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Warhammer 40,000 example

This example applies a multiplicative handicap to the Warhammer 40,000 to-wound chart.





In [1]:



    


import _initpath

import numpy
import dataset.csv
import dataset.wh40k
import zerosum.balance
from pandas import DataFrame

balance_7 = zerosum.balance.MultiplicativeBalance(dataset.wh40k.wh40k_7_to_wound).optimize()
balance_8 = zerosum.balance.MultiplicativeBalance(dataset.wh40k.wh40k_8_to_wound).optimize()

labels = [str(i + 1) for i in range(10)]

dataset.csv.write_csv('out/wh40k_7_to_wound_init.csv',
                      dataset.wh40k.wh40k_7_to_wound,
                      labels)

dataset.csv.write_csv('out/wh40k_8_to_wound_init.csv',
                      dataset.wh40k.wh40k_8_to_wound,
                      labels)

dataset.csv.write_csv('out/wh40k_7_to_wound_opt.csv',
                      balance_7.F, labels,
                      row_footers = balance_7.row_handicaps / balance_7.row_handicaps[0],
                      col_footers = balance_7.col_handicaps / balance_7.col_handicaps[0],
                      numeric_format = '%0.4f')
dataset.csv.write_csv('out/wh40k_8_to_wound_opt.csv',
                      balance_8.F, labels,
                      row_footers = balance_8.row_handicaps / balance_8.row_handicaps[0],
                      col_footers = balance_8.col_handicaps / balance_8.col_handicaps[0],
                      numeric_format = '%0.4f')

7th edition to-wound chart





In [2]:



    


DataFrame(data = dataset.wh40k.wh40k_7_to_wound, index = labels, columns = labels)



    


















    
Out[2]:











  
    

      
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
    

  
  
    

      1
      3.0
      2.0
      1.0
      1.0
      0.0
      0.0
      0.0
      0.0
      0.0
      0.0
    

    

      2
      4.0
      3.0
      2.0
      1.0
      1.0
      0.0
      0.0
      0.0
      0.0
      0.0
    

    

      3
      5.0
      4.0
      3.0
      2.0
      1.0
      1.0
      0.0
      0.0
      0.0
      0.0
    

    

      4
      5.0
      5.0
      4.0
      3.0
      2.0
      1.0
      1.0
      0.0
      0.0
      0.0
    

    

      5
      5.0
      5.0
      5.0
      4.0
      3.0
      2.0
      1.0
      1.0
      0.0
      0.0
    

    

      6
      5.0
      5.0
      5.0
      5.0
      4.0
      3.0
      2.0
      1.0
      1.0
      0.0
    

    

      7
      5.0
      5.0
      5.0
      5.0
      5.0
      4.0
      3.0
      2.0
      1.0
      1.0
    

    

      8
      5.0
      5.0
      5.0
      5.0
      5.0
      5.0
      4.0
      3.0
      2.0
      1.0
    

    

      9
      5.0
      5.0
      5.0
      5.0
      5.0
      5.0
      5.0
      4.0
      3.0
      2.0
    

    

      10
      5.0
      5.0
      5.0
      5.0
      5.0
      5.0
      5.0
      5.0
      4.0
      3.0

7th edition resulting payoff matrix





In [3]:



    


DataFrame(data = balance_7.F, index = labels, columns = labels)



    


















    
Out[3]:











  
    

      
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
    

  
  
    

      1
      3.185127
      2.650938
      1.827157
      2.336777
      0.000000
      0.000000
      0.000000
      0.000000
      0.000000
      0.000000
    

    

      2
      2.344233
      2.194957
      2.017164
      1.289890
      2.153756
      0.000000
      0.000000
      0.000000
      0.000000
      0.000000
    

    

      3
      1.710844
      1.708695
      1.766575
      1.506199
      1.257466
      2.050221
      0.000000
      0.000000
      0.000000
      0.000000
    

    

      4
      1.047064
      1.307185
      1.441563
      1.382726
      1.539178
      1.254768
      2.027517
      0.000000
      0.000000
      0.000000
    

    

      5
      0.647995
      0.808976
      1.115173
      1.140968
      1.428824
      1.553074
      1.254768
      2.050221
      0.000000
      0.000000
    

    

      6
      0.397436
      0.496171
      0.683971
      0.874740
      1.168458
      1.428824
      1.539178
      1.257466
      2.153756
      0.000000
    

    

      7
      0.238025
      0.297158
      0.409632
      0.523884
      0.874740
      1.140968
      1.382726
      1.506199
      1.289890
      2.336777
    

    

      8
      0.186115
      0.232352
      0.320297
      0.409632
      0.683971
      1.115173
      1.441563
      1.766575
      2.017164
      1.827157
    

    

      9
      0.135013
      0.168554
      0.232352
      0.297158
      0.496171
      0.808976
      1.307185
      1.708695
      2.194957
      2.650938
    

    

      10
      0.108146
      0.135013
      0.186115
      0.238025
      0.397436
      0.647995
      1.047064
      1.710844
      2.344233
      3.185127

8th edition to-wound chart





In [4]:



    


DataFrame(data = dataset.wh40k.wh40k_8_to_wound, index = labels, columns = labels)



    


















    
Out[4]:











  
    

      
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
    

  
  
    

      1
      3.0
      1.0
      1.0
      1.0
      1.0
      1.0
      1.0
      1.0
      1.0
      1.0
    

    

      2
      5.0
      3.0
      2.0
      1.0
      1.0
      1.0
      1.0
      1.0
      1.0
      1.0
    

    

      3
      5.0
      4.0
      3.0
      2.0
      2.0
      1.0
      1.0
      1.0
      1.0
      1.0
    

