Dungeons & Dragons Online

Ruminations on DMing: Understanding probability math and accommodating for outlier events is 100% necessary for a DM

Probabilities are something we hear about constantly in everyday life; this candidate has such odds of winning, there's these odds of rain today and so on. But despite that, probabilities are quite unintuitive for most of us. While we understand the concept of there being 10% odds for this or 37% odds for that on a cognitive level, we often don't quite grasp what that actually means in reality. Based on my experience, those of us who dont do maths for a living tend to consider only 3 different probabilities: 100%, 50% and 0%. That 95% shot in Xcom? Practically 100%. 1% chance of something happening? Basically 0%, unless its the lottery, then its 50%. Did the weird fortune teller lady say that theres 44% chance you left your stove on? Now thats 50%. Maybe this doesn't apply to you! And maybe I'm definitely exaggerating. But the point is, we don't tend to handle probabilities based what they actually are, but what they feel like.

If you are a DM, this is something you can't afford to do. And its a problem I've seen quite a few people on this subreddit run into. DMs handing players skill checks they think are very unlikely to succeed but they do, and they don't know how to handle that. DMs wiping players out because half the party failed their saving throws against paralysis 3 times in a row. Homebrewed items that have an intolerable outlier where something so bad or good happens that the entire session/campaign changes, and the DM is not prepared to deal with it.

You have to take probabilities and outliers into account when designing encounters, items, monster, features, everything. Your monsters will crit once every 20 attacks; that's probably at least once every other encounter. If you are running high damage monsters, you need to consciously make the decision that you are okay with the monster critting the player all the way into high orbit past the massive damage zone. You HAVE to take crits into account when designing your encounters. If you are giving players skill checks with a horrific failure state, it will happen sooner or later.

Beyond this, take multiplicative probability into account. Say you give your players 3 different skill checks in a row, all of which they must succeed. They have 85% chance to succeed on each of them. That's pretty high! But then when we consider them as a successive event in which each roll is dependent on the previous ones success, we get 0.85*0.85*0.85 = 0.61, so 61%. From 85%, which feels almost like 100%, we've arrived to 61%, which feels more like 50%. If you wanted your players to fail at things, giving them multiple rolls in a row would be an easy way to accomplish that, no matter how deceptively easy the rolls are. But if thats not your intention (and setting them up to fail probably shouldnt be), avoid consecutive rolls which they must succeed on.

Conversely, say you put the players up against a banshee. Say there's 4 of them, and for the sake of convenience lets say they have +4 con save each. When the banshee wails, each character must pass a DC 13 Con save, or be dropped to 0 hitpoints regardless of current health. DC 13 save – not terribly high. +4 modifier to roll on each player, thats pretty good! Each player has 60% of clearing the con save (must roll 9 or higher), so while half of them might fail, the others will survive, help them recover and we will have a tense fight against the creature! But hold on. That also means that theres a 40% chance a player fails it. So there's a 0.4*0.4*0.4*0.4 = 2.6% chance that they all fail it. There is a non-zero chance that the entire party gets absolutely wrecked by the banshee, on the first turn, in an entirely non-interactive fashion. If you are running a banshee, you NEED to accept that as a potential outcome beforehand. If everyone gets wiped because of a statistical outlier, most people will not feel any better about it just because it was unlikely; and you can't wash your hands of the situation.

If you are a DM, understand that in a game where random chance is inextricably a part of it, you have to be very careful with what you leave up to chance. Any time you let chance decide something, you are making the decision to accept the entire spectrum of possible outcomes as valid. You cant wash your hands clean of it by saying "well, the dice made the session suck, thats too bad". There is something to be said about managing failure states here as well (if the player jumps across a chasm, the failure state in most tables probably shouldnt be that they fall down and die), but this post is running long already and I'll let someone else make that rant.

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Maybe everything in this post has been completely obvious to you. But if so, you are not the DM I'm talking to! The one I'm talking to is likely much greener than you are, who has yet to learn that. So to that DM, this is the main takeaway of the post and something that will improve your DMing by leaps and bounds, and save you some tears in the future: Understand that you cannot ignore anything that has a non-zero chance of occurring, and you cant shirk responsibility for those outlier outcomes if you are the one who's setting them as possible outcomes to begin with.


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