## Quick-Contest Combat Stat Analysis

From: Ed King elk@atlas.cb.att.com

### DIE PERCENTAGES

```           1d            2d              3d
Roll  Chance Cum.   Chance  Cum.    Chance   Cum.
----------------------------------------------------
1:     17%  17%      0%    0%        0%     0%
2:     17%  33%      2%    2%        0%     0%
3:     17%  50%      5%    8%        0%     0%
4:     17%  67%      8%   16%        1%     1%
5:     17%  83%     11%   27%        2%     4%
6:     17% 100%     13%   41%        4%     9%
7:                  16%   58%        6%    16%
8:                  13%   72%        9%    25%
9:                  11%   83%       11%    37%
10:                   8%   91%       12%    50%
11:                   5%   97%       12%    62%
12:                   2%  100%       11%    74%
13:                                   9%    83%
14:                                   6%    90%
15:                                   4%    95%
16:                                   2%    98%
17:                                   1%    99%
18:                                   0%   100%

```

### ARMOR PIERCING ODDS

(That is, if you do X amount of damage, what are your odds of getting at least 1 point of damage through the DR? For higher damages, mentally increment the DR by one. e.g. doing 2 points against DR 0 has the same chance as doing 1 point against DR 1.)
```                        DR
Damage|  0  1   2   3   4   5   6   7   8
------+-----------------------------------
1d-3 | 50  33  17
1d-2 | 67  50  33  17
1d-1 | 83  67  50  33  17
1d   |100  83  67  50  33  17
1d+1 |100 100  83  67  50  33  17
1d+2 |100 100 100  83  67  50  33  17
1d+3 |100 100 100 100  83  67  50  33  17
1d+4 |100 100 100 100 100  83  67  50  33
1d+5 |100 100 100 100 100 100  83  67  50
1d+6 |100 100 100 100 100 100 100  83  67
2d-3 | 91  83  72  58  41  27  16   8   2
2d-2 | 97  91  83  72  58  41  27  16   8
2d-1 |100  97  91  83  72  58  41  27  16
2d   |100 100  97  91  83  72  58  41  27
2d+1 |100 100 100  97  91  83  72  58  41
2d+2 |100 100 100 100  97  91  83  72  58
2d+3 |100 100 100 100 100  97  91  83  72
2d+4 |100 100 100 100 100 100  97  91  83
2d+5 |100 100 100 100 100 100 100  97  91
2d+6 |100 100 100 100 100 100 100 100  97
3d-3 |100  99  98  95  90  83  74  62  50
3d-2 |100 100  99  98  95  90  83  74  62
3d-1 |100 100 100  99  98  95  90  83  74
3d   |100 100 100 100  99  98  95  90  83
3d+1 |100 100 100 100 100  99  98  95  90
3d+2 |100 100 100 100 100 100  99  98  95
3d+3 |100 100 100 100 100 100 100  99  98
3d+4 |100 100 100 100 100 100 100 100  99
3d+5 |100 100 100 100 100 100 100 100 100```

### Attack/Defense Odds

(Odds of scoring a hit using the normal attack/defend rules.)

``` A|                     Effective Attack Skill
D|  3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18
+---------------------------------------------------------------
3|  0   0   2   7  14  23  35  47  60  71  81  88  90  91  92  93
4|  0   0   2   7  14  23  35  47  59  70  80  87  89  90  91  92
5|  0   0   2   7  13  22  34  45  57  68  78  84  86  87  88  89
6|  0   0   2   6  13  21  32  43  55  65  74  80  82  83  84  85
7|  0   0   2   6  12  20  29  40  50  60  68  74  76  77  78  78
8|  0   0   2   5  10  17  26  35  44  53  60  65  67  68  69  69
9|  0   0   1   4   8  15  22  30  37  45  51  55  56  57  58  58
10|  0   0   1   3   7  12  17  24  30  36  40  44  45  46  46  46
11|  0   0   1   2   5   9  13  18  22  27  30  33  34  34  35  35
12|  0   0   0   1   3   6   9  12  15  18  21  23  23  24  24  24
13|  0   0   0   1   2   3   5   7   9  11  13  14  14  15  15  15
14|  0   0   0   0   1   2   3   4   5   6   7   8   8   8   8   8
15|  0   0   0   0   0   1   1   2   2   3   3   4   4   4   4   4
16|  0   0   0   0   0   0   0   0   1   1   1   1   1   1   1   1
17|  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
18|  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0 ```

