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Old 11-01-2020, 08:02 AM   #4
phiwum
 
Join Date: Jun 2008
Location: Boston area
Default Re: Auto success and failures, rule of 19

Quote:
Originally Posted by RobW View Post
This compares the chance of auto failures for the Legacy Edition p9 table (LE p9), and the rule of 19 above. That is, as the number of dice being rolled increases, how do the odds of automatic failure increase? The two rules behave almost identically.

https://www.dropbox.com/s/f803a05jrh...lures.pdf?dl=0

Here just zooming in on rolls of 8 and fewer dice, ie the kinds of rolls that could reasonably occur in a game

https://www.dropbox.com/s/verkwwa3kh...ures8.pdf?dl=0

As above, the big advantage of this system in my mind is that now everyone around the table can instantly tell whether there's been a critical success or failure, and if so just HOW critical.
I have a simple question. How did you generate that graph?

Did you come up with a smooth function that encodes the actual odds in a logical manner or did you calculate the odds for each of the seven integer values (2, 3, ..., 8) and apply a method to generate a smooth approximation?

Just curious. I assume the latter, but I'd be impressed if there's a continuous function easily expressed for the former. That is, if there's a natural (canonical) way to extend this discrete probability function to a continuous function with sensible values in between the integers.

I have to think about the numbers. The increased odds of auto-failure comes with an increased chance of critical failure. Since four dice is pretty common, this is a big change. If my off-hand calculation is correct, the new probability of critical failure on four dice is 9.2% 4.6%, using the rule that critical is one greater than auto. That's a huge large jump from 2.7% for RAW, leading to lots of dropped weapons.

(Edited above, since I made a significant error on the four dice critical roll. Using the rule of 19, an auto-failure on four dice occurs if you roll 15 or more on three dice, so a criticial requires 16 or more on three dice, hence 4.6%. The jump from 4.6% to 9.2% auto failure is larger, but applies only when adjDX -- or whatever stat -- is already 15 or more.)

Last edited by phiwum; 11-01-2020 at 07:08 PM.
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