probabilities of winning a DRN

[JimMorrison]

You know, I couldn't find this damned table for some time (after being told to go look at it), because it's on page *5*! Page 5 is for installing instructions, and "what this first menu means" kind of stuff.

Anyway, it explains right there that a 6 is not just rerolled and added. You subtract one, and reroll. So there is no statistical variation in odds between 5, 6, 7 etc. I roll of 5 is 5. A roll of 6 is 5 + (d6). So your odds of success are not affected by the DRN mechanics.


But Endo, it's not a 0-5. It's 1-5, with each roll of 6 simply being another 1-5 on top of that. 0 would just suck.

[Omnirizon]

ah, that would solve that problem then.

that KO and JK, they thought of everything.

[MaxWilson]

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]

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.

[MaxWilson]

But the area for 8 gets redistributed too (2+6). I guess that probably makes 6 the mode.

-Max

[JimMorrison]

The ripple is self correcting. Each number between 7-11 contains a 6. So yes, there is a slight deviation in favor of 6 - but not really. The fact that each value above 6 has a slightly lower chance of actually occurring is irrelevant, because it is ONLY replaced by a higher number.

Look at it this way, we'll expand that DRN rate table. Here are the normal probabilities, up to 12.


2
33
444
5555
66666
777777 **
88888 **
9999 **
10 10 10 **
11 11 **
12 *


Each asterisk, represents a roll that contains a 6. We see that out of 36 nominal rolls of 2d6, we get at least one 6, 11 times. This is absolutely not a reduced chance of success. Every time you roll a 6, you have a 17% chance of actually getting the number that you rolled (if you reroll a 1), but you have an 83% of rolling a higher number. While the 2d6 is capped at 12, all of these higher rolls that have a "reduced statistical chance" of occurring, are only shifted upwards. So you may have a reduced chance of hitting a natural 7, but that is nicely offset by a greatly increased chance of hitting a natural 30 - which would have otherwise been impossible.

[Sombre]

This thread is good and all, but I have a question.

Why was 3 scared of 7?

[danm]

789!