Chance of a wilderness encounter

[Kichwas]

I was looking at the wilderness encounter chances (pg 95), which are rolled per hour...

Should I make 24 rolls a day?

Lump them together into blocks?

Let's say I put them into 3 8 hour blocks, in the frontier wilderness there's now a 64% chance they'll encounter something every 8 hours.

Seems high...

Thoughts?

 

[James McMurray]

I was looking at the wilderness encounter chances (pg 95), which are rolled per hour...

Should I make 24 rolls a day?

Lump them together into blocks?

Let's say I put them into 3 8 hour blocks, in the frontier wilderness there's now a 64% chance they'll encounter something every 8 hours.

Seems high...

Thoughts?

It is definitely a bit high. But then again, the frontier wilderness in a world where dragons are the top of the food chain should be a fairly dangerous place. If you think it's too much, you could always drop the frequency of the rolls.

also, remember that an encounter doesn't always have to result in combat. The party could spot a band of rocs on the horizon (and not even recognize them for orcs), a dragon could just fly overhead rather than attack, etc.

 

[(Psi)SeveredHead]

You can even use a dance of giant eagles to be "poetry in motion", a merchant caravan, and so forth.

For some reason I don't have a problem posting on this computer.

 

[dcollins]

They are definitely too high, particularly if you use the standard mechanic of running wilderness encounters on a per-day (or even per 8-hour) basis. They should be revised downwards.

Notes:
- Mathemetically, if blocking them up, it's not correct to just sum them. More properly it's the inverse of the product of inverses. 8 hours in wilderness: not 64%, but rather 49%. (Although you should technically re-roll on success to look for multiples encounters.)

- By the rules it's not kosher to include something that you just see without having any effect on the party. It must be "a significant encounter... a monster, threat, or a challenge of some sort". Which reinforces the fact that the numbers are too high.

I still use 1st Ed. figures which check 3-6 times per day at a 1-in-10 to 1-in-20 chance each time. Much more playable.

 

[Kichwas]

Mathemetically, if blocking them up, it's not correct to just sum them. More properly it's the inverse of the product of inverses. 8 hours in wilderness: not 64%, but rather 49%. (Although you should technically re-roll on success to look for multiples encounters.)

So I want 'y' where:

For 8 hours with each hour at 8%:

1/y = 1/a * 1/b * 1/c

y in this case equals 16777216.

If I do an inverse of an inverse sum: 1/y = 1/a + 1/b + 1/c then y equals 1.

Where's the 49 come from?

Using my 64% idea I ended up with this for a 5 day trip into the woods:

Day by day:
Day 1: encounter 1700 hours (2 Gnolls).
Day 2: encounter at 0600 (ravens) and again at 2300 (Kobolds).
Day 3: encounter at 0800 (Miser Jackel) and noon (Giant).
Day 4: 0600 (Grippet), 1300 (Donkey), and 2400 (Orcs).
Day 5: encounter at 1500 (Owlbear) and 1700 (Ogres).

 

[WizWrm]

What dcollins means is this:

Say there's an 8% chance per hour for a random encounter. You can't just add them up, because once you hit 13 hours, that's more than 100% - and that's obviously not true, for two reasons. 1) You can't have more more than 100% probability of something, and 2) There's also still a chance you will NOT have had an encounter yet, which isn't being accounted for if you just add them up to over 100%.

So this is what you do:

Take the chance that there ISN'T an encounter that hour, which is 0.92. Multiply 0.92 times itself 8 times, for 8 hours.

0.92*0.92*0.92*0.92*0.92*0.92*0.92*0.92=0.5132887....

That number, 51.3%, is the chance you will NOT have an encounter in those eight hours. To figure out the chance you WILL have an encounter, just subtract that from 100%. Voila. About 49% chance for getting between one and eight encounters, and 51% for no encounters. There's a way to break it down to figure out the chance for exactly how many encounters, but it's simpler just to roll 8% eight times.

 

[Olgar Shiverstone]

Strictly speaking, an 8% chance per hour of an encounter leads to a binomial distribution in n hours. The chance of getting exactly x encounters in n hours is:

(n choose x) * (8%)^x * (92%) ^ (n-x)

which for n=8, x=1 works out to 35.7%.

Work that out for x=0, and subtract from one, and it is indeed 48.6% for at least one encounter in eight hours.

Work that out for different n and x and you can figure out the exact probability that you will have a certain number of encounters in a certain period. For example, in 24 hours, with an 8% chance of encounter per hour, the chance of having exactly x encounters is, the chance of having at least x encounters is, and the chance of having at most x encounters (note that rounding converts may to 0% or 100%):

x %ch of x % at least x % at most x
0 13.517857% 86.482143% 13.517857%
1 28.211180% 58.270962% 41.729038%
2 28.211180% 30.059782% 69.940218%
3 17.989738% 12.070044% 87.929956%
4 8.212707% 3.857337% 96.142663%
5 2.856594% 1.000744% 98.999256%
6 0.786598% 0.214145% 99.785855%
7 0.175885% 0.038260% 99.961740%
8 0.032501% 0.005760% 99.994240%
9 0.005024% 0.000735% 99.999265%
10 0.000655% 0.000080% 99.999920%
11 0.000073% 0.000007% 99.999993%
12 0.000007% 0.000001% 99.999999%
13 0.000001% 0.000000% 100.000000%
14 0.000000% 0.000000% 100.000000%
15 0.000000% 0.000000% 100.000000%
16 0.000000% 0.000000% 100.000000%
17 0.000000% 0.000000% 100.000000%
18 0.000000% 0.000000% 100.000000%
19 0.000000% 0.000000% 100.000000%
20 0.000000% 0.000000% 100.000000%
21 0.000000% 0.000000% 100.000000%
22 0.000000% 0.000000% 100.000000%
23 0.000000% 0.000000% 100.000000%
24 0.000000% 0.000000% 100.000000%

 

[Kichwas]

Ok that all makes sense.

So we're dealing with a roughly 48% chance of a meaningful encounter every 8 hours when out in the wilderness. Probably still way too high. I'll have to give this some though and then find a nice new number to use.

Maybe I should dig out my 1.0 Wilderness Survival Guide and see what advice it had.

 

[dcollins]

I have a very, very low opinion of the post-Gygax Survival Guides. Trying to use those clunky rules practically ruined my college campaign.

As an example, the WSG has no rules on encounter chances (other than as a function of hunting). That information was only in the 1st Ed. DMG.