There are several warcasters/warlocks in Warmahordes that modify dice rolls using feats, spells, and abilities. I'll try and cover all of them (except for Calandra's feat, because I can't figure out an easy way to calculate that!).
First of all, we'll do the most common, which is: Roll an additional dice for attack and/or damage; Drop the lowest. Both pVlad and eVlad have this, as well as eThagrosh. Just a comment on the below graphs: the V in the first column stands for Value, the second column is the probability to roll exactly the displayed value, the third column is the probability to roll the displayed value or higher.
3d6, drop lowest
V % = % ≥
2 0.463 100.000
3 1.389 99.537
4 3.241 98.148
5 5.556 94.907
6 8.796 89.352
7 12.500 80.556
8 15.741 68.056
9 16.667 52.315
10 15.741 35.648
11 12.500 19.907
12 7.407 7.407
Average = 8.45
4d6, drop lowest
This accounts for the ability to boost under the effects.
V % = % ≥
3 0.077 100.000
4 0.309 99.923
5 0.772 99.614
6 1.620 98.843
7 2.932 97.222
8 4.784 94.290
9 7.022 89.506
10 9.414 82.485
11 11.420 73.071
12 12.886 61.651
13 13.272 48.765
14 12.346 35.494
15 10.108 23.148
16 7.253 13.040
17 4.167 5.787
18 1.620 1.620
Average = 12.24
4d6, drop two lowest
Next up we have the situation of: roll an additional two dice, drop the two lowest. This happens with Drago under pVlad's Signs and Portents, Drago under eVlad's Hand of Fate, and Ashlynn's feat (not the chance of a crit, however).
V % = % ≥
2 0.077 100.000
3 0.309 99.923
4 1.157 99.614
5 2.469 98.457
6 5.015 95.988
7 8.333 90.972
8 13.194 82.639
9 17.284 69.444
10 20.139 52.160
11 18.827 32.022
12 13.194 13.194
Average = 9.34
5d6, drop two lowest
Next up is the above scenario, given the ability to boost.
V % = % ≥
3 0.013 100.000
4 0.064 99.987
5 0.193 99.923
6 0.527 99.730
7 1.157 99.203
8 2.186 98.045
9 3.807 95.859
10 6.044 92.052
11 8.552 86.008
12 11.330 77.456
13 13.567 66.127
14 14.853 52.559
15 14.288 37.706
16 12.024 23.418
17 7.845 11.394
18 3.549 3.549
Average = 13.43
3d6, drop highest
This one accounts for Calandra's spell, Star Crossed, which forces her enemy to roll an additional die to hit, and drop the highest.
V % = % ≥
2 7.407 100.000
3 12.500 92.593
4 15.741 80.093
5 16.667 64.352
6 15.741 47.685
7 12.500 31.944
8 8.796 19.444
9 5.556 10.648
10 3.241 5.093
11 1.389 1.852
12 0.463 0.463
Average = 5.54166666667
4d6, drop highest
Same as above, accounting for boosting.
V % = % ≥
3 1.620 100.000
4 4.167 98.380
5 7.253 94.213
6 10.108 86.960
7 12.346 76.852
8 13.272 64.506
9 12.886 51.235
10 11.420 38.349
11 9.414 26.929
12 7.022 17.515
13 4.784 10.494
14 2.932 5.710
15 1.620 2.778
16 0.772 1.157
17 0.309 0.386
18 0.077 0.077
Average = 8.75
4d6, drop two highest
Last of all, I'm going to cover the enemy portion of Ashlynn's feat, which is (most of the time) roll an additional two dice to hit, drop the two highest.
V % = % ≥
2 13.194 100.000
3 18.827 86.806
4 20.139 67.978
5 17.284 47.840
6 13.194 30.556
7 8.333 17.361
8 5.015 9.028
9 2.469 4.012
10 1.157 1.543
11 0.309 0.386
12 0.077 0.077
Average = 4.65
5d6, drop two highest
Again, same as above, accounting for boosting.
V % = % ≥
3 3.549 100.000
4 7.845 96.451
5 12.024 88.606
6 14.288 76.582
7 14.853 62.294
8 13.567 47.441
9 11.330 33.873
10 8.552 22.544
11 6.044 13.992
12 3.807 7.948
13 2.186 4.141
14 1.157 1.955
15 0.527 0.797
16 0.193 0.270
17 0.064 0.077
18 0.013 0.013
Average = 7.57
Many thanks go to the Troll dice roller, which I used to generate these results.
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