### Quick Contest Odds

(That is, given your skill & your opponent, what are the odds of you winning a quick contest. This chart may seem a little skewed, but that is because it takes into account the possibility of a crit by either opponent.)

```                                  Your skill

3   4   5   6    7    8    9   10   11   12   13   14   15   16   17   18
+---------------------------------------------------------------------------
3|0.5 1.8 4.6 9.2 16.0 25.6 37.0 49.3 61.5 72.9 82.4 89.2 93.7 96.5 97.9 98.3
4|0.5 1.8 4.6 9.2 16.0 25.6 37.0 49.3 61.5 72.9 82.4 89.2 93.8 96.6 97.9 98.3
5|0.5 1.8 4.5 9.0 15.8 25.3 36.6 48.9 61.2 72.6 82.2 89.1 93.7 96.5 97.9 98.3
6|0.5 1.8 4.4 8.7 15.3 24.6 35.8 48.0 60.2 71.7 81.4 88.5 93.3 96.3 97.8 98.3
7|0.5 1.8 4.2 8.2 14.5 23.4 34.3 46.2 58.4 69.9 79.8 87.2 92.4 95.7 97.5 98.2
8|0.5 1.8 3.9 7.6 13.4 21.7 32.0 43.6 55.5 67.0 77.1 85.0 90.7 94.5 96.7 97.8
9|0.5 1.8 3.6 6.8 11.9 19.5 28.9 39.8 51.4 62.7 73.1 81.5 87.9 92.5 95.4 97.0
10|0.5 1.8 3.2 5.9 10.3 16.8 25.3 35.2 46.1 57.2 67.6 76.5 83.8 89.4 93.2 95.6
11|0.5 1.8 2.9 5.0  8.5 13.9 21.1 29.9 39.9 50.4 60.8 70.2 78.3 85.0 89.9 93.4
12|0.5 1.8 2.6 4.1  6.8 11.0 16.9 24.4 33.2 42.9 52.9 62.6 71.5 79.1 85.3 90.0
13|0.5 1.8 2.3 3.3  5.2  8.3 12.9 18.9 26.4 35.1 44.5 54.1 63.4 71.9 79.4 85.4
14|0.5 1.8 2.1 2.7  4.0  6.1  9.4 14.1 20.1 27.5 36.0 45.1 54.5 63.7 72.1 79.4
15|0.5 1.8 2.0 2.3  3.0  4.4  6.7 10.0 14.6 20.6 27.9 36.3 45.4 54.9 63.8 72.1
16|0.5 1.8 1.9 2.1  2.4  3.2  4.6  6.9 10.2 14.8 20.8 28.1 36.6 45.9 54.9 63.8
17|0.5 1.8 1.9 1.9  2.1  2.5  3.3  4.7  6.9 10.3 14.9 20.8 28.5 37.4 45.9 54.9
18|0.5 1.8 1.8 1.9  1.9  2.1  2.5  3.3  4.7  6.9 10.3 14.9 21.6 29.7 37.4 45.9```

### APPLICATION

OK, what are your odds of hurting someone in plate mail?

1. Find your odds of hitting them (use appropriate chart, above).
2. Find your odds of doing them any damage (see armor piercing chart).
3. Multiply the two numbers.
4. Divide by 100.

Example: George has sword skill of 16 (15 in plate), PD 4, DR6. After modifiers, his total parry is 16. He does 2d+1 damage on a swing.

Evaine has rapier skill of 17; PD5, DR1. After modifiers, her parry is 16. She does 1d damage with it.

George's chance's of hitting Evaine AND DOING DAMAGE (under quick contest rules) are 36.6*100/100 == 36.6%. Under the normal rules, his odds of doing damage are: 1*100/100 == 1%.

Evaine's chances of hitting George AND DOING DAMAGE are 0 for a torso shot. If she takes an eyeslit shot, she can get it to 2.4%. Those are the quick contest rules. Under the standard rule set, her odds are still 0 for a torso shot. (Hitting doesn't matter if you can't penetrate the armor!) Her odds for an eyeslit shot are also 0 (OK, less than 1%).