Sisyphus' Probability Tables(updated April 8, 2008)

[Sisyphus]

Here are some handy probability tables for those that are interested. Each table goes from 1 to 10 attack left to right and 0 to 10 defense top to bottom unless otherwise indicated.

Use this information with caution since "there are lies, damned lies, and statistics."

Standard Figures


Average Damage:
Attack/Defense

This table shows the average amount of damage caused in an attack.

1 2 3 4 5 6 7 8 9 10
0 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000
1 0.333 0.750 1.208 1.688 2.177 2.672 3.169 3.668 4.167 4.667
2 0.222 0.556 0.958 1.403 1.872 2.354 2.845 3.339 3.837 4.335
3 0.148 0.407 0.750 1.150 1.589 2.052 2.530 3.017 3.510 4.005
4 0.099 0.296 0.580 0.932 1.334 1.770 2.230 2.705 3.189 3.680
5 0.066 0.214 0.444 0.747 1.107 1.511 1.947 2.405 2.878 3.361
6 0.044 0.154 0.337 0.593 0.910 1.278 1.685 2.121 2.579 3.050
7 0.029 0.110 0.254 0.466 0.741 1.071 1.446 1.856 2.294 2.750
8 0.020 0.078 0.190 0.363 0.598 0.889 1.230 1.612 2.026 2.464
9 0.013 0.055 0.141 0.281 0.479 0.733 1.038 1.389 1.776 2.193
10 0.009 0.039 0.105 0.216 0.380 0.599 0.869 1.187 1.546 1.939


Wound Chance:
Attack/Defense

This table shows the probability of an attack causing at least one wound. For squad figures and 1 life heroes it also shows the probability of an attack destroying the defending figure.

1 2 3 4 5 6 7 8 9 10
0 0.500 0.750 0.875 0.938 0.969 0.984 0.992 0.996 0.998 0.999
1 0.333 0.583 0.750 0.854 0.917 0.953 0.974 0.986 0.992 0.996
2 0.222 0.444 0.625 0.757 0.847 0.906 0.944 0.967 0.980 0.989
3 0.148 0.333 0.509 0.655 0.766 0.846 0.901 0.938 0.961 0.976
4 0.099 0.247 0.407 0.556 0.679 0.776 0.848 0.899 0.934 0.958
5 0.066 0.181 0.321 0.463 0.592 0.700 0.786 0.851 0.898 0.932
6 0.044 0.132 0.250 0.380 0.507 0.622 0.718 0.795 0.855 0.899
7 0.029 0.095 0.192 0.308 0.429 0.544 0.647 0.734 0.804 0.859
8 0.020 0.068 0.146 0.246 0.358 0.470 0.576 0.670 0.749 0.813
9 0.013 0.049 0.111 0.195 0.295 0.401 0.506 0.603 0.689 0.762
10 0.009 0.035 0.083 0.153 0.241 0.339 0.440 0.538 0.628 0.707




Counter Strike(Samurai, Charos)


Average Damage:
Attack/Defense

This table shows the average damage inflicted on the attacker due to an attack against a figure with counter strike(when excess shields count as unblockable hits).

1 2 3 4 5 6 7 8 9 10
0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.167 0.083 0.042 0.021 0.010 0.005 0.003 0.001 0.001 0.000
2 0.389 0.222 0.125 0.069 0.038 0.021 0.011 0.006 0.003 0.002
3 0.648 0.407 0.250 0.150 0.089 0.052 0.030 0.017 0.010 0.005
4 0.932 0.630 0.414 0.265 0.167 0.103 0.063 0.038 0.023 0.013
5 1.233 0.881 0.611 0.414 0.274 0.178 0.114 0.072 0.045 0.027
6 1.544 1.154 0.837 0.593 0.410 0.278 0.185 0.121 0.079 0.050
7 1.863 1.443 1.088 0.799 0.574 0.404 0.279 0.190 0.127 0.084
8 2.186 1.745 1.357 1.030 0.765 0.556 0.397 0.278 0.192 0.131
9 2.513 2.055 1.641 1.281 0.979 0.733 0.538 0.389 0.276 0.193
10 2.842 2.372 1.938 1.550 1.214 0.932 0.703 0.521 0.380 0.273


Wound Chance:
Attack/Defense

This table shows the probability of an attack inflicting at least one wound on the attacker when the defender has counter strike(when excess shields count as unblockable hits). For squad figures and 1 life heroes it also shows the probability of an attack destroying the attacking figure due to counter strike.

1 2 3 4 5 6 7 8 9 10
0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.167 0.083 0.042 0.021 0.010 0.005 0.003 0.001 0.001 0.000
2 0.333 0.194 0.111 0.063 0.035 0.019 0.010 0.006 0.003 0.002
3 0.481 0.315 0.199 0.123 0.074 0.044 0.026 0.015 0.009 0.005
4 0.605 0.432 0.296 0.197 0.127 0.081 0.050 0.031 0.019 0.011
5 0.704 0.539 0.395 0.279 0.192 0.128 0.084 0.054 0.034 0.021
6 0.781 0.632 0.490 0.365 0.264 0.186 0.128 0.086 0.057 0.037
7 0.839 0.711 0.577 0.450 0.340 0.250 0.179 0.125 0.086 0.058
8 0.883 0.776 0.654 0.531 0.417 0.318 0.237 0.172 0.123 0.086
9 0.915 0.828 0.720 0.605 0.492 0.389 0.299 0.225 0.166 0.120
10 0.939 0.869 0.777 0.672 0.563 0.459 0.364 0.282 0.214 0.159




Unleashed Fury(Anubian Wolves)


Average Damage:

Attack/Defense (d+ = +1 to D20 rolls, a+ = +1 attack bonus, etc)

This table shows the average damage an Anubian Wolf will cause in an attack before Unleashed Fury is rolled.

d+ d++ a+ a+d+ a+d++
0 1.775 1.975 2.150 2.275 2.475 2.650
1 1.488 1.679 1.850 1.965 2.160 2.333
2 1.236 1.417 1.581 1.680 1.869 2.038
3 1.020 1.188 1.343 1.424 1.604 1.767
4 0.837 0.991 1.136 1.198 1.367 1.522
5 0.683 0.823 0.956 1.000 1.158 1.303
6 0.554 0.681 0.802 0.830 0.975 1.111
7 0.448 0.562 0.671 0.685 0.817 0.942
8 0.362 0.462 0.559 0.563 0.682 0.796
9 0.291 0.379 0.465 0.460 0.567 0.670
10 0.233 0.310 0.385 0.375 0.470 0.562


Wound Chance:
Attack/Defense (d+ = +1 to D20 rolls, a+ = +1 attack bonus, etc)

This table shows the probability that an attack from an Anubian wolf will cause at least one wound before Unleashed Fury is rolled. For defending squad figures and 1 life heroes it also shows the probability of an attack destroying the defending figure.

d+ d++ a+ a+d+ a+d++
0 0.862 0.887 0.900 0.931 0.944 0.950
1 0.754 0.787 0.807 0.854 0.875 0.887
2 0.648 0.686 0.713 0.768 0.795 0.813
3 0.550 0.591 0.622 0.679 0.711 0.735
4 0.462 0.504 0.538 0.592 0.628 0.655
5 0.385 0.426 0.462 0.510 0.548 0.578
6 0.318 0.358 0.394 0.435 0.473 0.506
7 0.261 0.300 0.335 0.367 0.405 0.439
8 0.213 0.249 0.283 0.308 0.345 0.378
9 0.173 0.207 0.239 0.256 0.292 0.324
10 0.140 0.171 0.201 0.212 0.246 0.277




Stinger Drain(Marro Stingers)


Average Damage:
Attack/Defense (d+ = +1 to D20 rolls, a+ = +1 attack bonus, N = without Stinger Drain)

This table shows the average damage a Marro Stinger causes in an attack before Stinger Drain is rolled.

