Monday, December 05, 2005

Polyhedral Fudge

Do you never seem to have enough Fudge Dice around? Or perhaps you do, but just never acquired a taste for the unique fellas... Never fear -- Fudge is an ever adaptable beast and jives just fine with the rest of the polyhedral crew! In fact, here is a variant dice mechanic for Fudge that lets you use more of your dice collection with Fudge than ever before. Best of all, you can incorporate this without throwing out those precious Fudge Dice. So whether you are unintentionally missing Fudge Dice, intentionally missing them, or you're just up for something new and different, read on.

This is a method for using polyhedral dice instead of Fudge Dice as the core resolution mechanic. This method is much more linear than the standard 4dF and generates somewhat wild results - so is most suitable for very cinematic games. Those that enjoy d20 or who dislike Fudge Dice may find this to their taste. Also presented is a modified combat system. This variant was inspired by the Savage Worlds RPG.

One Question: Why??

A lot of gamers cut their teeth (figuratively, we hope) on polyhedral dice, and just about all gamers will agree that funky dice are symbolic of and virtually synonymous with the RPG hobby. As cool as Fudge Dice are, there are some good reasons to use polyhedral dice with Fudge:

  • You have a massive dice collection in a gallon-sized jar and you mean to use it.
  • You care more about simplicity and funky variety than statistical elegance.
  • You want to run a dungeon crawl in Fudge, and polyhedral dice help to set the mood.
  • You have a grognard in the group who refuses to try Fudge because he hates the weird dice.
  • You downloaded Fudge and want to play but don't have any Fudge Dice.
  • You like to try new things.

Choosing the Approach

So, having decided to use polyhedral dice, what is the best way to do it? There are innumerable ways to mangle the trait ladder and roll dice, but for this article I have set some requirements:

  • The technique should use the standard unmodified trait ladder, and should not change the meanings of the traits themselves.
  • The technique should be simple and intuitive, and should mirror the way polyhedral dice are used in other games (roll a single die against a target difficulty). No surprises or jumping through hoops. It should be easy to memorize.
  • The technique should start and end with an adjective. That is you should start with a "Good" skill and end up with a "Great" result, not a number. It should not require playing with numbers or arithmetic any more than necessary, though just as with standard Fudge Dice, it should have a numerical interpretation for those that prefer it.
  • The technique should preserve as much as possible the "Circularity of Fudge" concept, as described in the March 2003 Fudge Factor. That is, difficulty, skill, and performance are all measured on the same trait ladder, are interchangeable, and rolled degree provides an "absolute" measure of performance, not merely a relative pass/fail.

With those requirements in mind, I also have one non-requirement:

  • The technique does not need to duplicate the probability or results of the standard 4dF method. That is a solved problem; the goal here is to explore something new and to play to the inherent properties of polyhedral dice.

Examining the Differences

Before we start, let's consider the differences between Fudge Dice and polyhedral dice.

Fudge Dice have a curved distribution, meaning that results in the center of the range (+0) are far more likely than extreme results (+4, -4). Polyhedral dice have a linear distribution (when rolled singly), meaning that all results are equally likely. This changes the dynamic of play (making things feel more uncertain and random) and also makes extreme results much more likely.

Fudge Dice produce both positive and negative results, which allow them to be used as a modifier that is added to a trait level to produce a result. Polyhedral dice generate only positive numbers and do not include zero, which makes them poorly suited to the modifier approach. Games which use them in this way must denote skill levels as "minimum performance", but that is not compatible with Fudge, which describes the "average performance."

Fudge Dice have a fixed range (-4 to +4), while polyhedral dice are available in different ranges. With 4dF it is impossible for a Poor character to roll a Superb result, and the character is similarly guaranteed to have at least a chance at a Great result. With polyhedral dice, result ranges can be redefined, and multiple ranges can be implemented by using different dice for different situations.

Inspiration

Many games represent skill levels in terms of dice; some have dice pools, while others (such as Savage Worlds or The Window) assign individual polyhedral dice.

Savage Worlds is particularly interesting in that it only uses the five smaller dice (d4, d6, d8, d10, d12) and these correspond closely to the Fudge levels Mediocre through Superb; d6 is average, unskilled is d4-2, and Legendary is d12+N. There is much more to SW than this, and the rest is not particularly Fudge-like, but this concept can be used as the basis of a new Fudge resolution system.

