I am looking for ways to generate a probability distribution using dice which produces results that are skewed towards lower numbers, ideally as some kind of smooth decay.
For example, imagine a random encounter table sorted by difficulty, in which rolling would ensure that low-danger encounters are seen more often than high-risk ones, without requiring to fiddle around with number-ranges for each entry.
While generating uniform probabilities is easy (pick any die), and bell curves are also quickly doable with few dice (3D6 gives you a good curve, over almost the exact same range as D20), I am struggling to come up with an easy (requiring little brainpower) system requiring few dice (say less than four).
While the Savage Worlds exploding dice system can generate a somewhat exponential distributions over its success/raise scale, it falls off extremely quickly when only counting successes (that is, divide the result by four and round down), and fails in being smooth when looking at the raw numbers, being uniform over each interval and having a gap at the maximum number of the die.
Rolling a fistful of D6 and counting the number of sixes produces a smooth Poisson distribution, but fails at the number of dice requirement. When usually rolling 1D20, suddenly taking out the Shadowrun dice bag would be weird.
Are there any other ways you can think of that would quickly generate a smooth decaying distribution (say, over an interval of 1-10 approximately)?
1/xshape ... anyway, glad to see that you have attracted answers, since this kind of table is of interest to me. \$\endgroup\$