N d+ d++ Na+ a+ a+d+ a+d++
0 1.500 1.475 1.575 1.675 2.000 1.875 2.000 2.125
1 1.208 1.230 1.315 1.399 1.688 1.619 1.728 1.837
2 0.958 1.011 1.081 1.151 1.403 1.380 1.474 1.567
3 0.750 0.820 0.878 0.935 1.150 1.162 1.241 1.321
4 0.580 0.658 0.704 0.751 0.932 0.967 1.033 1.100
5 0.444 0.522 0.559 0.597 0.747 0.796 0.851 0.906
6 0.337 0.410 0.440 0.470 0.593 0.649 0.694 0.740
7 0.254 0.320 0.343 0.366 0.466 0.524 0.561 0.598
8 0.190 0.247 0.266 0.284 0.363 0.420 0.450 0.479
9 0.141 0.190 0.204 0.218 0.281 0.334 0.358 0.381
10 0.105 0.145 0.156 0.167 0.216 0.263 0.282 0.301


Wound Chance:
Defense (d+ = +1 to D20 rolls, a+ = +1 attack bonus, N = without Stinger Drain)

This table shows the probability of a Marro Stinger causing at least one wound in an attack before Stinger Drain is rolled. For squad figures and 1 life heroes it also shows the probability of an attack destroying the defending figure.

N d+ d++ Na+ a+ a+d+ a+d++
0 0.875 0.734 0.781 0.828 0.938 0.767 0.816 0.864
1 0.750 0.657 0.700 0.743 0.854 0.718 0.764 0.809
2 0.625 0.573 0.610 0.648 0.757 0.655 0.698 0.740
3 0.509 0.488 0.520 0.553 0.655 0.585 0.623 0.662
4 0.407 0.407 0.435 0.463 0.556 0.513 0.547 0.580
5 0.321 0.335 0.358 0.381 0.463 0.441 0.471 0.500
6 0.250 0.271 0.290 0.309 0.380 0.374 0.399 0.425
7 0.192 0.217 0.233 0.248 0.308 0.313 0.334 0.356
8 0.146 0.172 0.184 0.197 0.246 0.258 0.276 0.294
9 0.111 0.135 0.145 0.154 0.195 0.211 0.226 0.241
10 0.083 0.105 0.113 0.120 0.153 0.171 0.183 0.195




Double Strike(Minions of Utgar, Omnicron Snipers)


Average Damage:
Attack/Defense

This table shows the average amount of damage caused in an attack made with double strike(where each skull rolled counts as two hits).

1 2 3 4 5 6 7 8 9 10
0 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000
1 0.833 1.750 2.708 3.688 4.677 5.672 6.669 7.668 8.667 9.667
2 0.667 1.500 2.417 3.375 4.354 5.344 6.339 7.336 8.335 9.334
3 0.519 1.269 2.139 3.072 4.037 5.019 6.010 7.005 8.003 9.001
4 0.395 1.062 1.880 2.781 3.728 4.699 5.684 6.676 7.671 8.669
5 0.296 0.881 1.640 2.504 3.427 4.385 5.361 6.348 7.341 8.338
6 0.219 0.724 1.422 2.242 3.137 4.077 5.043 6.024 7.013 8.007
7 0.161 0.591 1.224 1.996 2.859 3.777 4.729 5.702 6.687 7.678
8 0.117 0.478 1.046 1.767 2.593 3.486 4.422 5.385 6.363 7.350
9 0.085 0.384 0.888 1.556 2.341 3.205 4.122 5.072 6.042 7.024
10 0.061 0.306 0.749 1.362 2.103 2.936 3.830 4.765 5.725 6.701

Wound Chance:
Attack/Defense

This table shows the probability of an attack made with double strike(where each skull rolled counts as two hits) causing at least one wound. For squad figures and 1 life heroes it also shows the probability of an attack destroying the defending figure.

1 2 3 4 5 6 7 8 9 10
0 0.500 0.750 0.875 0.938 0.969 0.984 0.992 0.996 0.998 0.999
1 0.500 0.750 0.875 0.938 0.969 0.984 0.992 0.996 0.998 0.999
2 0.444 0.694 0.833 0.910 0.951 0.974 0.986 0.993 0.996 0.998
3 0.370 0.620 0.778 0.873 0.928 0.960 0.978 0.988 0.993 0.996
4 0.296 0.543 0.718 0.831 0.901 0.943 0.968 0.982 0.990 0.995
5 0.230 0.469 0.656 0.786 0.870 0.923 0.955 0.974 0.985 0.992
6 0.176 0.401 0.594 0.737 0.836 0.900 0.940 0.965 0.979 0.988
7 0.132 0.338 0.533 0.687 0.797 0.873 0.922 0.953 0.972 0.983
8 0.098 0.283 0.474 0.634 0.756 0.842 0.900 0.938 0.962 0.977
9 0.072 0.234 0.417 0.581 0.712 0.809 0.876 0.922 0.951 0.970
10 0.052 0.192 0.364 0.529 0.667 0.772 0.849 0.902 0.938 0.961




One Shield Defense(Crixus)


Average Damage:
Attack/Defense

This table shows the average amount of damage caused in an attack defended by a figure with one shield defense(i.e. Crixus, if the defending figure rolls at least one shield, the most damage it can recieve is one wound).

1 2 3 4 5 6 7 8 9 10
0 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000
1 0.333 0.750 1.167 1.563 1.938 2.297 2.646 2.988 3.327 3.663
2 0.222 0.556 0.903 1.229 1.528 1.802 2.058 2.302 2.537 2.767
3 0.148 0.407 0.694 0.970 1.220 1.443 1.644 1.828 1.999 2.162
4 0.099 0.296 0.531 0.765 0.982 1.174 1.343 1.492 1.626 1.748
5 0.066 0.214 0.403 0.603 0.793 0.965 1.116 1.246 1.359 1.459
6 0.044 0.154 0.305 0.473 0.642 0.799 0.938 1.059 1.162 1.250
7 0.029 0.110 0.229 0.370 0.518 0.662 0.794 0.910 1.009 1.093
8 0.020 0.078 0.171 0.288 0.417 0.549 0.674 0.787 0.885 0.969
9 0.013 0.055 0.127 0.223 0.335 0.454 0.571 0.682 0.780 0.866
10 0.009 0.039 0.094 0.172 0.267 0.374 0.483 0.590 0.689 0.776




Gift of the Empress Aura(Einar Imperium/Empress Kiova)


Wound Chance:
Attack/Defense

This table shows the probability of an attack causing at least one wound when the defending figure rerolls all defense die that do not show shields(i.e. Einar Imperium in range of Empress Kiova's aura).

