Tuesday, January 25, 2011

FUDGE dice

FUDGE dice? See picture. You roll 4dF, add the pluses and minuses and that becomes your result, ranging from -4 to 4 (e.g., -1 in the picture). They're great. Why? Well, not because of the reasons I've read around the place. e.g.,
"A bell curve distribution such as this is excellent for RPG gaming because though it does indeed introduce a degree of randomness into an event, the bell curve's statistical properties still favor character traits over absolute randomness." (FATE wiki)
That statement is 100% false. Using FUDGE dice, or any dice rolling method, is no more or less random than any other (except weighted dice, I guess). The table they provide on the website clearly states that.

4dF Modifier Result
Chance of rolling this result exactly
Chance of rolling this result or higher
Chance of rolling this result or lower
+4 1/81 1.2% 1.2% 100.0%
+3 4/81 4.9% 6.2% 98.8%
+2 10/81 12.3% 18.5% 93.8%
+1 16/81 19.8% 38.3% 81.5%
0 19/81 23.5% 61.7% 61.7%
-1 16/81 19.8% 81.5% 38.3%
-2 10/81 12.3% 93.8% 18.5%
-3 4/81 4.9% 98.8% 6.2%
-4 1/81 1.2% 100.0% 1.2%

A "bell curve" property does not favour character traits over "absolute" randomness. e.g., your character has an engineering skill of 2. Lets say that to succeed at a task, she needs a result of 4. Using FUDGE dice, her chance is 18.5% (i.e., the chance of rolling two or more pluses.) Or use percentile dice, where less than 19% is a success. The randomness is essentially equivalent (give or take .5%) even though percentile dice are a uniform distribution rather than the normal distribution of FUDGE dice. Use one die, four dice, percentile dice, or a million dice, the randomness is the same. The chance of success is whatever the game designer, game master or players decide it is.

What FUDGE dice do, however, is give you a non-uniform distribution that you can use when you want to define varying possibly outcomes, each having varying probability. So, you could, for instance, define a series of results, such as:
  • 4: Your sword cuts deep into your opponents neck. They slump to the ground and die, quickly, as blood seeps from the mortal wound;
  • 3: The blade gashes armour and flesh from your opponent's left arm. They drop their weapon.
  • 1 or 2: Your blade strikes hard against your foe's armour. They're shaken, morale faltering, yet steady themselves and grimace.
  • 0, -1 or -2: Shield meets shield, bronze meets bronze. There is noise and sharp flashes of pain, but little else.
  • -3: You trip and fumble, slicing into your left thigh. Walking will be painful and slow, at least for two weeks.
  • -4: Not only do you fail to land a blow, your enemy ripostes and strikes your right hand. The weapon falls to the ground - you won't be able to use a weapon for two months.
You can assign fairly extreme results to 4 and -4 because they don't occur very often (1.2% chance). Zero, being the most common result can mean the status quo is maintained. Positive results can favour the roller and negative can punish them. They're good for making up a whole range of results, common and run of the mill to unlikely and extreme.

You can do all this on percentile dice, of course, but FUDGE dice are much faster to assign. You can also apply modifiers with ease using FUDGE dice, which is quite impractical using percentile dice.

Every roleplayer needs a set of FUDGE dice. Don't leave home without them.

The FATE RPG makes great use of FUDGE dice.


  1. A system with similar variable outcomes in the omni system. It uses a single d20.

    0 or negative is Critical Failure
    1-5 is Failure
    6-10 is Partial Failure
    11-19 is Success
    20 or more is Critical Success

    To get negatives or over 20 is caused by modifiers and base skill points.

  2. Yeah, that could work. I think FUDGE dice are still better, however. Having degrees of success/failure (rather than categories) can be very useful for other things. e.g., Diaspora uses the degrees of success in combat to translate into quantity of damage.

  3. Generally those comments are (unstatedly) comparing FATE's utilization of Fudge dice to D&D's utilization of D20s. The potential rolls are weighted more strongly toward the center of the range (as is always the case with adding dice) - having more dice does, in fact, help work against 'random chance' by simple dint of making each outlier affect the sum less.

    Now, you can take a percentile die and say "Alright, 19% or less is a success"... but that's a function of the system you use, rather than the dice. You can account for the even distribution of rolling just a single die relatively easily, but it has to happen within the system mechanics, rather than with the dice itself.