D&D Random Encounters by the Numbers

There are several visual elements to this one so I’ve embedded the video, transcript is below:

Hey everybody, we're doing a series on random encounters in Dungeons and Dragons, and other RPGs, which is a polarizing topic but I am a huge fan of them as you know if you've been watching this playlist. We already talked about their purpose, and how to make them better, now we're going to dig a little deeper into the number crunchy, mechanics side of things. Now, I was an English major, so I don't plan to drown you in math here. (And be sure to check below in the comments for what I got wrong.) But I think having a basic understanding of probability when we go reaching for dice is an important skill for a Dungeon Master. A lot of this will apply to other aspects of the game, and other games as well, but we're going to stay focused in on random encounters.

There is a two part formula for random encounters laid out in the Dungeon Master's Guide. First we roll dice to see if an encounter is triggered. On a positive result, we roll again, often using different kind of dice, and use that result to consult the table and see what we get. It feels like explaining it makes it sound more complicated than it is, in play it's pretty simple. Let's look at first part first.

How we check for an encounter effects how often a random encounter occurs. In the last one we talked about how often you roll that check make things more or less likely; if we check once an hour we're going to have more random encounters in our game than if we roll once per day. But the dice we use and what we set up as a positive result also makes a big impact. In Fifth Edition the DMG tells us to roll a d20, a twenty sided die, and on an 18 or higher, (18, 19, or 20) we get an encounter. This is kind of a legacy of the earliest editions of the game, where they used a d6 for everything because that's what most people had available, and the chance of a wandering monster coming upon you in the dungeon was 1 on the d6. Brace yourself, here comes math: 1 out of 6 is around 17 percent, 16.66 repeating to be precise, and 3 out of 20 is 15 percent. Pretty close. Now if you roll that check every twenty minutes of adventure time old school style vs every hour (assuming you check at all) in the new school way, we're three times as likely to trigger an encounter.

Now, I'm not advocating for a specific way to do things here, my goal is to help you figure out what's best for your game, and to better equip you to influence the chaos of random number generation. Beyond knowing that you can tinker with these things in the first place, I think the most useful concept on the checking for random encounters is that you can do it differently in different situations. Let's say the place the party is currently exploring is more dangerous than usual. Maybe they're in an enemy stronghold with a ton of monsters actively patrolling, or they're in a drow city with a big population, or they're literally in hell. It can go the other way too. They're traveling through the desert or far out in the ocean and there's just less going on here so we want to decrease the chance of an encounter. We can change how often we make the check, but we can also change what gives us a result, the DC basically.

I think the d20 is nice for thinking about probabilities because there's a 5% chance for every result. If I do two checks a day in the forest but only one in the desert, we're half as likely to get an encounter. But I can do a little more fine tuning by just saying “OK, in this region only the result of 19 or 20 triggers an encounter.” Or maybe you screwed up and caught a bad break and the denizens of this dungeon are now aware you are down here. Now on a 16 or above we're having an encounter. That's a 25% chance, and if you're mathematically minded you know that's the same odds we get from a d4. Which leads me to the other variable we can change here: the kind of die we roll.

I'm not going to break it all down, I'm sure I've lost a lot of people already, but here is the probability of roll a 1 (or any specific number really) on each kind of die we use in D&D. So if we're using the d6 for the check in the dungeon, and then the players do something like cast pass without a trace, for the next check we can roll a d8. If they've already cleared out most of this level then maybe it's a d12. This is more impactful if it's the players rolling for these checks, at least most of the time.

Another cool tweak here is to set different results for different numbers. Let's say we want to stick with that 15% chance and a d20, we could say on a two you roll on a wandering monster encounter table, on a one you roll on a more difficult wandering monster encounter table, and on a natural 20 you roll on a table of potentially beneficial encounters.

That might sound like a lot of work to prepare but it can actually be easier in my opinion. I'm better at coming up with good ideas for three d4 tables than one d12 table. That's the secret to a lot of things in life, break up big tasks into smaller tasks. You want to make a d100 table? Make 10 d10 tables. But I'm getting ahead of myself, let's talk about tables.