1 2 3 4 5 6 7 8 9 10
0 0.500 0.750 0.875 0.938 0.969 0.984 0.992 0.996 0.998 0.999
1 0.222 0.472 0.667 0.799 0.882 0.932 0.962 0.979 0.988 0.994
2 0.099 0.272 0.458 0.621 0.747 0.837 0.898 0.937 0.962 0.978
3 0.044 0.148 0.293 0.448 0.590 0.709 0.800 0.866 0.913 0.944
4 0.020 0.078 0.177 0.304 0.439 0.567 0.679 0.769 0.838 0.890
5 0.009 0.040 0.103 0.197 0.310 0.432 0.549 0.654 0.742 0.813
6 0.004 0.020 0.058 0.122 0.210 0.314 0.425 0.534 0.633 0.719
7 0.002 0.010 0.032 0.074 0.137 0.220 0.316 0.419 0.520 0.615
8 0.001 0.005 0.017 0.043 0.087 0.149 0.227 0.317 0.413 0.509
9 0.000 0.002 0.009 0.025 0.053 0.097 0.158 0.233 0.318 0.408
10 0.000 0.001 0.005 0.014 0.032 0.062 0.107 0.165 0.237 0.317




Shields of Valor(Sentinels of Jandar)


Wound Chance:
Attack/Defense

This table shows the probability of an attack causing at least one wound in which the defending figure recieves two blocks for every shield rolled(i.e. Seninels of Jandar). For squad figures and 1 life heroes it also shows the probability of an attack destroying the defending figure.

1 2 3 4 5 6 7 8 9 10
0 0.500 0.750 0.875 0.938 0.969 0.984 0.992 0.996 0.998 0.999
1 0.333 0.500 0.625 0.729 0.813 0.875 0.919 0.949 0.969 0.981
2 0.222 0.333 0.444 0.556 0.656 0.741 0.810 0.863 0.904 0.933
3 0.148 0.222 0.315 0.417 0.516 0.608 0.688 0.757 0.815 0.861
4 0.099 0.148 0.222 0.309 0.398 0.486 0.569 0.646 0.714 0.773
5 0.066 0.099 0.156 0.226 0.302 0.382 0.461 0.538 0.611 0.677
6 0.044 0.066 0.110 0.165 0.227 0.295 0.367 0.440 0.512 0.580
7 0.029 0.044 0.077 0.119 0.169 0.226 0.288 0.354 0.422 0.489
8 0.020 0.029 0.054 0.085 0.124 0.171 0.223 0.281 0.342 0.405
9 0.013 0.020 0.037 0.061 0.091 0.128 0.172 0.221 0.274 0.332
10 0.009 0.013 0.026 0.043 0.066 0.095 0.131 0.171 0.218 0.268




Heroic Defense Aura(Hatamoto Taro with Samurai/Ashigaru)


Average Damage:
Attack/Defense

This table shows the average amount of damage caused in an attack when the defending figure recieves Heroic Defense Aura(when Einar symbols count as shields).

1 2 3 4 5 6 7 8 9 10
0 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000
1 0.250 0.625 1.063 1.531 2.016 2.508 3.004 3.502 4.001 4.500
2 0.125 0.375 0.719 1.125 1.570 2.039 2.521 3.012 3.506 4.003
3 0.063 0.219 0.469 0.797 1.184 1.611 2.066 2.539 3.023 3.513
4 0.031 0.125 0.297 0.547 0.865 1.238 1.652 2.096 2.559 3.036
5 0.016 0.070 0.184 0.365 0.615 0.927 1.290 1.693 2.126 2.581
6 0.008 0.039 0.111 0.238 0.427 0.677 0.983 1.338 1.732 2.156
7 0.004 0.021 0.066 0.152 0.290 0.483 0.733 1.036 1.384 1.770
8 0.002 0.012 0.039 0.096 0.193 0.338 0.536 0.786 1.085 1.427
9 0.001 0.006 0.023 0.059 0.126 0.232 0.384 0.585 0.835 1.131
10 0.000 0.003 0.013 0.036 0.081 0.156 0.270 0.427 0.631 0.881

Wound Chance:
Attack/Defense

This table shows the probability of an attack causing at least one wound when the defending figure has Heroic Defense Aura(when Einar Symbols count as shields). For squad figures and 1 life heroes it also shows the probability of an attack destroying the defending figure.

1 2 3 4 5 6 7 8 9 10
0 0.500 0.750 0.875 0.938 0.969 0.984 0.992 0.996 0.998 0.999
1 0.250 0.500 0.688 0.813 0.891 0.938 0.965 0.980 0.989 0.994
2 0.125 0.313 0.500 0.656 0.773 0.855 0.910 0.945 0.967 0.981
3 0.063 0.188 0.344 0.500 0.637 0.746 0.828 0.887 0.927 0.954
4 0.031 0.109 0.227 0.363 0.500 0.623 0.726 0.806 0.867 0.910
5 0.016 0.063 0.145 0.254 0.377 0.500 0.613 0.709 0.788 0.849
6 0.008 0.035 0.090 0.172 0.274 0.387 0.500 0.605 0.696 0.773
7 0.004 0.020 0.055 0.113 0.194 0.291 0.395 0.500 0.598 0.685
8 0.002 0.011 0.033 0.073 0.133 0.212 0.304 0.402 0.500 0.593
9 0.001 0.006 0.019 0.046 0.090 0.151 0.227 0.315 0.407 0.500
10 0.000 0.003 0.011 0.029 0.059 0.105 0.166 0.240 0.324 0.412


Tough(Gorillinators)


Wound Chance:
Attack/Defense

This table shows the probability of an attack causing at least one wound when the defending figure has Tough(when defending figure receives one automatic shield). For squad figures and 1 life heroes it also shows the probability of an attack destroying the defending figure.

1 2 3 4 5 6 7 8 9 10
1 0.000 0.167 0.375 0.563 0.708 0.813 0.883 0.928 0.957 0.975
2 0.000 0.111 0.278 0.451 0.604 0.726 0.816 0.880 0.923 0.952
3 0.000 0.074 0.204 0.356 0.506 0.636 0.741 0.821 0.879 0.920
4 0.000 0.049 0.148 0.278 0.417 0.548 0.662 0.755 0.827 0.880


Poison Sting(Sujoah)


This table shows the average damage caused by Sojoah's Poison Sting Special Attack and the probability that Sojoah's Poison Sting kills a figure by rolling a 20.

Average Damage Kill Chance
0 2.93750 0.09375
1 2.54167 0.08542
2 2.15972 0.07569
3 1.80556 0.06551
4 1.48765 0.05556
5 1.20988 0.04630
6 0.97257 0.03800
7 0.77366 0.03077
8 0.60966 0.02463
9 0.47635 0.01951
10 0.36932 0.01531



Counter Strike vs. Double Strike


Wound Chance:
This table shows the probability of an attack causing at least one wound to the attacker with double strike

(when each skull rolled counts as two hits) when the defender has counter strike(when excess shields count as

unblockable hits). For squad figures and 1 life heroes it also shows the probability of an attack destroying

the attacking figure due to counter strike.

