Maths problem: fatigue vs critical hits

[Pehmyt]

I don't know if you are still interested in this, but I was, as it says "maths problem" in the title For future reference, if nothing else, the actual probability distributions for 1d6oe and 2d6oe (=DRN in the manual) are:


and for the original question,

In all expressions X=5n+r, with 1<=r<=5 (note limits!).

The first one is more or less trivial, the second is proven by induction in n and the third follows from that by straightforward summation.

[Revolution]

I started reading all of this and thought of this picture...

[moderation]

So that is what kids are learning in school these days.

[Wick]

With only a little calculus long, long ago I can't play math, but I do enjoy watching it.

[lch]

Pehmyt said:

In all expressions X=5n+r, with 1<=r<=5 (note limits!).

With a little redesign, this translates into python code as follows: Code:

---

# p(2d6oe) >= x (Pehmyt's version)

def doubledrn_3(x):

	n = (x-1) / 5

	r = (x-1) % 5

	r += 1

	return float((62-15*r+r*r)*5*n+70+3*r-r*r)/(2*6**(n+2))

---

which produces the right output. Very nice! I think that if you lose the tricky quotient/remainder representation of yours and just work on x-1 like I did in my third attempt, your formula might look a little simpler than the current one.

[lch]

Okay, the result isn't as great as I hoped, this is what Maple makes out of it: Code:

---

> p := ((62-15*r+r*r)*5*n+70+3*r-r*r)/(2*6^(n+2));

                                                              2                  2

                                              5 (62 - 15 r + r ) n + 70 + 3 r - r

                                         p := ------------------------------------

                                                              (n + 2)

                                                           2 6

> factor(subs(r=r-1, p));

                                                                2               2

                                          390 n - 85 n r + 5 n r  + 66 + 5 r - r

                                          ---------------------------------------

                                                           (n + 2)

                                                        2 6

---

[Micah]

I'm still amused over the painstaking research to figure out how something works when it doesn't actually follow the behavior described.

I just tested this with a troll king with a robe of invulnerability vs 12 and 13 damage chaff (25 body prot, somewhat more on the head since the chassis has a helmet). Under 15 fatigue he gets damaged twice over 8 rounds of combat in melee. As soon as he crests 15 fatigue he starts taking about 2 damaging hits EVERY ROUND. The chances for a crit at 15-30 fatigue should be 1 in 36, since it requires a one on both dice (open ended rolling doesn't kick in til way later). He's only taking 21 swings per round. In addition, even if a crit lands it only has about a 50% chance of doing damage (half his prot value still is equal to the damage of the attacks).

The crit system as described in the rulebook does not mesh with reality. I've observed this phenomenon time and again while playing with SCs, but now I actually sat down and counted swings.