Rethinking the Trait Ladder

The standard trait ladder is at the core of Fudge, and any dicing mechanic for Fudge must be reconciled in some fashion to the trait ladder. Taking the SW dice (d6 = Average) and matching them up with the Fudge trait ladder, we get:

Die Trait Level
  Legendary
d12 Superb
d10 Great
d8 Good
d6 Fair
d4 Mediocre
  Poor
  Terrible

A basic axiom of Fudge is that a Fair character will achieve at least a Fair performance most of the time (to be precise, about 62% of the time using 4dF). If we are using a d6 to represent Fair, then 4-6 would be 50% of the time:

1d6   Trait Level
17% 6 Great
33% 5 Good
50% 4 Fair
67% 3 Mediocre
83% 2 Poor
100% 1 Terrible

That 50% is reasonably close. Conveniently, we also find that Good (d8) will get a Good or better (5+) result 50% of the time, Great (d10) will get a Great or better(6+) result 50% of the time, etc! So our tentative trait ladder looks like this:

Target
Number
Trait Level Die
12 Legendary 5th d12+5
11 Legendary 4th d12+4
10 Legendary 3rd d12+3
9 Legendary 2nd d12+2
8 Legendary d12+1
7 Superb d12
6 Great d10
5 Good d8
4 Fair d6
3 Mediocre d4
2 Poor d4-1
1 Terrible  
0 Sub-Terrible / Nonexistent  

So far so good, we've defined Mediocre through Superb which covers 90% of what we need. Let's now examine the details and see if it holds together.

All skill levels except trans-Superb can now get a Terrible result. Some will not like this, but fumbles are true to the traditions of single-die games (like D&D), and mean that highly skilled characters are not immune to failure. For some, this will add welcome variety and fun to their games.

Results of 8+ are Legendary but are otherwise not differentiated... a roll of 12 is no different than a roll of 9.

Superb: Rolling a d12, a Superb character can get anything from Terrible to Legendary, which extends the lower end of the range a fair bit.

Legendary: We can treat Legendary as trans-Superb; each level of Legendary adds +1 to the d12, so Legendary 2nd is d12+2, and so forth. Since legendary levels are optional this seems like a clean approach. Also, that means a Legendary trait will never have a rolled degree less than Poor.

Poor: Since this is the unskilled default it is actually somewhat common in emergencies. The lowest we can ever roll is Terrible (1). That actually seems reasonable, although it seems that a Poor or Terrible character ought to have a chance to get a sub-Terrible on a fumble. So, let's call Poor d4-1, for a range of 0-3. This means that a Poor (untrained) character will never achieve even a basically competent result of Fair, and likewise has a serious chance to fumble and get a sub-Terrible result.

The trait ladder is designed around a curved distribution centered on "Fair". This could be done with polyhedral dice by rolling multiple dice and renumbering the trait ladder; for example, rolling 2d4 and setting Fair equal to 5. However, such an approach really adds little except additional arithmetic, and you also run into the problem that the dice can no longer be added to the trait level.

In standard Fudge, you generate a die result from -4 to +4, and add or subtract that many levels from your trait in order to get a result.

Since polyhedral dice have no negative results, two modifications are made to the standard technique: First, the traits are renumbered from -4/+4 to +0/+8. Second, instead of adding the dice to your trait level, you add them to "Abysmal" (+0).

Each trait level above Terrible has an associated die:

Level Die
Legendary (2nd) d12+2 (etc)
Legendary d12+1
Superb d12
Great d10
Good d8
Fair d6
Mediocre d4
Poor d4-1
Terrible none
Abysmal none

The usual range of skill levels is Mediocre to Superb, which corresponds nicely to the five standard dice d4, d6, d8, d10, and d12. There are no unique dice to assign to Poor or Legendary, but these are unusual trait levels and a simple modifier will suffice when they are needed. Terrible and Abysmal are very rare as skill levels, so no dice have been suggested, although you could use d4-2 and d4-3 if you really need these.

Rolling the dice and adding to Abysmal produces the following probabilities:

Skill: Poor Med. Fair Good Great Superb Legendary
Legendary+       13% 30% 42% 50%
Superb       25% 40% 50% 58%
Great     17% 38% 50% 58% 67%
Good     33% 50% 60% 67% 75%
Fair   25% 50% 63% 70% 75% 83%
Med. 25% 50% 67% 75% 80% 83% 92%
Poor 50% 75% 83% 88% 90% 92% 100%
Terrible 75% 100% 100% 100% 100% 100%  
Abysmal 100%            

Note that at any given skill level, you have 50% chance to roll your trait level or better. This is somewhat lower than standard Fudge, but it offset by the more linear distribution and general inability to roll below Terrible.