1 2 3 4 5 6 7 8 9 10
0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.167 0.083 0.042 0.021 0.010 0.005 0.003 0.001 0.001 0.000
2 0.278 0.139 0.069 0.035 0.017 0.009 0.004 0.002 0.001 0.001
3 0.370 0.194 0.102 0.053 0.028 0.014 0.008 0.004 0.002 0.001
4 0.457 0.256 0.142 0.078 0.042 0.023 0.012 0.007 0.004 0.002
5 0.539 0.323 0.189 0.108 0.061 0.034 0.019 0.010 0.006 0.003
6 0.616 0.392 0.241 0.144 0.084 0.048 0.028 0.016 0.009 0.005
7 0.685 0.461 0.296 0.183 0.111 0.066 0.038 0.022 0.013 0.007
8 0.746 0.528 0.353 0.227 0.141 0.086 0.052 0.031 0.018 0.010
9 0.798 0.591 0.411 0.273 0.176 0.110 0.068 0.041 0.024 0.014
10 0.842 0.649 0.468 0.321 0.213 0.137 0.086 0.053 0.033 0.020


Wound Chance(with Heroic Defense Aura):
This table shows the probability of an attack causing at least one wound to the attacker with double strike

(when each skull rolled counts as two hits) when the defender has counter strike(when excess shields count as

unblockable hits) when the defending figure is boosted by Heroic Defense Aura(Einar symbols count as

shields). For squad figures and 1 life heroes it also shows the probability of an attack destroying the

attacking figure due to counter strike.

1 2 3 4 5 6 7 8 9 10
0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.250 0.125 0.063 0.031 0.016 0.008 0.004 0.002 0.001 0.000
2 0.375 0.188 0.094 0.047 0.023 0.012 0.006 0.003 0.001 0.001
3 0.500 0.281 0.156 0.086 0.047 0.025 0.014 0.007 0.004 0.002
4 0.625 0.391 0.234 0.137 0.078 0.044 0.024 0.013 0.007 0.004
5 0.734 0.500 0.320 0.197 0.118 0.069 0.040 0.023 0.013 0.007
6 0.820 0.602 0.410 0.267 0.167 0.103 0.062 0.036 0.021 0.012
7 0.883 0.691 0.500 0.342 0.225 0.144 0.089 0.055 0.033 0.019
8 0.926 0.768 0.586 0.421 0.289 0.192 0.124 0.078 0.048 0.029
9 0.954 0.830 0.665 0.500 0.358 0.247 0.165 0.107 0.068 0.043
10 0.972 0.878 0.734 0.576 0.429 0.306 0.212 0.142 0.093 0.060

Average Damage:
This table shows the average damage caused to the attacker with double strike(when each skull rolled counts

as two hits) on an attack against a figure with counter strike(when excess shields count as unblockable

hits).

1 2 3 4 5 6 7 8 9 10
0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.167 0.083 0.042 0.021 0.010 0.005 0.003 0.001 0.001 0.000
2 0.333 0.167 0.083 0.042 0.021 0.010 0.005 0.003 0.001 0.001
3 0.519 0.269 0.139 0.072 0.037 0.019 0.010 0.005 0.003 0.001
4 0.728 0.395 0.213 0.114 0.061 0.032 0.017 0.009 0.005 0.003
5 0.963 0.547 0.307 0.171 0.094 0.051 0.028 0.015 0.008 0.004
6 1.219 0.724 0.422 0.242 0.137 0.077 0.043 0.024 0.013 0.007
7 1.494 0.924 0.557 0.329 0.192 0.110 0.063 0.035 0.020 0.011
8 1.784 1.145 0.713 0.434 0.259 0.153 0.089 0.051 0.029 0.017
9 2.085 1.384 0.888 0.556 0.341 0.205 0.122 0.072 0.042 0.024
10 2.394 1.639 1.083 0.695 0.437 0.269 0.163 0.098 0.058 0.034

Average Damage(with Heroic Defense Aura):
This table shows the probability of an attack causing at least one wound to the attacker with double strike

(when each skull rolled counts as two hits) when the defender has counter strike(when excess shields count as

unblockable hits) when the defending figure is boosted by Heroic Defense Aura(Einar symbols count as

shields). For squad figures and 1 life heroes it also shows the probability of an attack destroying the

attacking figure due to counter strike.

1 2 3 4 5 6 7 8 9 10
0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.250 0.125 0.063 0.031 0.016 0.008 0.004 0.002 0.001 0.000
2 0.375 0.188 0.094 0.047 0.023 0.012 0.006 0.003 0.001 0.001
3 0.500 0.281 0.156 0.086 0.047 0.025 0.014 0.007 0.004 0.002
4 0.625 0.391 0.234 0.137 0.078 0.044 0.024 0.013 0.007 0.004
5 0.734 0.500 0.320 0.197 0.118 0.069 0.040 0.023 0.013 0.007
6 0.820 0.602 0.410 0.267 0.167 0.103 0.062 0.036 0.021 0.012
7 0.883 0.691 0.500 0.342 0.225 0.144 0.089 0.055 0.033 0.019
8 0.926 0.768 0.586 0.421 0.289 0.192 0.124 0.078 0.048 0.029
9 0.954 0.830 0.665 0.500 0.358 0.247 0.165 0.107 0.068 0.043
10 0.972 0.878 0.734 0.576 0.429 0.306 0.212 0.142 0.093 0.060

I have been getting a lot of requests on how these tables were produced so here are some helpful equations. P(w) gives the probability that an attack of A dice will inflict a wound against a figure with D defense(i.e. kill a squad member). The specialized tables in this thread come from this formula with only slight modifications. E(w) gives the expected number of wounds an attack with A dice will inflict on a figure with D defense(i.e. average damage to a hero if the hero has at least A life). The third equation is the definition of a combination which is used in the first two formulas. "n choose m" is the number of ways you can choose n items in a set of m elements. For example if I roll three attack dice, I can get two skulls in three different ways. The skulls can be on the first and second dice, the first and third dice, or the second and third dice.

http://img102.imageshack.us/img102/2650/12079451.tif

[MrBarkypants]

This should be a sticky. It gets referenced in many threads.

[oracle92]

Just to point out, you spelled snipers wrong.

[rdhight]

Awesome, awesome, sticky-worthy post.

One interesting takeaway I noticed is that when attack and defense dice are tied, the chance of at least one wound is tied at 3-3, in the attacker's favor at 4-4 and above, and in the defender's favor at 2-2 and below. That right there is going to change the way I play some squad figures, I think.

[Boozehammer]

Sisyphus, great post. I wanted to save this thread from becoming buried by congratulating you for posting such helpful information.

[gamjuven]

I like it. Very helpful! Although I would continue to update it and maybe label your tables a little better so we know what column represents dice and what column represents damage inflicted.

[Jexik]

I was just thinking about this thread today, and how I should bump it. Useful stuff. I think the biggest lesson for me at least is to remember that you still need one more Skull than shield to wound, and one more shield or more to get a counterstrike.

Since 4 Attack dice equal about as much skulls on average as 6 Defense gets in shields, you need one more attack die to have about a 50% chance to wound.

I like comparing something to a coin toss, because 50% odds are the easiest for me to wrap my head around in a game. Against squad figures...

1 A, >50% chance of wounding 0 D and below.
2A, "" 1 D
3A, "" 3 D
4A, "" 4 D
5A, "" 6 D
6A, "" 7 D
7A, "" 9 D

[Shades fan]

How about we get it stickied!

[dragonfire]

I read the threads title as Syphilis problem tables. So, yeah, this thread is a bit different than I thought.....