    

      4
      5.0
      5.0
      4.0
      3.0
      2.0
      2.0
      2.0
      1.0
      1.0
      1.0
    

    

      5
      5.0
      5.0
      4.0
      4.0
      3.0
      2.0
      2.0
      2.0
      2.0
      1.0
    

    

      6
      5.0
      5.0
      5.0
      4.0
      4.0
      3.0
      2.0
      2.0
      2.0
      2.0
    

    

      7
      5.0
      5.0
      5.0
      4.0
      4.0
      4.0
      3.0
      2.0
      2.0
      2.0
    

    

      8
      5.0
      5.0
      5.0
      5.0
      4.0
      4.0
      4.0
      3.0
      2.0
      2.0
    

    

      9
      5.0
      5.0
      5.0
      5.0
      4.0
      4.0
      4.0
      4.0
      3.0
      2.0
    

    

      10
      5.0
      5.0
      5.0
      5.0
      5.0
      4.0
      4.0
      4.0
      4.0
      3.0

8th edition resulting payoff matrix





In [5]:



    


DataFrame(data = balance_8.F, index = labels, columns = labels)



    


















    
Out[5]:











  
    

      
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
    

  
  
    

      1
      1.311712
      0.536910
      0.616361
      0.738436
      0.833954
      0.973079
      1.045450
      1.191852
      1.283667
      1.468578
    

    

      2
      1.739950
      1.281953
      0.981103
      0.587709
      0.663730
      0.774457
      0.832056
      0.948575
      1.021649
      1.168817
    

    

      3
      1.429785
      1.404575
      1.209317
      0.965887
      1.090827
      0.636402
      0.683733
      0.779482
      0.839530
      0.960463
    

    

      4
      1.138606
      1.398163
      1.284049
      1.153773
      0.868677
      1.013595
      1.088979
      0.620738
      0.668557
      0.764862
    

    

      5
      0.940358
      1.154721
      1.060477
      1.270511
      1.076141
      0.837112
      0.899371
      1.025317
      1.104303
      0.631688
    

    

      6
      0.805509
      0.989133
      1.135504
      1.088318
      1.229095
      1.075604
      0.770400
      0.878285
      0.945945
      1.082207
    

    

      7
      0.749748
      0.920660
      1.056898
      1.012979
      1.144011
      1.334861
      1.075604
      0.817486
      0.880462
      1.007291
    

    

      8
      0.680320
      0.835405
      0.959027
      1.148969
      1.038073
      1.211250
      1.301335
      1.112678
      0.798929
      0.914014
    

    

      9
      0.631659
      0.775652
      0.890432
      1.066789
      0.963824
      1.124614
      1.208256
      1.377457
      1.112678
      0.848638
    

    

      10
      0.572354
      0.702828
      0.806831
      0.966629
      1.091666
      1.019026
      1.094815
      1.248130
      1.344280
      1.153442

Weighting example

Optionally, instead of a uniform Nash equilibrium we can balance for a weighted Nash equilibrium.





In [6]:



    


strength_weights = numpy.array([0.0, 0.0, 2.0, 2.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0])
toughness_weights = strength_weights

balance_7_weighted = zerosum.balance.MultiplicativeBalance(dataset.wh40k.wh40k_7_to_wound, strength_weights, toughness_weights).optimize()

dataset.csv.write_csv('out/wh40k_7_to_wound_weighted_opt.csv',
                      balance_7_weighted.F, [str(i + 1) for i in range(10)],
                      row_footers = balance_7_weighted.row_handicaps / balance_7_weighted.row_handicaps[0],
                      col_footers = balance_7_weighted.col_handicaps / balance_7_weighted.col_handicaps[0],
                      numeric_format = '%0.4f')

DataFrame(data = balance_7_weighted.F, index = labels, columns = labels)



    


















    
Out[6]:











  
    

      
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
    

  
  
    

      1
      3.929799
      2.900320
      1.745733
      2.254267
      0.000000
      0.000000
      0.000000
      0.000000
      0.000000
      0.000000
    

    

      2
      2.836837
      2.355388
      1.890310
      1.220480
      1.778420
      0.000000
      0.000000
      0.000000
      0.000000
      0.000000
    

    

      3
      1.933953
      1.712785
      1.546415
      1.331258
      0.969920
      1.274734
      0.000000
      0.000000
      0.000000
      0.000000
    

    

      4
      1.124837
      1.245249
      1.199246
      1.161441
      1.128261
      0.741418
      1.408949
      0.000000
      0.000000
      0.000000
    

    

      5
      0.653315
      0.723252
      0.870666
      0.899434
      0.982956
      0.861245
      0.818330
      1.797270
      0.000000
      0.000000
    

    

      6
      0.521280
      0.577083
      0.694704
      0.897072
      1.045734
      1.030780
      1.305891
      1.434041
      2.695878
      0.000000
    

    

      7
      0.390033
      0.431786
      0.519793
      0.671209
      0.978052
      1.028337
      1.465645
      2.145962
      2.017115
      4.408250
    

    

      8
      0.317791
      0.351810
      0.423516
      0.546887
      0.796896
      1.047334
      1.592236
      2.622727
      3.287006
      3.591750
    

    

      9
      0.274185
      0.303536
      0.365403
      0.471846
      0.687550
      0.903624
      1.717196
      3.017132
      4.253968
      6.197814
    

    

      10
      0.250561
      0.277383
      0.333920
      0.431191
      0.628309
      0.825766
      1.569239
      3.446464
      5.183253
      8.495700

Content source: ajul/zerosum

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