Sunday, December 19, 2010

Probability in RPGs

Dice rolling is one of the core features of basically every role-playing game (except Amber Diceless). However, when probability is involved, people often get sucked into weird beliefs and numerological thinking.

There are a couple of good documents on probability in RPGs. See here and here. I have a few extra comments, especially regarding RuneQuest.

The percentile rolls in RPGs use two ten-sided dice. (I don't think anyone actually uses d100s.) One die represents the tens, the other, units. This means that one of the dice is an order of magnitude more important that the other. Only one in ten rolls of the second die is worth rolling (i.e., you need 64%; only a 6 on the tens die makes the second die relevant). RuneQuest, however, offers a couple of subtleties - critical successes and fumbles - that brings the usefulness up to 3 in 10 rolls. I've also noticed, with opposed rolls, that that number goes up to 4 in 10. Therefore, RuneQuest is mostly a d10 system, rather than percentile. However, the second die is used about a third of the time and gives some rare probabilities that makes it quite intruiging.

Comparing the percentile system of RuneQuest (Call of Cthulu, Basic Role-Playing and others) with D20 (D&D, Star Wars, etc.), I find the d100 system more satisfying. This is because
  1. It's very easy to judge your chances of success when using percentiles. With D20, it's not immediately obvious what your chances are when you need 24+ and you roll 1d20+10. Sure, you can quickly figure it out, but it would be better if you didn't have to.
  2. Little touches in RuneQuest, like fumbles that occur when rolling 99 or 100 and varying chances for critical success (depending on your skill level), break up the standard roll of 1 for automatic failure and 20/18-20 for critical success of D&D/D20.
  3. Critical hits in D20 require re-rolls. This wastes more time.
  4. In D20, the player, when rolling, does not know the chance of success unless they ask the game master. With percentile systems, the player knows the chance of success, unless the game master modifies it. The latter is better as it gives more determinacy of the result to the player.
The above concerns transparency and clarity, there isn't a real difference in probabilities between a percentile or D20 system. It's a single roll and the probability of each result is linear (can just as easily roll 33% or 99% in RuneQuest or 2 or 20 in D20). On the other hand, there are a few other game systems that provide either real differences to the probability or more superficial complexity. They are:
  • Normal distribution systems, like the approach of Traveller, GURPS and Fudge. E.g., roll two dice and add them together. The non-linear distribution is cool in the sense that more often than not you'll roll near the average. However, the downside is the probability of success is tricky to figure out, especially when you don't want to have to put much effort into thinking about it. It also requires arithmetic, slowing down the evaluation of the result.
  • The dice pools (e.g, grab a number of d10s relational to your ability) of World of Darkness, Warhammer Fantasy, d6 Star Wars and The Burning Wheel games also sounds pretty cool, but again, it's not overly obvious what your chances are to achieve a task. Also, more dice means more time to evaluate. Not good.
  • The step dice of Savage Worlds, EarthDawn and Serenity seems very promising. You use 1d4 when unskilled, 1d6 if you're a bit more competent and 1d10 if you know what you're doing. The probability is easy to figure out and it's fast to evaluate. Having said that, Savage Worlds, at least, has complexities. Wild Cards (PCs and important NPCs) have two dice to roll (one normal die and one Wild Die) and re-roll if you ace (get a 6 on 1d6, for instance). This takes time and obscures the evaluation of probability. Nevertheless, I'd really like to play one of these games.
My preferences then, based on transparency and speed of evaluation are:
  1. Percentiles (RuneQuest)
  2. Step dice (Savage Worlds)
  3. Roll and add modifiers (D20/D&D)
  4. Normal distribution (Traveller)
  5. Dice pools (World of Darkness)

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