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Old 06-08-2022, 05:12 PM   #1
dataweaver
 
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Default 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.
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Old 06-08-2022, 06:11 PM   #2
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Default 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.
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Old 06-08-2022, 07:34 PM   #3
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Default 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.
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Old 06-08-2022, 07:34 PM   #4
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Default Re: 4dF

Quote:
Originally Posted by Anthony View Post
Overall, the core task mechanic for FATE is about the same level of variance as the core task mechanic for GURPS.
I don't know about FATE, which I don't play. But I've been running FUDGE for one of my current campaigns. My experience has been that characters get really high or really low scores more often than seems quite right.

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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Old 06-08-2022, 07:51 PM   #5
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Default Re: 4dF

Quote:
Originally Posted by whswhs View Post
I don't know about FATE, which I don't play. But I've been running FUDGE for one of my current campaigns. My experience has been that characters get really high or really low scores more often than seems quite right.
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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Old 06-08-2022, 07:53 PM   #6
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Default Re: 4dF

Quote:
Originally Posted by dataweaver View Post
+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%
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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Old 06-08-2022, 07:57 PM   #7
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Default Re: 4dF

Quote:
Originally Posted by whswhs View Post
I don't know about FATE, which I don't play. But I've been running FUDGE for one of my current campaigns. My experience has been that characters get really high or really low scores more often than seems quite right.

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.
Actually, “Fair” is entry-level competence; “Mediocre” is “needs training before you can do the job”. “Good” is “you've been doing this for some time now, and you know the ropes”. “Great” is “you're among the best in the company”. “Superb” is “you are the best”. The chance of someone with Fair Ability achieving a Legendary result is 1/81, comparable to a Critical Success in GURPS.

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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Old 06-08-2022, 07:59 PM   #8
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Default Re: 4dF

Quote:
Originally Posted by Agemegos View Post
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.
That's the chance of a specific result, not the chance of success. The cumulative probability (to get X or better) is:
+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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Old 06-08-2022, 07:59 PM   #9
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Default Re: 4dF

Quote:
Originally Posted by Anthony View Post
FATE doesn't use the same adjective system as Fudge; there are 7 levels between Terrible and Legendary in Fudge, 10 in Fate.
That's a good thing, because Fate Points regularly boost your effective level.
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Old 06-08-2022, 08:12 PM   #10
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Default Re: 4dF

Quote:
Originally Posted by Anthony View Post
That's the chance of a specific result, not the chance of success.
Right, and therefore it is the difference between the chances of success for two successive values of difficulty. And therefore it is the smallest adjustment to chance of success that I can make in that part of the domain of the probability function.

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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