Thursday, February 23, 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.

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