06-08-2022, 05:12 PM | #1 |
Join Date: Aug 2004
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4dF
The probability spread of 4dF (four Fudge dice) looks like this:
+4: 1/81, or 1.23% +3: 4/81, or 4.93% +2: 10/81, or 12.35% +1: 16/81, or 19.75% 0: 19/81, or 23.46% –1: 16/81, or 19.75% –2: 10/81, or 12.35% –3: 4/81, or 4.93% –4: 1/81, or 1.23% Or something like: +4: -- +3: -------- +2: -------------------- +1: -------------------------------- +0: -------------------------------------- –1: -------------------------------- –2: -------------------- –3: -------- –4: -- Nearly ⅔ of all results end up between –1 and +1; and nearly 8 out of every nine results are between –2 and +2. That's a quarter and a half of the maximum deviation, respectively. By comparison, 1d6–1d6 looks like this: +5: 1/36, or 2.8% +4: 1/18, or 5.6% +3: 1/12, or 8.3% +2: 1/9, or 11.1% +1: 5/36, or 13.8% 0: 1/6, or 16.7% –1: 5/36, or 13.8% –2: 1/9, or 11.1% –3: 1/12, or 8.3% –4: 1/18, or 5.6% –5: 1/36, or 2.8% Graphically, +5: ----· +4: --------- +3: -------------· +2: ------------------ +1: ----------------------· +0: --------------------------- –1: ----------------------· –2: ------------------ –3: -------------· –4: --------- –5: ----· You're as likely to get between a –2 and +2 on this spread as you are to get between a –1 and +1 on 4dF; and you're as likely to get a –4 to a +4 as you would be to get a –2 to +2 on the Fudge dice. That is, 80% of the maximum deviation. For a 3d6 curve, the equivalent figures are: A –1 to +1 on 4dF is like rolling between 8 and 13 on 3d6; A –2 to +2 on 4dF is like rolling between 6 and 15 on 3d6; A –4 or +4 on 4dF is like rolling a 3, 4, 17, or 18 on 3d6. |
06-08-2022, 06:11 PM | #2 |
Join Date: Feb 2005
Location: Berkeley, CA
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Re: 4dF
For any number of d6s, the standard deviation is sqrt( 35/12 * nDice ), or 2.96 for 3d6. For any number of d3s (fudge dice), the standard deviation is sqrt( 2/3 * nDice ), or 1.63. For any choice of dice, a single die is flat, two dice is a pyramid, and three or more will start resembling a normal distribution, so we can basically evaluate fate skill levels as being about 1.8 GURPS skill levels.
If we interpret a 10 skill in GURPS as a +1 (Average) in Fate, the lowest FATE skill level (Horrifying, -4) is equivalent to a GURPS skill level of 1, the highest (Legendary, +8) as a GURPS skill level of 23, and the best skill of a starting character (generally Great, +4) is roughly a GURPS skill of 15. Note that extremely low skill levels are reserved for NPCs, PCs have no skills below Mediocre(+0). GURPS has a documented set of task difficulty modifiers ranging from +10 to -10 (20 points), Fate doesn't specifically say that skill levels are also task difficulties but it's a natural assumption, so the FATE range is about 22 points in GURPS. Overall, the core task mechanic for FATE is about the same level of variance as the core task mechanic for GURPS. |
06-08-2022, 07:34 PM | #3 |
Join Date: Jul 2006
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Re: 4dF
A +1 bonus using 4dF results in a far higher increase in the chance of success compared to the 3d6 bell curve that GURPS uses.
The more dice you use the steeper the slope is of the central peak of the bell curve which causes a more radical change in the odds when you add or subtract modifiers. Anydice charts https://anydice.com/program/293ed You can see the difference in these two simulators only differ because one uses 4dF and the other d6-d6. 4dF https://www.batintheattic.com/mwrpg/ 2D6 https://www.batintheattic.com/mwrpg66/ Another example involving 2d12, 3d8, and 4d6. The more dice you add odds of the central peak occurring keeps rising. https://anydice.com/program/dfb6 Last edited by robertsconley; 06-08-2022 at 07:44 PM. |
06-08-2022, 07:34 PM | #4 | |
Join Date: Jun 2005
Location: Lawrence, KS
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Re: 4dF
Quote:
The rules of FUDGE say that a Legendary skill or attribute level is beyond the normal range of human variability. So I figure that if you are rolling against Body, or Strength, or whatever represents raw muscular force, a Legendary result indicates that you've exhibited the strength of a bear or something; if you are rolling against Art, you've created a transcendentally beautiful work. But if you have a Good trait (which I figure is about what an entry level professional has in their field), you have 5 chances out of 81 of getting a Legendary result, or about one in sixteen. That seems unreasonably high.
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Bill Stoddard I don't think we're in Oz any more. |
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06-08-2022, 07:51 PM | #5 |
Join Date: Feb 2005
Location: Berkeley, CA
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Re: 4dF
FATE doesn't use the same adjective system as Fudge; there are 7 levels between Terrible and Legendary in Fudge, 10 in Fate.
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06-08-2022, 07:53 PM | #6 |
Join Date: May 2005
Location: Oz
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Re: 4dF
I'n happy to concede that I don't actually notice a difference of 5% in a probability of success near the middle of the range, and therefore that a system that gets me to the nearest multiple of 10% is good enough and that I ought to accept it. Rolls of 10 and 11 on 3d6 have probabilities of 12.5%, which makes a +1 to a roll a slightly coarser adjustment to probability than I would prefer, right around 50% where I need it most. And this distribution is not to my taste at all.
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Decay is inherent in all composite things. Nod head. Get treat. |
06-08-2022, 07:57 PM | #7 | |
Join Date: Aug 2004
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Re: 4dF
Quote:
It's still a bit more common that l than I'm comfortable with, and I personally say that there's another level between Superb and Legendary so that a Fair ability has no chance of achieving a Legendary or Abysmal result. Then “Good” gets the aforementioned 1/81 chance, Great gets 5/81, and Superb gets 15/81. |
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06-08-2022, 07:59 PM | #8 | |
Join Date: Feb 2005
Location: Berkeley, CA
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Re: 4dF
Quote:
+4: 1.2% +3: 6.2% +2: 18.5% +1: 38.2% +0: 61.7% -1: 81.5% -2: 93.8% -3: 98.8% |
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06-08-2022, 07:59 PM | #9 |
Join Date: Aug 2004
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Re: 4dF
That's a good thing, because Fate Points regularly boost your effective level.
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06-08-2022, 08:12 PM | #10 | |
Join Date: May 2005
Location: Oz
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Re: 4dF
Quote:
The difference between 38% and 62% is too large for my taste. Adding the probabilities up to get cumulative probabilities and the subtracting back again to get the differences does not alter my conclusion.
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Decay is inherent in all composite things. Nod head. Get treat. |
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