Random Encounter Tables: Second Thoughts (Heavy Lifting)

I had some Second Thoughts about Random Encounter Tables.  Erik Tenkar likes using three dice for his random encounter tables because he likes the curve, and planned to have deliberate, potentially large gaps in the table so he could combine the random encounter check (determine whether there is one) and the encounter selection (determine what the encounter is).  That’s fair enough.

It’s not to my taste, though.  I have historically preferred two dice, usually mismatched, because of the ‘pyramid curve’ they give me.  However, as described in the Second Thoughts post yesterday I think there might be a better way.  Use three dice but have one of them, in addition to adding to the roll to determine the encounter also be used to determine an encounter modifier.

This feels pretty good, and has some good possibilities.  However, I like to back these things up with numerical analysis to make sure that it makes sense.

Math happens, but it’s mostly tables.  I can provide spreadsheets if anyone is really interested.

Frequency Analysis

As normal for this sort of thing, I’m going to do some frequency analysis to see what I can expect from this.

I’m going to look first at d8+d10+d12.  This has a curve very close to that of 3d10, but not exactly the same.

Total	960	100.00	1000	100.00
Value	d8+d10+d12	d8+d10+d12 %	3d10	3d10 %
3	1	0.10	1	0.10
4	3	0.31	3	0.30
5	6	0.63	6	0.60
6	10	1.04	10	1.00
7	15	1.56	15	1.50
8	21	2.19	21	2.10
9	28	2.92	28	2.80
10	36	3.75	36	3.60
11	44	4.58	45	4.50
12	52	5.42	55	5.50
13	59	6.15	63	6.30
14	65	6.77	69	6.90
15	69	7.19	73	7.30
16	71	7.40	75	7.50
17	71	7.40	75	7.50
18	69	7.19	73	7.30
19	65	6.77	69	6.90
20	59	6.15	63	6.30
21	52	5.42	55	5.50
22	44	4.58	45	4.50
23	36	3.75	36	3.60
24	28	2.92	28	2.80
25	21	2.19	21	2.10
26	15	1.56	15	1.50
27	10	1.04	10	1.00
28	6	0.63	6	0.60
29	3	0.31	3	0.30
30	1	0.10	1	0.10

Looking more closely, at this point there is little practical difference between them.  What I’m going to say for the next bit will likely have very close to the same effect on 3d10 if you select a ‘d10 Dragon Die’, as Dragon Age has a d6 Dragon Die.

One of the things I didn’t care for with Erik’s planned solution was the large gaps in the table, and that tweaking the frequencies for non-encounters and the like depends on knowing the frequencies for the multiple-die rolls.  Many of use are fairly familiar with 3d6 (after years or decades of D&D), but how many are familiar with 3d8, 3d10, or 3d12?

Going to a single encounter modifier die makes the modifications much easier to predict, because single-die value frequencies are linear.

• d8 has 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, 1 (or 12.5%, 25%, 37.5%, 50%, 6.25%, 75%, 87.5%, 100%).  Off the top of my head, dead easy.
• d10… I won’t insult anyone by describing the value frequencies.
• d12, on the other hand, has some interesting characteristics.  It handles many of the common fractions: 1/12, 1/6, 1/4, 1/3, 5/12, 1/2, 7/12, 2/3, 3/4, 5/6, 11/12, 1 — only three that cannot be simplified into common fractions.  These are 8.33%, 16.67%, 25%, 33.33%, 41.67%, 50%, 58.33%, 66.67%, 75%, 83.33%, 91.67%, 100%… funky percentages, I really like the fractions better.

For the following sections I’m going to pretend the encounters are all creature encounters — ‘wandering monsters’, if you want — for the sake of simplicity.

d10 Encounter Modifier Die

Let’s start with the easiest frequency set, d10.  I can imagine having four distinct frequency modifiers — evidence only (you don’t see the encounter itself, but you see where it happened, or have some other clue of its presence or potential presence), reduced (less dangerous — the creature is wounded, underequipped (caster is mostly without spells), fewer in number than usual), normal (standard encounter of this type, or mutually-balanced modifications such as small numbers but waiting in ambush), and enhanced (more creatures than usual, better gear, waiting in ambush, and so on).  If the encounter table is arranged from least threat to greatest threat you can have the highest numbers being out of the PCs’ capability (sufficient for TPK, say) and the lowest mere nuisances.  If you then assign 1-4 on the d10 to enhanced encounters, 5-7 to regular encountesr, 8-9 to reduced encounters, and 10 to evidence only you get some interesting characteristics.

First, the weaker the threat on the table, the more likely it will be enhanced.  In fact, it will be impossible for anything in the first four slots on the table to not be enhanced (the only ways you can roll 6 or less requires that the d10 be no higher than four).  Similarly, you can only find evidence of the greatest threat on the table (the only way you can roll a 30 requires a 10 on the d10).  What else happens, though?