[Sisyphus]

Ah, cool my thread is stickied. I generated some tables for Hatamoto Taro. I'll add them when I get back to the computer in which they are on.

I read the threads title as Syphilis problem tables. So, yeah, this thread is a bit different than I thought.....

Believe it or not you are not the first person who has confused my name with Syphilis. :(

[spider_poison]

I'm glad to see this thread got stickied. I actually printed out a few of the probability tables when you first made this thread. It helped me realize why I could never put a wound on that stupid soulborg :evil:

[Shades fan]

I'm glad to see this thread got stickied. I actually printed out a few of the probability tables when you first made this thread. It helped me realize why I could never put a wound on that stupid soulborg :evil:
It is weird because I did the exact same thing.

[Sisyphus]

Added a couple of tables outlining Heroic Defense Aura.

[Sisyphus]

Added a table for Gorillinator's Tough ability.

[Jexik]

You can probably toss in a mention of Gurei Oni's Evil Eye Defense now. It should be mathematically equivalent to Counterstrike, so you won't need to add a new table.

[Sisyphus]

Added a table for Sujoah's Poison Sting ability. Doesn't look like Q9 has to worry too much.

[Brownsfan82]

Hey man, I was wondering if anyone said anything about the double strike.

It should be 0.500 with one attack against 0 defense dice, because it is still a 50/50 chance to roll one skull (even though it counts as two)

[Sisyphus]

Hey man, I was wondering if anyone said anything about the double strike.

It should be 0.500 with one attack against 0 defense dice, because it is still a 50/50 chance to roll one skull (even though it counts as two)

The relevant table does show there is a 50/50 chance of destroying a zero defense squad figure with 1 attack double-strike. Perhaps you were looking at the table describing average damage.

[Sisyphus]

Added several tables showing the probabilities of counter-strike against double-strike with and without Heroic Defense Aura.

[CheddarLimbo]

Hi Sisyphus! How about Chilling Touch? Or is that straightforward enough that it doesn't need a table?

[Sisyphus]

Hi Sisyphus! How about Chilling Touch? Or is that straightforward enough that it doesn't need a table?

Well, wound chance is quite easy (8/20 without modifiers) average damage is only slightly more complicated and it turns out that Chilling Touch will do on average 0.95 wounds/turn to a multi-life hero.

I'll eventually probably do a table with chilling touch w/ Sonya and/or Lodin combined/not combined with normal attack.

[Noxious Ghoul]

Haha, me and a few of my buddies were just talking about the probability of a figure being able to wound others like this. Although we did not go this in depth with it! This is probably one of my favorite posts I've looked at yet, mostly because I so badly wanted to make something of this nature myself. Great work.
10.7/10

[arp12]

I think you mean deadly strike instead of double strike. Deadly Shot/Strike is the name of the ability the Omnicron Snipers and Minions of Utgar have.

[LeChevalierdeBalibari]

You spelled Sujoah wrong.
This table shows the average damage caused by Sojoah's Poison Sting Special Attack and the probability that Sojoah's Poison Sting kills a figure by rolling a 20.

[Jaz1597]

This is the first time I've really taken a look at this thread, and I can see why people rely on these tables so much. They're a fantastic resource. Nice job, Sisyphus!

[MKSentinel]

Love this as a resource. Wondering about a couple things though:

1.) Could you label your x/y axis better on these for retards like me?
2.) Could you examine the Deadly Shot ability of the Omicron and Zetacron? Curious about the strike probability vs different defenses.
3.) Can I get my hands on the source files? These are a HUGE help in my army construction and for articles like my Ninjas and Microcorp builds.

YOU ARE THE MAN!

[scottishlad5]

I can't believe I just now saw this, this is awesome!

[Sisyphus]

Love this as a resource. Wondering about a couple things though:

1.) Could you label your x/y axis better on these for retards like me?


I will eventually do something to clean everything up but I'm pretty swamped right now.

2.) Could you examine the Deadly Shot ability of the Omicron and Zetacron? Curious about the strike probability vs different defenses.

The intent of the tables is so that you can figure that sort of stuff on your own.:p Though a good rule of thumb is that many small attacks are better against squadies and one big attack is better against heroes.

3.) Can I get my hands on the source files? These are a HUGE help in my army construction and for articles like my Ninjas and Microcorp builds.

I don't really have source files. I have one or two functions that I keep modifying slightly to generate each table when I feel like it. It's bad software engineering practice I know but it gets simple things like this done quickly.


YOU ARE THE MAN!

Well, that goes without saying. :p

[MKSentinel]

[quote=MKSentinel;701610]2.) Could you examine the Deadly Shot ability of the Omicron and Zetacron? Curious about the strike probability vs different defenses.

The intent of the tables is so that you can figure that sort of stuff on your own.:p Though a good rule of thumb is that many small attacks are better against squadies and one big attack is better against heroes.

[

Well if I was smart enough to figure it out on my own I wouldn't be asking you the question. :P

Seriously though, you roll x number of dice, but for every skull you roll, your opponent has to roll 2 shields to block all damage. Not sure how to place that into the existing tables.

[Sisyphus]

[quote=MKSentinel;701610]2.) Could you examine the Deadly Shot ability of the Omicron and Zetacron? Curious about the strike probability vs different defenses.

The intent of the tables is so that you can figure that sort of stuff on your own.:p Though a good rule of thumb is that many small attacks are better against squadies and one big attack is better against heroes.

[

Well if I was smart enough to figure it out on my own I wouldn't be asking you the question. :P

Seriously though, you roll x number of dice, but for every skull you roll, your opponent has to roll 2 shields to block all damage. Not sure how to place that into the existing tables.

Let's say you are interested in comparing how a squad of Omnicron snipers compare to Zetacron against Major Q9 on level ground.

Q9 has defense 7, Omnicron snipers have attack 1 so you go to row 7, column 1 of the average damage table for Double Strike. You see that the entry is 0.161. However since there are three Omnicrons to a squad you multiply 0.161 by 3 to get 0.483. A squad of omnicrons will do an average of 0.483 damage per turn against Q9. Zetacron has an attack of 2 so you go to row 7, column 2 of the same table and you see 0.591. Zetacron does an average of 0.591 wounds per turn against Q9.

Of course you can look at different parts of the tables to try out different defenses. Against squads you would look at the would chance table rather than the average damage table.

[DrRansom]

..
The intent of the tables is so that you can figure that sort of stuff on your own.:p Though a good rule of thumb is that many small attacks are better against squadies and one big attack is better against heroes.


May I first just say thanks so much for giving geeks like me an edge. :)

I am compiling a list of documents and programs for using on a Nintendo DS and currently I have the old jumbled text version of the information above in a txt file on my DS (I just copied and pasted) which works but get hard to read as the numbers get bigger.

I was wondering if you have ever made a clean looking pdf version (that I could easily port into CBDS). Otherwise, I'll probably wind up going in and fixing the spacing of my own document by hand.

Thanks!

[TOG]

I was wondering if you have ever made a clean looking pdf version (that I could easily port into CBDS). Otherwise, I'll probably wind up going in and fixing the spacing of my own document by hand.

Thanks!

Could you not just use CutePDF to convert the text tables to PDF?

