Tobold's Blog
Friday, February 24, 2012
 
Random numbers in D&D

As I told before, the last combat of my last Dungeons & Dragons session was rather dramatic, with the fighter reduced to 0 hitpoints at one point, and the group struggling to kill the 10 rats I had put in their path. One major contributing factor was how random numbers work in D&D, as opposed to MMORPGs. In Dungeons & Dragons generally anything to do with a chance of success is determined with a 20-sided die. You add a modifier and have to be higher than a target number, meaning that you can have anything between a 5% and a 95% chance of succeeding, in 5% steps.

Now statistics tells us that if you throw a 20-sided die often enough, the average will be 10.5. You have a 50% chance to roll 11 or higher, and a 50% chance to roll 10 or lower. In the combat I had, the players had a base +4 attack modifier, and had to hit an armor class of 15 of the giant rats, meaning they had a 50% chance to hit. As the giant rats were minions, which are eliminated with one hit, that should have gone fast enough. So what went wrong?

The thing is that real random numbers in small batches have a tendency to cluster. Thus if you have a fight of 6 rounds, and roll your 20-sided die 6 times, you can't count on having 3 hits and 3 misses. In this case one of my players had 6 misses and no hit at all, while another had 5 misses and 1 hit. That was "bad luck", but not statistically outrageously so. But the rats actually had a better chance to hit than the players, and even if they only did 3 points of damage per hit, that quickly added up to some serious damage when they weren't dispatched as quickly as foreseen.

In addition one of the rats was a "standard" monster, a dire rat with 38 hitpoints, dealing 1d10+5 damage. I was rolling for the monsters out in the open to show that I don't fudge dice, and promptly rolled a natural 20, which in the D&D 4E system means a critical hit for maximum damage. These 15 points of damage was what felled the fighter. Again "bad luck" for the players, but well within statistical likelihood.

In the end the players won the fight and everybody survived, so I didn't have to intervene. And the last fight of an adventure being highly dramatic and dangerous isn't a bad thing. But the event was a warning to me how difficult it is to plan combat encounters as a DM. You do want them to be neither trivial nor impossibly deadly, but with the clustering of random numbers and a bit of bad luck, things can quickly go wrong. In a pen & paper game, total party kills (aka "wipes" in MMO speak) are not something you want to have, unless the players are doing something stupid and reckless.

MMORPGs avoid that by making random number mostly irrelevant. A typical hit chance against a monster of your level is 90% or more, not 50%. And your damage is more likely to be something like "330-360", giving you only a small variation between minimum and maximum damage. There are also more "turns" in a MMO fight than in a D&D fight. Thus basically if you have a streak of bad luck in a MMORPG, you don't even notice. There simply is no way to end up like in my D&D game, missing your opponent with every hit for the whole fight. And that is before even discussing the quality of the random number generator, which if not properly done is likely to be less clustered than real random numbers.

Having said that, 4th edition D&D has less problems with random numbers than previous editions. Hitpoints are generally higher, and one-shot kills a lot less likely. A first edition AD&D mage had between 1 and 4 hitpoints, plus maybe a few more from the constitution modifier. In 4th edition a wizard has 10 hitpoints plus his constitution SCORE (not modifier), so probably more than 20 points. And 4E characters gain a fixed amount of hitpoints per level, not a random number between 1 and something. Overall the result is that fights last a bit longer; the longer the battle, the lower the probability that you fail all your rolls. As an added advantage, the longer battles make maneuvering and tactics more important, which adds to the fun. Still, one better be aware that clustering of random numbers and bad luck can happen.
Comments:
Random swingy combat is a real problem at low levels of DnD throughout the most recent editions.

A quick fix is to even the bell curve by rolling 2d10 or 3d6.

You can extend the crit range by a number or two if you still want those big smashing rolls, but adding more dice adds a lot more stability and predictability to a fight.
 
Also comment moderation is still super lame. Seriously.
 
Also comment moderation is still super lame. Seriously.