Total	960	40.00	30.00	20.00	10.00	100.00
Value	d8+d10+d12	Enhanced	Standard	Reduced	Evidence	Frequency
3	1	0.10				0.10
4	3	0.31				0.31
5	6	0.63				0.63
6	10	1.04				1.04
7	15	1.46	0.10			1.56
8	21	1.88	0.31			2.19
9	28	2.29	0.63			2.92
10	36	2.71	0.94	0.10		3.75
11	44	3.02	1.25	0.31		4.58
12	52	3.23	1.56	0.52	0.10	5.42
13	59	3.33	1.88	0.73	0.21	6.15
14	65	3.33	2.19	0.94	0.31	6.77
15	69	3.23	2.40	1.15	0.42	7.19
16	71	3.02	2.50	1.35	0.52	7.40
17	71	2.71	2.50	1.56	0.63	7.40
18	69	2.29	2.40	1.67	0.73	7.19
19	65	1.88	2.19	1.67	0.83	6.77
20	59	1.46	1.88	1.67	0.83	6.15
21	52	1.04	1.56	1.67	0.83	5.42
22	44	0.63	1.25	1.56	0.83	4.58
23	36	0.31	0.94	1.35	0.83	3.75
24	28	0.10	0.63	1.15	0.73	2.92
25	21		0.31	0.94	0.63	2.19
26	15		0.10	0.73	0.52	1.56
27	10			0.52	0.42	1.04
28	6			0.31	0.31	0.63
29	3			0.10	0.21	0.31
30	1				0.10	0.10

40% of all encounters are enhanced, 30% of all encounters are standard, 20% are reduced, and 10% are evidence only.  However, things are weighted such that the greater the (base) threat, the less likely the PCs are going to run into it at full strength.  It is still possible!  There is a slim chance that they could run into a ‘slot 24’ threat that has been enhanced… but only very slightly more than 0.1% of the time (a little bit is lost in the rounding).

Assuming the threat is ‘level appropriate’ in the 16-17 range (middle of the table), then the most common overall is a few slots below that but enhanced, normal encounters are most common right there, reduced encounters are slightly higher, and evidence only are a little higher yet.

This appears to exhibit the behavior I predicted.  I’m mildly surprised at how small some of these numbers are, but I suppose I shouldn’t be — there are some 112 distinct entries here.

For more fun you could have each cell be an entirely different encounter… but I wouldn’t.  On ‘enhanced’ you find the BBEG with an ally or most of his retainers, ‘standard’ you find him with his usual group of hangers-on, ‘reduced’ you find him alone or injured or out of spells, and evidence you find that he was here and there’s nothing left but the desiccated corpses of his enemies.

Okay, let’s see what happens if we use the d8 as the encounter modifier.

d8 Encounter Modifier Die

Less explanation this time.  Let’s say that 3/8 the encounter is enhanced, 2/8 the encounter is normal, 1/8 the encounter is reduced, and 2/8 the encounter is evidence only.

Total	960	37.50	25.00	12.50	25.00	100.00
Value	d8+d10+d12	Enhanced	Standard	Reduced	Evidence	Frequency
3	1	0.10				0.10
4	3	0.31				0.31
5	6	0.63				0.63
6	10	0.94	0.10			1.04
7	15	1.25	0.31			1.56
8	21	1.56	0.52	0.10		2.19
9	28	1.88	0.73	0.21	0.10	2.92
10	36	2.19	0.94	0.31	0.31	3.75
11	44	2.50	1.15	0.42	0.52	4.58
12	52	2.81	1.35	0.52	0.73	5.42
13	59	3.02	1.56	0.63	0.94	6.15
14	65	3.13	1.77	0.73	1.15	6.77
15	69	2.81	1.98	0.83	1.35	7.19
16	71	2.50	2.08	0.94	1.56	7.40
17	71	2.19	2.08	1.04	1.77	7.40
18	69	1.88	1.98	1.04	1.98	7.19
19	65	1.56	1.77	1.04	2.08	6.77
20	59	1.25	1.56	0.94	20.8	6.15
21	52	0.94	1.35	0.83	1.98	5.42
22	44	0.63	1.15	0.73	1.77	4.58
23	36	0.31	0.94	0.63	1.56	3.75
24	28	0.10	0.73	0.52	1.35	2.92
25	21		0.52	0.42	1.15	2.19
26	15		0.31	0.31	0.94	1.56
27	10		0.10	0.21	0.73	1.04
28	6			0.10	0.52	0.63
29	3				0.31	0.31
30	1				0.10	0.10

Again the predicted percentages happen.  Each slot is as likely to come up as before (as could be expected), and the odds of (enhanced, standard, reduced, evidence) is as predicted.  Again, the higher the encounter slot, less likely it will be enhanced and the more likely it will be reduced or evidence only.

