Let's say you're adventuring, and you run into a nasty encounter that leaves your party with injuries. Maybe even a dead PC. Or you've just been unlucky and had so many encounters that although no single one of them has done much harm to the PCs, you're starting to be ground down by sheer numbers. Eventually, you're going to need to rest, so that your characters can get that sweet, sweet natural healing (and so the spellcasters can regain spells).
The problem, though, is that you have to decide whether to stop and make camp, or to press through the fatigue and worry until you can make it back to town or some other known-to-be-safe location.There's a risk assessment involved: How likely is it that you'll encounter something? How dangerous is the encounter likely to be? How disruptive will the encounter be, regardless of whether it's dangerous (if you camp and a random encounter disturbs the party's sorcerer while she's trying to sleep, for example, is it going to hinder you from being on time for something)? Some of these questions are impossible to answer if you're not the DM, but you can guess at others. The likelihood of having a random encounter is somewhat predictable. Either it's nil, which certainly is a possibility depending on the DM, or it's a percentile chance. Assuming that your DM uses the Core Rules as a guideline for this, the chance of having a random encounter is as follows:
|Type of Area||d% Chance|
|Desolate/wasteland||5% chance per hour|
|Frontier/wilderness||8% chance per hour|
|Verdant/civilized area||10% chance per hour|
|Heavily traveled||12% chance per hour|
Based on these percentile chances, you can calculate how likely you are to have at least one encounter over a given span of time. To do that, first turn each % chance into a decimal, and subtract it from 1. So a 12% hourly chance becomes 0.88, for example. This number represents the failure chance for a random encounter. That is, it represents the likelihood that you will NOT experience the event. Raise this number to an exponential power equal to the number of hours that you expect to travel or camp. If you're going to travel for four hours through a heavily-traveled region, that'd be 0.884 = 0.5997, just for example. Once you have done this, subtract the result from 1, and restate the difference as a percentage—40.03%—to determine your overall chance of having at least one encounter during the four hours of travel. No matter the length of time or the likelihood of having an encounter, this method always produces a chance of encounter that is less than 100% but greater than 0%. To state the procedure as an algorithm that you can use anywhere you like, it's this:
p = is the encounter chance per hour, expressed as a positive number greater than 0 but less than 1
We need to produce a chance of "failure," from this variable. So
x = 1 - p
gives us a "no encounter" chance per hour, and
y = # of hours
allows us to calculate
z = xy
the total "no encounter" chance, and use that to get
n = 1 - z
the chance of an encounter during a period of hours at a given chance per hour, by solving for n.
There are a couple of things you can do with the output of this procedure. One of them is to calculate the chance that something's going to pop up during the eight hours or so that your characters are trying to rest. I'm a nice guy, so I'll just go ahead and provide that for you.
|Type of Area||d% Chance|
|Desolate/wasteland||34% chance per eight hours|
|Frontier/wilderness||49% chance per eight hours|
|Verdant/civilized area||57% chance per eight hours|
|Heavily traveled||64% chance per eight hours|
Now, it's admittedly possible that your DM is using some other method of tracking the chance of having an encounter. That's something I can't help with; we can't conjecture about whatever non-standard system might have been cooked up by one person acting on his or her own. The technique I've shown here also doesn't do much to indicate the possibility that you might experience more than one encounter within a specified period of time. All it does is show you the chance that you're going to make it through a given period without being disturbed. Since the "rest" and "fatigue" mechanics for D&D v3.5 both are tied to eight-hour increments, this second chart is widely useful to players because it allows you to make a rational forecast of your chances of surviving a trip to town versus a night in the open.
There are a couple of caveats to think over, though. First, it's possible that your DM has certain encounters that only happen if you're sitting still, or only happen if you're traveling. For example, you'll almost never encounter a web-spinning spider in my games if you're sitting still; they're ambush predators that stay with their webs. They aren't moving around, so if you're camped you can't encounter one. And in similar vein, a dryad is compelled to remain within a fixed distance from her tree. If she leaves, she dies, so encountering her demands that you pass through the area surrounding the arbor in question. That's not laid out in the Core Rules, or anything, but it's something that I think makes sense.