Many years of experience in running a MMORPG blog proved that having an unmoderated comment section was not possible, because MMORPG players are likely to get extremely agitated about even the most minor detail, and then quickly descend into insults and mudslinging. Just look at the World of Warcraft official forums, that is not a community I want to reproduce here!

I wonder if pen & paper roleplayers are a calmer sort of people than MMORPG players. So if I stopped completely to write about MMORPGs, maybe I could turn comment moderation off.
 
Yeah, I never played 1st ED but in 2nd, goodness gracious. A mage with a bit of bad luck in level ups very quickly becomes a bit of a joke.

Fighting 4th level monsters when you have less than 10 HP? Not fun, all though I suppose it is your fault for ignoring CON
 
As DM I never roll in front of the players. Sometimes it's because I'll get 3 crits in a row and they'd be wiped out. Sometimes it's all misses all night, thus no excitement.

Also with damage rolls I can tailor the damage to be enough to create threat without killing them. Many a time there would have been a wipe of all the players if I had the DM rolls in the open.

As you can see I am a believer in the story telling aspect rather than the "gamey" aspect of D&D. Also when we played it was 1st edition.
 
One thing to note about 4e is that it has a tendency to produce fights that looks hopeless from the players' side, but they still somehow manage to win it, often through a critical event that swings the combat.

I started a campaign last autumn with 3 veterans and one 4e rookie (experienced roleplayer though). The second combat encounter was a fight in the bowels of a magical steam ship, where a crew of saboteurs had rigged the boiler to blow and the PCs had to fight through them before they could even start to figure out how to prevent the explosion. At the end the rookie went "Wow! That was fantastically tense, soo close!" - but the others told him "Eh, totally normal. You get used to it."

I think it's partly a result of the monsters often being just as synergistic as the PCs, but they lack a way to get back in the fight if they get taken down (PCs get a quick healing word or even a heal check to trigger second wind and they're back in the game).
 
I don't remember who told me this: "dice are for making rolling noises behind the GM screen". Meaning that storywise, GM-controlled rolls are a whole lot better :)
 
There are both advantages and disadvantages of the DM fudging dice rolls behind the screen. If the players believe that the DM will always fudge the dice to avoid killing them, there is less perception of danger.

I actually thought it to be a progress of the 4th edition rules that you can more easily role dice in the open with less fear that a single roll of the dice leads to extreme results. A 4E crit might at worst take half of your hitpoints, while in previous editions a hit with maximum damage might take you from full health to dead, especially for mages.
 
I agree, players should not see the GM's rolls. Whole I will be happy to kill a character for being stupid, I don't want to have player death because Bob the orc rolled well.

Dramatic death is great, random death not so much for most RPGs.
 
One option might be to only let the heroes have critical hits, and not the monsters. Or, as Neio suggests, roll multiple dice for one or both as appropriate.

MMORPGs have a tendency to flee from randomness. DPS-ers complain when their damage depends a lot on the random number generator. And a coupkle of years ago, WoW removed the 1% chance of missing a mob when your to-hit statistic was maxed. I don't know why, really, I never saw it make an actual difference in combat (I mage-tanked Krosh many times with spell hit far from maxed and it was never a problem, though I think I had to recast spellsteal occasionally) . For me, taking away the 1% makes things seem that bit less real.
 
So how do you handle aggro? Do you use an artificial mechanic to allow a heavily armored player to hold aggro or rely on things like having him stand between the target and other party members?
 
So how do you handle aggro?

D&D 4E has a mix of game mechanics for that. One is as you said the tank physically standing in front of the mage. That is aided by each character having a zone of control of the 8 squares surrounding him: An enemy leaving one of these squares and moving more than 1 square total, gets hit with an opportunity attack.

In addition to this, "tanks" get the ability to "mark" a target. A marked target deciding to hit somebody else than the tank that hit him, receives a -2 malus to his attack.

Other than that the DM has to apply a bit of common sense to make the decision of which player gets attacked by the monsters. A highly intelligent foe might react differently than a wild animal.
 