[DrRansom]

I was wondering if you have ever made a clean looking pdf version (that I could easily port into CBDS). Otherwise, I'll probably wind up going in and fixing the spacing of my own document by hand.
Thanks!
Could you not just use CutePDF to convert the text tables to PDF?
Yeah, but I'd have to get all the indents and spacings correct. It wouldn't take too long but I was wondering if anyone's allready done it. It would save me a little time. :)

[Sisyphus]

I have been getting a lot of requests on how these tables were produced so here are some helpful equations. P(w) gives the probability that an attack of A dice will inflict a wound against a figure with D defense(i.e. kill a squad member). The specialized tables in this thread come from this formula with only slight modifications. E(w) gives the expected number of wounds an attack with A dice will inflict on a figure with D defense(i.e. average damage to a hero if the hero has at least A life). The third equation is the definition of a combination which is used in the first two formulas. "n choose m" is the number of ways you can choose n items in a set of m elements. For example if I roll three attack dice, I can get two skulls in three different ways. The skulls can be on the first and second dice, the first and third dice, or the second and third dice.

http://img102.imageshack.us/img102/2650/12079451.tif

[Purplebeard]

I have been getting a lot of requests on how these tables were produced so here are some helpful equations. P(w) gives the probability that an attack of A dice will inflict a wound against a figure with D defense(i.e. kill a squad member). The specialized tables in this thread come from this formula with only slight modifications. E(w) gives the expected number of wounds an attack with A dice will inflict on a figure with D defense(i.e. average damage to a hero if the hero has at least A life). The third equation is the definition of a combination which is used in the first two formulas. "n choose m" is the number of ways you can choose n items in a set of m elements. For example if I roll three attack dice, I can get two skulls in three different ways. The skulls can be on the first and second dice, the first and third dice, or the second and third dice.



http://img10.imageshack.us/img10/8506/87448383.tif

:shock:.......Sigh. Brilliant. +rep.

I will now go pick out all the red M&M's out of my bag and line them up in rows for my mathematical feat of the day.

[StarofEarendil]

Sisyphus, I like the formulas, but have found I cannot get the problems to work out right. So I was wondering if you could give a demonstration of sorts to show some of the younger nerds on the site how to work these formulas.:)

[twilkerson]

You miss 100% of the shots that you don't take.
-Wayne Gretzky

[Ullar/utgar own]

very good idea. these are extremely useful.

[jaamartin]

The specialized tables in this thread come from this formula with only slight modifications.

Sisyphus, I like the formulas, but have found I cannot get the problems to work out right. So I was wondering if you could give a demonstration of sorts to show some of the younger nerds on the site how to work these formulas.:)

Star, I shortened the post to highlight Sisyphus's statement about modifying the formula a little. The thing is, Sisyphus never speaks of the changes made. Looking at the formula's just about anything can be changed a tad, and without getting the original formula to match up with his generic table, I don't trust myself to just make changes.

Here is an example of what I get.

For A=1 :

D Result
0 0.5
1 0.333
2 0.222
3 0.148
4 0.099
5 0.066
6 0.044
7 0.029
8 0.0195
9 0.013
10 0.0087


But when I try the next column, I get differences.

For A=2

D Result
0 1
1 0.8333
2 0.6667
3 0.5185
4 0.3951
5 0.2963
6 0.2195
7 0.1610
8 0.1171
9 0.0845
10 0.0607


This does not correlate properly with the posted values at the beginning.

Sisyphus, what errors am I making? I have only looked at P(w) at the moment since that is the one I will most likely use for a while until it become ingrained in my brain...

Jason

[dok]

Well, without looking over your shoulder neither I nor Sisyphus can check your work. But I have looked at the formulas, and they are accurate.

Just to give you one example... looking at the A=2, D=1 entry, you should get

.5*(2/3) + .25*(2*2/3 + 1/3)
Which does reduce to .75, not .833.

[jaamartin]

dok, I am not sure what I am messing up though. Here is what I have entered into MathCAD:

http://www.thumbprintpro.com/heroscape/probability.png

Again, I am looking at the function P(w). I will run this out by hand tonight when I get to my folks house and see if it isn't just MathCADs uncanny ability at yielding incorrect results.

[Sisyphus]

dok, I am not sure what I am messing up though. Here is what I have entered into MathCAD:

http://www.thumbprintpro.com/heroscape/probability.png

Again, I am looking at the function P(w). I will run this out by hand tonight when I get to my folks house and see if it isn't just MathCADs uncanny ability at yielding incorrect results.

Well, at least you understand your biggest mistake is using MathCAD. :p

I think your problem is that you need to pass "little a" as a parameter to your BigA function. IIRC, MathCAD evaluates everything from top to bottom which means that the "little a" in your BigA function is not the same "little a" as in the Pw function.

[jaamartin]

I know that software will corrupt the brain when it comes to math, but I was in a pinch at work and supposedly doing other things:shock:.

Thanks for pointing that out! Everything is matching up now.

[Obsidian]

I saw that there was no table for counterstrike against a normal attack when defending with HEROIC DEFENSE AURA, so here are some numbers that I found using my heroscape probability calculator. (http://www.heroscapers.com/community/showthread.php?t=25738)

The odds that an attacker will receive at least one wound when attacking a figure with COUNTERSTRIKE and HEROIC DEFENSE AURA.

Att 0 1 2 3 4 5 6 7 8 9 10
Def
1 0.500 0.250 0.125 0.063 0.031 0.016 0.008 0.004 0.002 0.001 0.000
2 0.750 0.500 0.313 0.188 0.109 0.063 0.035 0.020 0.011 0.006 0.003
3 0.875 0.688 0.500 0.344 0.227 0.145 0.090 0.055 0.033 0.019 0.011
4 0.938 0.813 0.656 0.500 0.363 0.254 0.172 0.113 0.073 0.046 0.029
5 0.969 0.891 0.773 0.637 0.500 0.377 0.274 0.194 0.133 0.090 0.059
6 0.984 0.938 0.855 0.746 0.623 0.500 0.387 0.291 0.212 0.151 0.105
7 0.992 0.965 0.910 0.828 0.726 0.613 0.500 0.395 0.304 0.227 0.166
8 0.996 0.980 0.945 0.887 0.806 0.709 0.605 0.500 0.402 0.315 0.240
9 0.998 0.989 0.967 0.927 0.867 0.788 0.696 0.598 0.500 0.407 0.324
10 0.999 0.994 0.981 0.954 0.910 0.849 0.773 0.685 0.593 0.500 0.412

[galvornman]

Greetings all,

After having my ass handed to me by Jexik on a few occasions, I asked myself - how many attacks would it take for a figure with M attack dice vs. a defender with N defense dice to inflict one wound, on the average?

Rather than deal with probability calculations - I ran simulations. I used R (code available to anyone who wants it), and each element in the table represents an average over 1000 simulated battles. Essentially the algorithm is the following:

Roll attack dice & count skulls.
Roll defense dice and count shields.
Is the number of skulls greater than the number of shields?
If it is, the number of attacks necessary to inflict one wound is 1, and we move on to the next simulation.
If it isn't, we try again, and keep counting the number of attacks until I get skulls greater than shields. This number will necessarily be something greater than 1, and I record it.

I do this process 1000 times, for every combination of attack and defense dice (up to 10 attack and 10 defense), then taking the average of all 1000 results.

