Thursday, November 26, 2009

Dice Pools vs Single Dice: Just Fiddle the Target Numbers

Initially, I was attracted to the idea of a dice pool because it provides a bell-curve distribution of results. With a pool of dice, the average number is far more likely to be rolled than the extreme lows or highs of the range. See http://en.wikipedia.org/wiki/Dice_pool for more information on this concept.

This web page (http://catlikecoding.com/anydice/) will help you prove all things to yourself as we go along. It will give you a graph of the distribution and the probability of exceeding various rolls.

By contrast to a dice pool, a single dice (say a D20 as a good example) has a linear distribution. Rolling a 10 is exactly as likely as rolling a 20. Try it out on anydice: the probability of each number is identical, no matter how many sides the die has.

However, from the game design perspective, there is no reason to draw the conclusion that a dice pool is an inherently more balanced means of randomising combat. Here's why: target numbers don't have to be linear any more than dice results have to be linear.


Let's use AnyDice to roll 3D6.

So what's my point? The point is that you can use any combination of dice you like in your combat mechanism, and still have the odds of success be exactly the same! There are some qualifications. Firstly, not every combination of dice can hit every percentage chance of success. There's a bit less resolution in the 3D6 pool than in a D100. This is more of a problem for smaller dice pools such as 1D6 or 2D6. D20 is nearly okay, but still not nearly as precise as a D100.

 The other qualification is if the degree of success is relevant. It's not really a problem, but again the degree of success is not linear for a dice pool. You are much more likely to exceed your threshold by just a little, rather than a whole lot. This is just something else that needs to be considered when designing a mechanic.

So the fact that a dice pool has a normal distribution rather than a linear distribution does not in fact make it 'better' to work with as a designer, at face value. It is possible to design-in the same success ratios by tailoring the target numbers, rather having linear target numbers and a normal outcome distribution.

So far however we have only considered rolls against a specified target number. How do dice pools affect the chances of success in an opposed roll? More soon on this point...

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