I avoid strict dice-based combat as much as possible in my D&D 1E games. Every monster encounter I throw at my characters, I make sure to give them plenty of opportunities to resolve things in more creative ways than just endlessly slinging dice across the table for 20 minutes.

I add furniture/obstacles to hide behind, ambush areas to sneak attack from, alternate routes to avoid the monsters entirely (yes, believe it or not, old-school D&D was just as much about avoiding combat - and XP was awarded for doing such), and other room features to make things more interesting.

This is another reason why I love old-school D&D - dice were a last resort not the end all be all. In many cases I'll double or triple the rewards (treasure, XP, secrets, etc) if my players can avoid dice "grinding" a combat encounter. There's no reason why we have to turn D&D sessions into the super boring, formulaic MMO model of combat.
 
I likely got the idea from a Dragon Magazine article, but in my AD&D campaign in the early 80's, you didn't "die" until you hit -10 HP.

When you hit 0 or below, you would be unconscious, and bleed 1 HP per round until a friendly NPC or player character bound your wounds. Then a potion or healing spell would bring you back, but at a weakened state.

Thus our party typically had a few "henchman" which would function like medics.

Protecting the squishy magic user and henchmen were a high priority and made for fun roleplaying with henchman that were motivated by treasure, but scared out of their wits, and the magic user pc acting like a fragile princess.

One favorite henchman disappeared (really just an oversight on my part), and I just played along and ended up creating an extended rescue campaign. Tthat's when I learned that the game is so much better if you can get your PC's to actually care about NPC's.

Rescuing my friend that saved my life and made me laugh is so much more inresting than rescuing a faceless princess who we think might give us money or magic.

And who knew that henchman had an old family heirloom +2 sword with a "rust" curse on it that just needed to be blessed to cleanse?
 
In a pen & paper game, total party kills (aka "wipes" in MMO speak) are not something you want to have, unless the players are doing something stupid and reckless.

Then why are you using a system where total party wipes can occur?

Or at the very least, why aren't you using a house rule like the last PC standing always gets away (so as to give a chance at coming back to recover bodies for resurection)

Why run all these numbers if you want a 100% chance of winning? Why bother rolling in front of them if your going to intervene in the end, anyway?

Just say there's a battle, they won, here's some XP.

Otherwise it's all a charade.
 
Forgive me for bringing up the same Fate system in second thread in a row, but I just can't help it. Looks like it just really solves many problems that bother you, so you should take a look at it.

In Fate, any character may avoid going below zero HP (and any other stats that can be damaged, like Mental stress or Money or whatever) by turning some damage into "consequence". It means the character basically soaks some amount of damage for free, but gets to live with a negative thing after a battle for a while. This can be "sprained ankle", "owes money to Yakuza", "shaking hands" and so on.

This means the character survives, but has to face consequences of his bad decisions afterwards. The exact effect of consequences isn't set in the rulebook and is freely roleplayed when appropriate instead (with some clever mechanics to back it up, of course).

If you see it from this point, many traditional narratives have this pattern, from Odin plucking out his eye to Luke losing his hand. The character survives (that's good), and you, as a GM, have more things to roleplay in the future (which is also good). Everybody wins!

And another thing. In my opinion, if the players act intelligently, they should win. The only reason for danger to exist is to provide drama. Losing because of dice seems unfair to me, so either you have to be good GM and constantly struggle with the system, or switch to some other system with ideology closer to yours. I'm pretty weak GM, so I had to choose the later.
 
"MMORPGs avoid that by making random number mostly irrelevant. A typical hit chance against a monster of your level is 90% or more, not 50%."

I recently had a major problem with this system breaking down in WoW. In attempting to make the most overpowered level 19 character possible, I found I needed to skin the corpses of level 30 beasts. My chance to hit was 0% on some of these, but even leading up to that, I killed some things with a 3% hit chance. Despite the level difference, it still only took 3 hits to kill one. Going entire fights without a single hit and dying because of it is seriously frustrating. =|
 
Espoire, I cannot tell if your simply noting WOW can do low percentages as well, or if you are actually complaining?
 
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