Below I attach a table with my results. Note that these results have been rounded. Example interpretation: For an attacker with 3 dice (A3) against a defender with 3 defense dice (D3) I can expect to attack twice (2) in order to inflict one wound.

(apologies for the poor formatting!)


D1 D2 D3 D4 D5 D6 D7 D8 D9 D10
A1 3 5 7 10 15 23 33 51 81 116
A2 2 2 3 4 5 8 11 15 20 28
A3 1 2 2 3 3 4 5 7 9 12
A4 1 1 2 2 2 3 3 4 5 7
A5 1 1 1 1 2 2 2 3 3 4
A6 1 1 1 1 1 2 2 2 2 3
A7 1 1 1 1 1 1 2 2 2 2
A8 1 1 1 1 1 1 1 1 2 2
A9 1 1 1 1 1 1 1 1 1 2
A10 1 1 1 1 1 1 1 1 1 1

I was a bit surprised at first by the first row, specifically the A1 vs. D1. The average is, of course, not the whole story - simulations show that about 34% of the time one attack is enough to inflict one wound against a defender with 1 die (this is not surprising). In 22% of the simulations in this case it took 2 attacks, and in 13% of the simulations it took 3. The average, being sensitive to outliers, is pushed up by the presence of a few large cases - 12% of the observations were greater than 5 in this particular case.

For me, this table demonstrates what we've known all along - rolling a few attack dice many times trumps rolling a lot of dice only a few times.

Why is Q9 so good? He rolls a few dice many times, resulting in more net wounds.

Why are 4-man squads so dominant? If they have at least 3 attack dice and are ranged - again, lots of opportunities to roll dice and inflict wounds.

Why are rats good? If attacked by a 2-4 dice attacker, it takes an average of two attacks to take each one down - and in this time they get to move (assuming normal attacks) and cause trouble.

Why do the Deathwalkers die? Even 3 attack dice squads need only roll against DW9K an average of 9 times before he falls.

Nilfheim/Zelrig good? 3 attacks.

Why is bonding so awesome? More attacks.

Apologies if this work offers no new insight into this great game - it only confirms what we already know by experience. Excluding counter drafting and gimmicks (Thorian speed vs. normal ranged attacks), winning armies are those that allow you to roll a few dice as often as possible. Squadscape isn't going anywhere anytime soon.

[padlock]

For me, this table demonstrates what we've known all along - rolling a few attack dice many times trumps rolling a lot of dice only a few times.



That of course depends on who you are attacking. I did the math, and it turns out that if you had a large pool of dice and were able to split them up as you saw fit when attacking a group of single life figures, then the optimal number was always equal to defense of the figures you were attacking.

For example, if you were given a hundred dice and told to attack a horde of stingers, you would be best off doing 33 attacks of 3 (followed by 1 attack of 1). If however, you were attacking a group of minions, you'd be better of doing 16 attacks of 6 (followed by 1 attack of 4).

When fighting multi-life heroes, the numbers change and it becomes much more beneficial to have fewer large attacks then many small ones.

If higher defense squads and more multi-life heroes ever become really popular, then I suspect that relatively low attack squads (like the 4th mass) will become less dominant.

[bmaczero]

Thanks for sharing the formulas, Sisyphus! I've got a quick question, though. What's the meaning of the "A" over "a" term (the first one inside the sum). I've never seen that before :?

EDIT: Nevermind, I stumbled across it on Wikipedia ;).

[CheddarLimbo]

Could someone help me calculate the odds of an outcome?

What is the probability someone will (a) get initiative (b) roll a 14 or higher to summon Retchets with Iskra, and the (c) roll all skulls on a 3 die attack to Lethal Sting a figure?

[Bonecrusher]

I am wrong.

[CheddarLimbo]

Could someone help me calculate the odds of an outcome?

What is the probability someone will (a) get initiative (50%) (b) roll a 14 or higher to summon Retchets with Iskra, and the (35%) (c) roll all skulls on a 3 die attack to Lethal Sting a figure (12.5%)?

0.021875%.

So, the outcome is roughly one in five thousand?

[Bonecrusher]

Still way wrong.

[Warlord Alpha]

Could someone help me calculate the odds of an outcome?

What is the probability someone will (a) get initiative (50%) (b) roll a 14 or higher to summon Retchets with Iskra, and the (35%) (c) roll all skulls on a 3 die attack to Lethal Sting a figure (12.5%)?

0.021875%.

So, the outcome is roughly one in five thousand?

Actually it is exactly 7 out of every 32000. But yes, roughly.


However, assuming we take initiative out of the mix, that leaves you with 0.04375, quite a bit better. However, you also have 3 Retchets, not just one. So, that makes 3 attempts to roll 3 skulls 37.5%. So, that means you have a 0.13125% chance, without initiative. Halve that number with initiative. Thats not quite nearly as bad as 0.021875%. You are 6 times as likely to summon the Retchets and Lethal Sting somebody assuming initiative doesn't matter and with 3 Retchets than with initiative not guaranteed and with only one Retchet.

[Bonecrusher]

By Sisyphus and padlock's math below, I got this.

5.776367188%

[Sisyphus]

Could someone help me calculate the odds of an outcome?

What is the probability someone will (a) get initiative (b) roll a 14 or higher to summon Retchets with Iskra, and the (c) roll all skulls on a 3 die attack to Lethal Sting a figure?

5.776%, so approximately the chance of rolling a 20 on the D20.

P(I) = Probability of winning initiative = 0.5
P(S) = Probability of summon = 7/20 = 0.35
P(A) = Probability of rolling 3 skulls on 3 attack die = 0.5^ 3 = 0.125
P(~A) = Probability of not rolling 3 skulls on 3 attack die = 1 - P(A) = 1 - 0.125 = 0.875
P(~B) = Probability of not rolling 3 skulls on 3 attack die in 3 attempts = P(~A)^3 = 0.875^3 = 343/512
P(B) = Probability of not not rolling 3 skulls on 3 attack die in 3 attempts (i.e. probability of rolling 3 skulls at least once) = 1 - P(~B) = 1 - 343/512 = 169/512

P(I)*P(S)*P(B) = Probability of winning initiative, then successfully summoning, and then lethal stinging at least one figure in three attempts = 0.05776 = 5.776%.

[padlock]

Could someone help me calculate the odds of an outcome?

What is the probability someone will (a) get initiative (b) roll a 14 or higher to summon Retchets with Iskra, and the (c) roll all skulls on a 3 die attack to Lethal Sting a figure?

Get initiative = .5
Roll 14 or higher = .35
roll 3 skulls for 1 retchet = .5^3 = .125
roll 3 skulls with at least 1 of the 3 retchets = 1- (1 - .125) ^3) = .33

Total = .5 * .35 * .33 = .05775 or 5.775%

[Warlord Alpha]

nevermind, I seem to have failed. See what summer has done to me? :|

[Sisyphus]

Could someone help me calculate the odds of an outcome?

What is the probability someone will (a) get initiative (b) roll a 14 or higher to summon Retchets with Iskra, and the (c) roll all skulls on a 3 die attack to Lethal Sting a figure?

