5  alive H8 veinal H4 
        -300:      0.00      0.00      0.00      0.00 
        -290:      0.00      0.00      0.00      0.00 
        -280:      0.00      0.00      0.00      0.00 
        -270:      0.00      0.00      0.00      0.00 
        -260:      0.00      0.00      0.00      0.00 
        -250:      0.00      0.00      0.00      0.01 
        -240:      0.00      0.00      0.00      0.01 
        -230:      0.00      0.00      0.00      0.01 
        -220:      0.00      0.00      0.00      0.02 
        -210:      0.01      0.00      0.00      0.03 
        -200:      0.01      0.00      0.01      0.03 
        -190:      0.01      0.01      0.02      0.04 
        -180:      0.01      0.02      0.03      0.04 
        -170:      0.03      0.02      0.04      0.06 
        -160:      0.04      0.05      0.08      0.09 
        -150:      0.07      0.07      0.13      0.13 
        -140:      0.13      0.13      0.21      0.20 
        -130:      0.24      0.24      0.35      0.35 
        -120:      0.45      0.45      0.57      0.64 
        -110:      0.78      0.75      0.90      1.00 
        -100:      1.24      1.26      1.48      1.65 
         -90:      2.03      2.05      2.32      2.64 
         -80:      3.27      3.28      3.57      4.06 
         -70:      5.00      5.09      5.39      6.01 
         -60:      7.63      7.69      7.92      8.72 
         -50:     11.12     11.01     11.33     12.35 
         -40:     15.73     15.39     15.95     17.07 
         -30:     20.98     20.75     21.48     22.69 
         -20:     27.56     27.33     27.77     29.03 
         -10:     34.96     34.69     34.81     36.08 
           0:     42.81     42.62     42.98     43.96 
          10:     51.38     51.17     51.82     52.23 
          20:     60.29     60.16     60.57     60.49 
          30:     68.72     68.19     68.47     68.28 
          40:     76.16     75.03     75.16     75.11 
          50:     82.32     80.95     80.89     80.69 
          60:     87.38     85.82     85.68     85.47 
          70:     91.14     89.71     89.61     89.34 
          80:     93.93     92.90     92.78     92.55 
          90:     95.93     95.19     95.15     94.92 
         100:     97.51     96.84     96.68     96.54 
         110:     98.41     97.98     97.82     97.76 
         120:     99.05     98.73     98.58     98.51 
         130:     99.42     99.16     99.12     99.05 
         140:     99.67     99.52     99.43     99.43 
         150:     99.80     99.71     99.64     99.61 
         160:     99.88     99.82     99.80     99.77 
         170:     99.93     99.88     99.89     99.85 
         180:     99.96     99.93     99.93     99.92 
         190:     99.98     99.96     99.95     99.94 
         200:     99.99     99.98     99.96     99.97 
         210:     99.99     99.99     99.96     99.98 
         220:    100.00    100.00     99.98     99.99 
         230:    100.00    100.00     99.99     99.99 
         240:    100.00    100.00    100.00    100.00 
         250:    100.00    100.00    100.00    100.00 
         260:    100.00    100.00    100.00    100.00 
         270:    100.00    100.00    100.00    100.00 
         280:    100.00    100.00    100.00    100.00 
         281:    100.00    100.00    100.00    100.00 
         282:    100.00    100.00    100.00    100.00 
         283:    100.00    100.00    100.00    100.00 
         284:    100.00    100.00    100.00    100.00 
         285:    100.00    100.00    100.00    100.00 
         286:    100.00    100.00    100.00    100.00 
Back to top