probabilities of winning a DRN

Renojustin · #1 July 31st, 2008, 02:46 PM

lol... RTFM.

MaxWilson · #2 July 31st, 2008, 02:51 PM

Yes, it is different because it assumes normality and uses statistical methods. Use the manual table for values within the table's range, but otherwise Omniziron's formula might be a useful approximation if you want to extrapolate to +/- 20 or so.

-Max

Omnirizon · #3 July 31st, 2008, 02:52 PM

i never look in that end of the manual

but hey! it appears they are even with the log distribution. nice

Omnirizon · #4 July 31st, 2008, 02:55 PM

it doesnt' account for the wave caused by the open ended roll though, the probability for 8 should actually be higher than for 7

Renojustin · #5 July 31st, 2008, 02:55 PM

Values outside of the table's range really aren't that necessary to extrapolate, now are they Max? There's not a whole lot of difference between a 1% chance and a 1.1% chance of success, is there?

I just feel kinda bad for Omni after that whole thing. But it IS funny! lol

Omnirizon · #6 July 31st, 2008, 03:00 PM

hmmm... and I tossed and turned all last nite in bed thinking about it too. I couldn't wait to get up this morning and look up mean and variance formulas for open ended rolls.

course, i did notice the wave, which the manual doesn't mention.

the wave! the wave! it matters. maybe not really, very rare for anything to get to a difference of 8.

Omnirizon · #7 July 31st, 2008, 03:16 PM

hmmm...

and actually the oscillation is very significant right at 7 and 8, the 6 isn't affected by it. the probability for 7 is dropped, while the probability for 8 is raised. where normally 7 is 8% and 8 is 6%, 7 is closer to 5% and 8 is 11%!

A crafty player may find ways to exploit that!

The oscillation continues and increases in frequency but drops precipitously in magnitude. the reason is simple, every number that would usually be attained by rolling a 6 on the dice is now having a way in which that number could usually be rolled shifted upward. A depression in the bell curve is created where the number losing a way to be rolled is, while the number above essentially gains that extra opportunity to be rolled.

think about this when kitting up your mage with extra penetration. maybe can hit that sweet spot, and you might actually hurt your chances to soul slay that SC by pumping penetration up one more!

MaxWilson · #8 July 31st, 2008, 04:39 PM

Quote:

Omnirizon said:
think about this when kitting up your mage with extra penetration. maybe can hit that sweet spot, and you might actually hurt your chances to soul slay that SC by pumping penetration up one more!

That turns out not to be the case. It is always true that a success by X+1 also succeeds by X.

-Max

Omnirizon · #9 July 31st, 2008, 04:52 PM

well, with jim morrisons post, the issue is solved, however it would be true, you can count it up yourself and see.

the rows show how many possible ways to roll each number on 2d6 open ended

2
33
444
5555
66666
7777
88888

normally, 7 would be the mean. here it dips because it is no longer possible to roll a 7 with 6+1, it would now be a 6,?,1; and the area of the curve normally under seven gets pushed towards the end. count it yourself and see.

Endoperez · #10 July 31st, 2008, 03:20 PM

Rerolls are actually made with a dice that's 'numbered' 0-5. IIRC, probability of rolling anything under 6 with one open-ended dice is equal, and probability of getting anything above 5 and below 12 is equal, etc.

So something like:
5/6 chance of result 1-5.
1/6 chance of first 6; 1/6*5/6 chance of a result 6-10
1/36 chance of second 6; 1/6*1/6*5/6 chance of a result 11-15

Then I tried thinking about two dice, and gave up and decided that the manual table is good enough.