Get initiative = .5
Roll 14 or higher = .35
roll 3 skulls for 1 retchet = .5^3 = .125
roll 3 skulls with at least 1 of the 3 retchets = 1- (1 - .125) ^3) = .33

Total = .5 * .35 * .33 = .05775 or 5.775%

You've got to work quick around here. :p

[CheddarLimbo]

In the situation I am citing getting initiative was relevant. The first turn Summon/Lethal sting allowed my opponent to destroy a figure that had my 1 & 2 OM's on it. If I'd gone first I would have taken a turn with the figure in question. It may have even been out of range of the Retchets at that point...but maybe not. It was a narrow map, so there weren't a lot of place they could not get to.

[padlock]

Could someone help me calculate the odds of an outcome?

What is the probability someone will (a) get initiative (b) roll a 14 or higher to summon Retchets with Iskra, and the (c) roll all skulls on a 3 die attack to Lethal Sting a figure?

Get initiative = .5
Roll 14 or higher = .35
roll 3 skulls for 1 retchet = .5^3 = .125
roll 3 skulls with at least 1 of the 3 retchets = 1- (1 - .125) ^3) = .33

Total = .5 * .35 * .33 = .05775 or 5.775%

You've got to work quick around here. :p

No fair. You edited your post to show your work only after I posted mine :)

I'll get you next time!

[CheddarLimbo]

So, wait. Now I'm confused. Which is it? One in 5,000 or 1 in 20?

[Warlord Alpha]

So, wait. Now I'm confused. Which is it? One in 5,000 or 1 in 20?

Well, more people got 1 in 20 so I say go with them. I think the one in 5000 is due to decimals not getting moved.

[lefton4ya]

Question, how about probabilities of double attacks (or multiple attacks from squads) on the same figure. Always wanted to know what was better in situations such as:
Triple attack of 3 or single attack of 5 against defense of 3 for figure with three life left (Q9)
Double attack of 4 or singe attack of 6 against defense of 4 with one life.
Etc.

It would be more than figuring out the probability of one attack times or plus the probability of a second, because you have to take into consideration wounds (sometimes a second attack would not be applicable).

In my experience more attacks is usually better because you have a better chance you doing good and the other person throwing dud dice in one of 2-3 rolls as opposed to just one. but I'd like to see math back me up.

[ollie]

The tables in the first post let you calculate such things. The reason that there aren't tables anywhere for them is that there are so many variables. If there is a specific instance/unit that interests you then checking through the Books ( http://www.heroscapers.com/community/showthread.php?t=8099) is a good place to start. For instance, Q9's Book (http://www.heroscapers.com/community/showthread.php?t=8597) has some good discussion about the Queglix options in various circumstances and this post (http://www.heroscapers.com/community/showpost.php?p=608014&postcount=22) in the Book of Laglor (http://www.heroscapers.com/community/showthread.php?t=8580) is a strong contender for most pointless bit of math in this vein.

[Gold-dust-hydra]

Dang, this i amazing, although my friend defies you! he has rolled 3 20s in a row on the d20 and is probably the luckiest person on earth. Pack of MTG cards-Bam! mythic rare/foil. I envy him.

[dok]

I noticed that we don't have average damage tables for tough multi-life heroes. So, here they are.

Tough(Heirloom, Mogrimm, Hatamoto Taro)

Average Damage:
Attack/Defense

This table shows the average amount of damage caused in an attack defended by a figure that has Tough (when the defending figure receives one automatic shield).

1 2 3 4 5 6 7 8 9 10
0 0 0.250 0.625 1.063 1.531 2.016 2.508 3.004 3.502 4.001
1 0 0.167 0.458 0.833 1.260 1.719 2.195 2.682 3.175 3.671
2 0 0.111 0.333 0.646 1.024 1.448 1.901 2.373 2.856 3.346
3 0 0.074 0.241 0.495 0.823 1.206 1.629 2.080 2.548 3.029
4 0 0.049 0.173 0.377 0.654 0.994 1.382 1.806 2.255 2.722
5 0 0.033 0.123 0.284 0.515 0.811 1.161 1.554 1.980 2.429
6 0 0.022 0.088 0.213 0.403 0.656 0.967 1.326 1.724 2.151
7 0 0.015 0.062 0.158 0.312 0.526 0.799 1.122 1.489 1.891
8 0 0.010 0.044 0.117 0.240 0.419 0.654 0.942 1.277 1.651
9 0 0.007 0.031 0.086 0.184 0.331 0.532 0.785 1.087 1.431
10 0 0.004 0.022 0.063 0.140 0.260 0.429 0.649 0.918 1.232Iron Tough(Iron Golem)

Average Damage:
Attack/Defense

This table shows the average amount of damage caused in an attack defended by a figure that has Iron Tough (when the defending figure receives two automatic shields).

1 2 3 4 5 6 7 8 9 10
0 0 0 0.125 0.375 0.719 1.125 1.570 2.039 2.522 3.012
1 0 0 0.083 0.271 0.552 0.906 1.313 1.754 2.218 2.697
2 0 0 0.056 0.194 0.420 0.722 1.085 1.493 1.933 2.395
3 0 0 0.037 0.139 0.317 0.570 0.888 1.259 1.669 2.109
4 0 0 0.025 0.099 0.238 0.446 0.720 1.051 1.429 1.842
5 0 0 0.017 0.070 0.177 0.346 0.579 0.870 1.212 1.596
6 0 0 0.011 0.049 0.131 0.267 0.462 0.714 1.020 1.372
7 0 0 0.007 0.035 0.097 0.204 0.365 0.582 0.852 1.171
8 0 0 0.005 0.024 0.071 0.156 0.287 0.471 0.707 0.992
9 0 0 0.003 0.017 0.052 0.118 0.224 0.378 0.582 0.834
10 0 0 0.002 0.012 0.038 0.089 0.174 0.302 0.476 0.697

Wound Chance:
Attack/Defense

This table shows the chance of inflicting a wound in an attack defended by a figure that has Iron Tough (when the defending figure receives two automatic shields).

1 2 3 4 5 6 7 8 9 10
0 0 0 0.125 0.313 0.500 0.656 0.773 0.856 0.910 0.945
1 0 0 0.083 0.229 0.396 0.552 0.682 0.783 0.856 0.906
2 0 0 0.056 0.167 0.309 0.457 0.591 0.704 0.792 0.857
3 0 0 0.037 0.120 0.238 0.372 0.504 0.623 0.722 0.801
4 0 0 0.025 0.086 0.182 0.299 0.424 0.543 0.649 0.738
5 0 0 0.017 0.062 0.138 0.238 0.352 0.467 0.576 0.672
6 0 0 0.011 0.044 0.104 0.188 0.289 0.397 0.505 0.604
7 0 0 0.007 0.031 0.077 0.146 0.234 0.334 0.437 0.537
8 0 0 0.005 0.022 0.057 0.113 0.189 0.278 0.375 0.473
9 0 0 0.003 0.015 0.042 0.087 0.150 0.229 0.318 0.412
10 0 0 0.002 0.011 0.031 0.067 0.119 0.187 0.267 0.355

[dok]

I added a wound chance table and listings for defense 0-6 for Iron Tough. Currently there are no figures that would use these new entries, but, y'know, just in case.

[yamissflash]

Had a epic battle last night, I told my opponent that we should look at your data tables to see wether Braxas should bite or breathe on a Phantom Knight. We went with the bite since it was .029 better. Since it worked, my opponent is now a believer in your tables!!!:D

Edit: In case you were wondering, after the last PK came Jotun. End of story.