Second, these tables don't take into account the possibility that you've done things that either make you harder to find (thereby reducing the chance of having an encounter) or make you easier to find (raising the chance). Again, this isn't something that the Core Rules take into account, but your DM might nudge the percentile chance for an encounter up or down, ad hoc, to reflect the fact that you're moving more slowly than normal in order to hide and move silently, or because you've decided to camp on a hilltop and light a bonfire.
These percentile chances also are based on the proposition that you're spending the entire time within a single type of area. That is, you're not moving from a "heavily traveled" to a "desolate/wasteland" region. That's fine if you're camping, but if you're traveling for a whole day, it's entirely possible that you're crossing boundaries between one or more categories. Let's say that you travel for two hours through a heavily traveled region (a major road) and then turn off into a desolate/wasteland area (a haunted forest) and travel for three additional hours. The "no encounter" procedure yields 0.774 for the road and .857 for the forest, which you then multiply to get 0.663, and subtract from 1 to get 33.7%. The algorithm here, for general use, is as follows.
N = 1 - (z1 * z2)
We solve for N with the understanding that z1 and z2 are "no encounter" chances for two periods where the value of p, from our previous algorithm, are distinct and the value of y may also be distinct. In the long form, our example with the road and haunted forest works out like so.
p1 = 0.12
p2 = 0.05
x1 = 1 - p1 = 0.88
x2 = 1 - p2 = 0.95
y1 = 2
y2 = 3
z1 = x1y1 = 0.882 = 0.774
z2 = x2y2 = 0.953 = 0.857
N = 1 - (z1 * z2) = 1 - (0.882 * 0.953) = 1 - 0.663 = 0.337 = 33.7%
This method works with any number of different percentile chances for encounter, over any length of time. You can adapt it to lots of other situations, too. Concealment, stabilization, and anything else that involves multiple attempts with a d% chance of success/failure are all susceptible to analysis by this same process. You also can use it anytime you can reduce a d20, d12, d6, or any other die to a percentile chance. That's a little outside of the scope of this discussion, but it's useful if you're a DM trying to gauge the risks of an encounter you're planning for a given set of PCs.
Anyway, it's really not that hard to figure out how likely you are to experience a random encounter, if you know roughly what kind of area you're in and how long you'll be in it. Most of the time, at least if your PC is not lost, your DM is going to be able and willing to tell you how far you are from a given place. And you know that if you rest, it's going to be for a minimum of eight hours. So most of the time, you (as a player) can easily calculate your chances of having at least one encounter.
This is metagaming, of course, unless your character knows enough about the locale and its geography to have some idea how much traffic moves through it. Unfortunately, the Core Rules don't have much to say about how to determine whether a PC has that information. I'm inclined to say that Survival is the skill that best suits this task, because it's what you use to avoid getting lost, it's applicable to any environment, and it's synergized by Knowledge (dungeoneering), (geography), and (planes) depending on whether you're trying to find your way through an underground, aboveground, or extraplanar environment. But I also am willing to consider that Knowledge (geography), Knowledge (dungeoneering), or Knowledge (planes) might also be acceptable as alternatives, especially if they apply at a penalty compared to Survival. Knowledge skills, when you get down to it, are concerned with either handing out plot tokens or with administrating the flow of metagame knowledge into the PCs' decision-making. So it seems clear to me that there's a basis for using them. I'd be interested in hearing what other people think. I'm also not really sure where to set a DC for this check, regardless of the skill being used.
The other half of assessing the risks of camping versus running back to town is that you may not have a lot of information about the nature of the threats that face you when you're in the open. If the DM is just building his random encounter tables by throwing everything that could possibly live in an environment onto the table, giving it a % chance to show up, and assigning a whatever-sided die to determine how many you encounter, it's unlikely that even he is going to know how dangerous it is for you to stay out, much less for him to dole out a threat assessment to a PC who ought to have enough knowledge to be able to make informed decisions. Again, I feel as if Survival or Knowledge skills ought to allow something like this to take place, but it's not something that's addressed well by the Core Rules, even though it probably ought to be.