I've crunched some numbers; I've written some programs. I know how likely it is to roll some given number on Fudge dice, and I know how many tries on average it takes to beat a given Bar. Would you like to know?

Basic Probability

First of all, there are 81 possible outcomes when rolling 4 dice, each of which can have 3 possible values: 3⁴ = 81. Of course, we're not particularly interested in each and every one of those 81 possible configurations; we're interested in what happens when you add them up. Given the premise that any combination is equally probable when you roll the dice, this means that we can determine how likely it is for a particular total to come up by simply counting the different ways that each total can be formed and dividing by 81. I've done it for you.

I love the way things trail off on the ends but are pretty high and level in the middle; this bell curve is one of the reasons why I like Fudge dice and not just a single die roll. It's more like real life: people perform at their level far more often than they spectacularly outperform or underperform their expectations. It's just a better model.

Meet or Beat Probability

But anyway, we're not actually as interested in exactly getting a particular total on the dice as we are in meeting or exceeding some given total. What are the chances of success when the Bar is set to +2? Let's see.

It's just as easy to calculate this: for a given total, count up the number of ways the dice can meet or beat that total, then divide by 81.

So my chances of meeting or beating that +2 are about 18.52%. It'd sure be nice to have Ranks in a Trait that helped with this. A Rank of +1 would more than double my chances to 38.27%. This is why a Rank of +1, which doesn't sound all that significant by itself, is actually very important.

How Many Tries

When trying to increase Traits, you can spend Points (and these calculations are where the Point costs come from), or you can try to roll higher than your Ranks in a given Trait; equalling it doesn't raise it. But how many rolls would it take you, on the average, to beat a given Rank? Is it worth spending the Points, or should you try to roll for it? Well, the chance to do something is just a fraction of successes over tries. The average number of tries it takes to do something is just the reciprocal of this: tries per success.

So if I've got a 0 in some Trait and want a +1, I can spend a Point and roll the bones. I've got 31 chances out of 81 of exceeding my current 0 Ranks (which is a 38.27% chance), so on the average it would take me between 2 and 3 tries. If I make it, I just got a +1 for only 1 Point! Of course, that 2.613 is an average. It could take me 12 tries. It's a gamble.

Or I can use the There Can Be Only One Table and just buy the +1. Of course, it will cost me 3 Points, but it's certain, and what's certain in today's world?

Does This Work?

Interested in seeing whether experimentation actually bore this out (but too lazy to roll dice millions of times), I wrote some C code to roll the dice for me and tabulate the results. All of this is borne out by my computer experiments. So you can write your own code or take my word for it, but these probabilities really work. Now you know.