## Charts to Handle Semi-Mass-Combat

by Steffan O'Sullivan
Updated 5-02-89

There are times when you have to make a lot of die rolls. Sometimes this is no problem, sometimes it's a pain. For those times when it's a pain, the following three charts are offered.

First of all, credit: this is modified for GURPS from a September, 1986, Dragon (tm) magazine article called "One roll, to go," by Larry Church. He wrote the charts for d20 use; I merely took the idea and did the math to create them for 3d6. He used percentile dice for these charts, which would make a lot more sense, but I've stuck to 3d6, as I believe GURPS works better with less clutter. He does give a lot more "How to use" than I do, and I recommend you read the article if my description is too brief.

Okay, now what are these charts? They are the odds of rolling a number of successes, given 5 or 10 or 20 rolls at the same odds. Thus, one die roll will give you how many out of 10 bullets hit, for example. I have only made three charts, one for computing 5 rolls, one for computing 10 rolls, and one for computing 20 rolls. Thus, 35 shots at the same skill could be done in 3 rolls: one on the 20-roll chart, one on the 10-roll chart, and one on the 5-roll chart. 33 shots would actually take more rolls: one on the 20-roll chart, one on the 10-roll chart, and 3 individual shots. You could make one for 100-rolls if you were a masochist – I'll pass, thanks.

To use them, it is assumed that all the Effective Skill or Attribute levels are the same. Look across the top of the chart to the correct Effective Skill level. If you're shooting 10 bullets, and your effective skill is 12, for example, go across to the 12 column in the "10 rolls" chart. Then roll 3d6. Look down the column until you see the number you rolled, or the next highest if it's not on there. Read across to the left, and the result is the number of bullets that hit the target. If the die roll is larger than the largest number in the column, all rolls missed. In the above example, if a 12 is rolled, reading across we see that 7 bullets hit the target; if you rolled a 16, only 5 bullets hit the target. Voila! 10 die rolls resolved in one roll!

There are two special cases: when you roll a 3 or an 18. These are NOT treated as criticals, by the way. You have to roll again in each case. For example, if you have 10 archers firing at the party, all at effective skill 8, and you roll a 3, you'll notice that there are four 3's in the 8 column. Which one do you use? What that means is that 7 of the archers definitely hit – you have to roll again for the other three. They MAY have hit. If you have more archers yet to fire, add three to their number – otherwise roll three times against a skill of 8. The general rule for rolling a 3: read across the chart from the 3 closest to the bottom of the chart – that many rolls succeeded for certain. Count the number of 3's in the chart and subtract 1 (or you could say count the number of 3's left – same thing) – that many more rolls MAY hit: roll again.

For 18s, it is similar, but with a slight difference. If the 10 archers' skill were 12, and you rolled an 18, look down and read the 18 closest to the top of the chart – in this case, reading across we get a 4. That means that AT THE MOST 4 archers hit the target, you have to reroll for ALL of them, as they may have all missed. Count the number of 18's in the column, and reroll for that many (not that number minus one, as for 3).

I have NOT figured any critical hits or misses into the charts. When doing large numbers of rolls, you could simply ignore the possibility, or assign them straight by the numbers: 1.9% chance of either, unless skill is 15+ or abysmally low. That means roughly one out 50 rolls for each – I'd ignore them below that.

If you have any questions, post them on the general GURPS board, ask me, or look up the Dragon (tm) article. The math is pretty straightforward probability theory, and I used a spreadsheet to calculate it, double-checking my formulae and checking against his results, so it should be accurate. I did round off sometimes, but usually required the more difficult number. For example, there were a number of times when the percentage was 62.3% – obviously I rounded that up to an 11. But a 57% I went ahead and required a 10 to get. This is where it becomes clear that percentile dice are better for this sort of thing.

```5 Rolls:                Effective Skill or Attribute Level:
\  3    4    5    6    7    8    9   10   11   12   13   14   15   16
Hits:  \--------------------------------------------------------------------
5  \  3    3    3    3    3    3    4    4    6    7    9   11   12   14
4  \  3    3    3    3    3    4    5    7    9   11   12   14   16   18
3  \  3    3    3    4    4    6    8   10   12   14   15   17   18   18
2  \  3    3    4    5    7    9   11   12   14   16   18   18   18   18
1  \  4    6    7    9   10   12   14   15   17   18   18   18   18   18

10 Rolls:               Effective Skill or Attribute Level:
\  3    4    5    6    7    8    9   10   11   12   13   14   15   16
Hits:  \-------------------------------------------------------------------
10  \  3    3    3    3    3    3    3    3    4    5    7    9   11   13
9  \  3    3    3    3    3    3    3    4    5    8   10   12   14   17
8  \  3    3    3    3    3    3    4    5    7   10   12   15   17   18
7  \  3    3    3    3    3    3    5    7    9   12   15   17   18   18
6  \  3    3    3    3    3    4    6    9   11   14   17   18   18   18
5  \  3    3    3    3    4    6    8   11   13   16   18   18   18   18
4  \  3    3    3    4    5    8   10   13   15   17   18   18   18   18
3  \  3    3    4    5    7   10   12   15   17   18   18   18   18   18
2  \  3    4    6    8   10   12   14   17   18   18   18   18   18   18
1  \  5    7    9   11   13   15   17   18   18   18   18   18   18   18

20 Rolls:               Effective Skill or Attribute Level:
\  3    4    5    6    7    8    9   10   11   12   13   14   15   16
Hits:  \-------------------------------------------------------------------
20  \  3    3    3    3    3    3    3    3    3    3    4    7    9   11
19  \  3    3    3    3    3    3    3    3    3    4    6    9   12   15
18  \  3    3    3    3    3    3    3    3    4    5    9   12   15   17
17  \  3    3    3    3    3    3    3    3    4    7   11   14   17   18
16  \  3    3    3    3    3    3    3    4    5    9   12   15   18   18
15  \  3    3    3    3    3    3    3    4    7   10   14   17   18   18
14  \  3    3    3    3    3    3    3    5    8   12   15   18   18   18
13  \  3    3    3    3    3    3    3    6   10   13   17   18   18   18
12  \  3    3    3    3    3    3    4    8   11   15   18   18   18   18
11  \  3    3    3    3    3    3    5    9   13   16   18   18   18   18
10  \  3    3    3    3    3    4    7   10   14   17   18   18   18   18
9  \  3    3    3    3    3    5    8   12   15   18   18   18   18   18
8  \  3    3    3    3    3    6   10   13   17   18   18   18   18   18
7  \  3    3    3    3    4    8   11   15   18   18   18   18   18   18
6  \  3    3    3    3    5    9   13   16   18   18   18   18   18   18
5  \  3    3    3    4    7   11   14   17   18   18   18   18   18   18
4  \  3    3    4    6    9   12   15   18   18   18   18   18   18   18
3  \  3    3    5    8   11   14   17   18   18   18   18   18   18   18
2  \  3    5    8   10   13   16   18   18   18   18   18   18   18   18
1  \  5    8   11   13   15   17   18   18   18   18   18   18   18   18
```

Note: "Hits" should actually be "Successes", but Hits fits better.