To make this more interesting, we can use "exploding" dice: whenever you roll max on a die, re-roll and add; continue until you get something other than a maximum result. For example, if you roll 6 on 1d6, roll again; if the second roll is 6, roll a third time; if the third roll is 4, the final result is 6+6+4=16. Extending the top of the scale also counterbalances the lower 50% chance of rolling your trait level.

Also, since very low (sub-Terrible) results are not really possible any more, we can add a "snake eyes" rule: if your initial roll is 1, roll again; if the second roll is also 1, it is a fumble and is treated as the worst (sub-Terrible) result possible.

These additions modify the probabilities:

  Skill: Poor Mediocre Fair Good Great Superb Legendary
8 Legendary 6% 6% 14% 12% 30% 42% 50%
7 Superb 6% 12% 17% 25% 40% 50% 58%
6 Great 12% 19% 17% 38% 50% 58% 67%
5 Good 19% 25% 33% 50% 60% 67% 75%
4 Fair 25% 25% 50% 62% 70% 75% 83%
3 Mediocre 25% 50% 67% 75% 80% 83% 92%
2 Poor 50% 75% 83% 88% 90% 92% 100%
1 Terrible 75% 100% 100% 100% 100% 100%  

Adding trait numbers 1-8 to the trait ladder makes it easier to convert the die results back into adjectives; purists may feel this is violates the spirit of Fudge, but it is really no different than putting -4 to +4 on the ladder, and will be memorized just as quickly. Indeed, this is probably faster since the numbers are absolute and there is no level arithmetic going on. The trait ladder now looks like this:

Level Die
8+ Legendary d12+1
7 Superb d12
6 Great d10
5 Good d8
4 Fair d6
3 Mediocre d4
2 Poor d4-1
1 Terrible d4-2
** Abysmal  

Fudge Points

Spending a Fudge Point on a roll is treated as if you rolled max; so you get to roll again and add. Multiple Fudge Points can be spent to guarantee ridiculously over-the-top results.

Method Summarized

Roll the die indicated for your trait level and add any modifiers. Look up the result on the trait table to get your final trait level. Example: Indiana Joe has Good climbing, so rolls a d8 and gets a result of 6, a Great result.

Snake Eyes: If your initial roll is a 1, roll again; if you get another 1, it is a disaster. Treat it as the worst possible result (usually sub-Terrible). Example: Joe rolls a 1 on his climbing check; this is already a Terrible result, so the GM rules he has encountered an overhang and cannot continue. Taking a deep breath and kissing the die, the player re-rolls -- and gets a 1. The rock crumbles under Joe's weight and he falls...

Exploding Dice: If you roll max on a die, roll again and add the result. Continue rolling until you get something other than a max result. The scale only goes to 8, so very high results are usually discarded, but it is fun to see how high you can get. And for some results -- like rolling damage -- high results do count! Example: Indiana Joe is falling amid tumbling rocks and needs a Superb result to grab at his safety rope. He has Fair Agility and rolls a d6, getting a 6 (Great)! He re-rolls and gets another 6, bringing his total to 12; a third roll comes up 1, so his grand total is 13 -- well past Superb. Joe grabs the rope and swings Tarzan-like to the top of the cliff, where he lands nimbly on his feet and strikes a heroic pose.

Melee Damage

Method 1: Add your weapon damage to the relative degree and subtract armor. With this system, rolling really high on exploding attack dice will give a huge damage bonus!

Method 2: Roll strength (again, this is an exploding roll), add your weapon modifier, and subtract armor.

Weapons and Armor have the same bonuses as in Vanilla Fudge.

Missile Damage

Method 1: Rate each weapon with Lethality trait, and then roll damage based on that trait.

Method 2: Use the relative degree of your ranged attack for base damage, and add a weapon bonus.

Method 3: Assign raw dice to each missile weapon, like 1d8, 2d6, or 1d4+6.

Taking Damage

Everyone has a Damage Rating (DR). Your base DR is equal to the Trait Number (TN) for your Damage Capacity (or some other trait if the GM chooses). For example, a person with Great Damage Capacity would have a base DR 6.

DR = Base DR + Armor + Scale

So a knight with Great Damage Capacity and Chain Mail (+3) would have DR 9. Any damage that exceeds DR is applied to the wound track:

Damage Wound
1-4 Scratched
5-8 Hurt
9-12 Very Hurt
13-16 Incapacitated
17+ Near Death

The addition of a DR and the expanded wound track offsets the effect of the exploding dice, as well as the fact that Fair is now +4 instead of +0. If you want to use the standard wound track and no DR, cap exploding dice at 8 (Legendary) and it should work okay.