I read with much interest the question about Fudge dice, but what are these dice useful for?
In Fudge, your character has skills and abilities that are ranked on the Fudge Scale: Terrible -3, Poor -2, Mediocre -1, Fair 0, Good +1, Great +2, and Superb +3. The dice, 4dF are zero-centered. You typically roll the dice and add the result to your relevant skill to determine the outcome of your attempt. An elegant system in all actuality.
Fudge dice are good for generating a nice bell curve centered on zero. Each die is six-sided, with two minus (–), two blank ( ), and two plus (+) sides, which correspond to -1, 0, and +1 respectively. You roll them and then add up the pluses and minuses to get your result.
For example, 4dF will get you a result from -4 to +4 with a mode of 0 and a narrow bell curve centred on zero, with low probabilities of anything outside the -1 to +1 range:
-4 o 1 ( 1%) -3 oooo 4 ( 5%) -2 oooooooooo 10 (12%) -1 oooooooooooooooo 16 (20%) 0 ooooooooooooooooooo 19 (23%) +1 oooooooooooooooo 16 (20%) +2 oooooooooo 10 (12%) +3 oooo 4 ( 5%) +4 o 1 ( 1%)
Fudge and FATE typically use 4dF and represent skills by a number you add to the roll, which biases the bell curve so that it's centred on the value of the skill instead of zero.
Fudge dice were originally used for the Fudge role-playing game. The basic mechanism is a "ladder" or "scale" of adjectives:
-3 Terrible -2 Poor -1 Mediocre 0 Fair +1 Good +2 Great +3 Superb
Fudge dice have two sides with a plus, two sides with a minus, and two sides with a blank. A typical roll consists of rolling four Fudge dice (4dF) and letting the plus sides cancel the minus sides, then reading the net pluses or minuses. For example, a roll of ++-b (plus, plus, minus, blank) is a net +1. In Fudge, a player would use this roll to shift a trait or ability (also described on the adjective scale) up or down according to the roll. For example, given Mediocre (-1) Intelligence and a roll of ++-b, which is Good (+1), that results in a Fair (0) Intelligence result.
The FATE role-playing game is based on Fudge, which was released under the Open Game License. FATE uses the adjective ladder and Fudge dice in more or less the same way.
Look for these FATE-based games on bookshelves and PDF sellers' websites:
Other games use Fudge dice but are not based on the Fudge or FATE game systems:
Fudge and Fate use them. Mathematically, they are 1d3-2. The normal use is to step up or down the skill rankings, using 4dF, each plus up a step, each minus down one. Then compare the resulting rank to the needed; if same or higher, succeed.
Fate is an engine; the best known games using it seem to be Diaspora, Spirit of the Century, and Starblazer Adventures.
Fudge is an engine and system construction set; the various Fudge based games do different subsets, and so vary widely, but most use 4dF; a few use alternate dice options like 2d6-7, 4d3-8 (mathematically the same), or 2d6 dark & 2d6 light, keep lowest untied die, with dark being negative and light being positive.
Another game that uses Fudge dice in a totally different way is Galileo Games' How We Came To Live Here.
Pluses are attacks and minuses are defenses, and the combat system is full of maneuvers and techniques for turning one face into another, gaining additional dice, etc.