… I really like that ‘evidence only’ idea.  Thanks Chakat Firepaw!

One last table, for completeness, but I am fairly confident in the outcome.

d12 Encounter Modifier

In fact, I’m confident enough that I think I’ll mix things up a bit.  I’m using a d12 encounter modifier, with (1, 5, 9) being enhanced, (4, 8, 12) being normal, (2, 6, 10) being reduced, and (3, 7, 11) being evidence only.

Note that I am unlikely to do this for real, I just want to see what happens.

Total	960	25.00	25.00	25.00	25.00	100.00
Value	d8+d10+d12	Enhanced	Standard	Reduced	Evidence	Frequency
3	1	0.10				0.10
4	3	0.21		0.10		0.31
5	6	0.31		0.21	0.10	0.63
6	10	0.42	0.10	0.31	0.21	1.04
7	15	0.63	0.21	0.42	0.31	1.56
8	21	0.83	0.31	0.63	0.42	2.19
9	28	1.04	0.42	0.83	0.63	2.92
10	36	1.25	0.63	1.04	0.83	3.75
11	44	1.46	0.83	1.25	10.4	4.58
12	52	1.67	1.04	1.46	1.25	5.42
13	59	1.77	1.25	1.67	1.46	6.15
14	65	1.88	1.46	1.77	1.67	6.77
15	69	1.88	1.67	1.88	1.77	7.19
16	71	1.88	1.77	1.88	1.88	7.40
17	71	1.77	1.88	1.88	1.88	7.40
18	69	1.67	1.88	1.77	1.88	7.19
19	65	1.46	1.88	1.67	1.77	6.77
20	59	1.25	1.77	1.46	1.67	6.15
21	52	1.04	1.67	1.25	1.46	5.42
22	44	0.83	1.46	1.04	1.25	4.58
23	36	0.63	1.25	0.83	1.04	3.75
24	28	0.42	1.04	0.63	0.83	2.92
25	21	0.31	0.83	0.42	0.63	2.19
26	15	0.21	0.63	0.31	0.42	1.56
27	10	0.10	0.42	0.21	0.31	1.04
28	6		0.31	0.10	0.21	0.63
29	3		0.21		0.10	0.31
30	1		0.10			0.10

… I suppose in retrospect I shouldn’t be surprised at all by these results.  Having equal percentages for each group resulting in them having the same curves, just slightly shifted, should have been obvious.  More interesting distributions might have been (4, 2, 1, 5) or (3, 6, 1, 2).

Closing Comments

This is a far from exhaustive examination, but it appears that using three different dice like this provides some very broad possibilities.  Applying only one of the dice as a modifier die makes it very easy to get the math right.  Despite the funkiness of some of the percentages above, a single die is going to have linear frequency per value so it is very easy to predict what percentage of encounters will be attached to each modifier.  Careful selection of the specific values used let you tune the final result so it has desired characteristics, such as enhancing lesser threats more than greater threats, and reducing greater threats, possibly to ‘evidence only’ so the PCs see the threat exists without having it bite their legs off.

Between having lots of slots for different encounters and applying one of the dice (I think it doesn’t really matter which one, so pick the one that provides the fractions you like) as an encounter modifier die you can produce a remarkable range of encounters, all off the same table.  In many cases the encounter modifiers can be done on the fly (enhancement might be ‘more monsters’, ‘ambush’, or even as simple as “+2 attack bonus and +2 damage”, or even just “full, maximum hit points”.  I don’t see a need to get tricky here.

Or enhancement by rolling again for another creature type, or even just removing the encounter modifier die and applying that one as an allied standard encounter.  A reduced encounter could be done the same way, but the two encounter types are in conflict.  You roll a 4, a 6 and an 8, for a reduced ‘slot 18’ — they’re fighting whatever is in slot 10.  Or, if the 4 is the modifier, they are allied with ‘slot 14’.

I now feel an urge to see if there is some way I can treat each die as a modifier of some kind, without resulting in my brains dribbling out my ears.  I’m almost considering something like ‘sum of dice is the base encounter, one die is number of creatures or DC of trap or whatever, one die is (enhanced, normal, reduced, evidence), and one die is something else’.  This might be overthinking the problem, or maybe I’ve just found a hammer and am looking for nails.

As written right now, this looks like this could be a very powerful tool in the hands of a GM who likes winging things.

Ehehehexcellent.

… Crap.  Erik’s going to see this, and he’s running us through some ACK starting in a couple of weeks.  What have I done?