However you determine it, once the dice tell you it's time for a random encounter (or you just decided it's time because you're the DM and you can do that,) we roll on the table to see what we get. How big of a table we need comes down to preference and the situation, but for me generally less is more. 100 basic entries can be useful when I'm trying to come up with ideas in prep, but during the game I'd rather have a table with fewer, more developed entries. If you're making yourself a table for tonight's game night, if you create twenty encounters odds are you're going to be more excited about some than others. You might right your best ideas first and then run out of steam, but you also might find that after you burn through the easy, familiar stuff those later entries where you had to stretch your imagination turn out pretty cool. It's good to experiment, give yourself a lot of options, and then edit it down and embellish the smaller list. Ten well designed entries are going to be more useful than twenty lackluster ones.

Obviously the fewer entries on the table, the more likely we are to get a specific result. I'm going to put the dice probabilities up again. You can alter these further by having some entries on the table take up several spaces. For instance, you're more likely to encounter gnolls in the Broken Lands compared to anything else, so on a one, two, or three we get that result. If you really want to dial in probabilities you can use a d100 table and set different ranges to each entry. This is a popular approach, but, though it's statistically unlikely I always find when that 63 gives us the same thing that 58 got us a few sessions ago, it kind of falls flat. I like each number to have a unique entry, which is why my preferred method to play with the probabilities is by using multiple dice, mostly 2d6.

If we roll a single die, each result is as likely as any other, unless it's defective or you're cheating. But interesting stuff happens when we start using combinations of dice. Rolling a d12 there's an 8% chance for every entry, but take a look at the results of 2d6. Interesting right? There are 5 different combinations that will get us an 8, but only 1 way to get to 2. We're going to get a 7 roughly 3 times as often as we hit 11. I call this a bell curve pretty often but that's technically not true. Still, I find it's useful to think of it like that, because we can put our common results in the middle and the real crazy stuff on the outer edges. We're about have as likely to hit 12 on the 2d6 as we are to get a natural 20 on the d20, so when that 12 comes up it's significant.

The example random encounter table in the DMG uses 1d8 + 1d12, and that gives us really interesting results. I'm going to graph it on Anydice.com, if you're still watching this video and enjoy stuff like this, you might enjoy messing around on that website. We get this really distinct platuea from 9 to 13, then the outside becoming less and less likely. A little over half the time we roll on this we should land on 8 to 14, so I'd make 7 down to 2 progressively scarier, and 15 to 20 progressively more rewarding. And if I decide I want flatten this curve and make the chance of every result the same I can just roll a d20 on a table like this, and have a 1 mean reroll, roll twice, or DM's choice.

I love the customization and control using these probabilities gives me. If I want something really elusive in a region, I want bigfoot in this forest or Nessie in this lake, I can fine tune it so that common things are way more likely but there's always a chance you'll stumble on the exotic. The main criticism of tables like this is that you'll mostly get the results in the middle and that's where you'll put the boring stuff. I have two responses to that. One, you decide what goes there, so if you want something to happen put it in the middle, or just decide it happens, you're the Dungeon Master. And Two, there shouldn't be any boring entries here. If you fill up a table with 19 entries and half of them are boring, edit it down and try d6 + d4.

Different designs are going to give you different results so I recommend experimenting, try some different things, and see what works for you. You can go crazy with it too. Look at this real quick. Those outliers on the 1d8 + 1d12 are two groups of 6 or 7, depending how you look at it. Between town and the dungeon is a forest where fey creatures and an evil wizard are having a war for control. The most likely outcomes, that top of the trapezoid, are going to be stuff like elves with blink dogs battling zombies and hell hounds, or the aftermath of one of these battles. Maybe if we trigger an encounter in the clear light of day we're only rolling a d6 or 2d4 on that outlier side that's all fey, and if it's the middle of the night we roll the on the all evil side. Or maybe one side eventually wins if the players get involved or don't get involved. I've seen other tables where you simply add a modifier for night time, so there are 10 entries but you're only rolling a d6 or d8.

The next level of complexity has to be the nested table. I guess the simplest version of this is an entry like d8 goblins and d4 worgs, but what I'm really talking about is you roll and you get goblins, and then you roll on another set of entries to see if they're riding worgs, setting traps, hunting giant centipedes, or limping home after the kobolds beat them up. I use this type of table a lot in my home game now, crossing out and occasionally replacing entries as things come up or the situation changes.

In the next video I'm going to show you exactly how I've been using random encounter tables to give me the most satisfying open-world game I've ever played. I'm also going to share a set of tables I've made that you can use and customize for your game. I'm really looking forward to that, until next time...