[Pre-BB] MapleStory Formula Compilation

I was bored without internet:


Iron Arrow:
Per-monster Multiplier: 0.9 ^ (monster# - 1)
Cumulative Multiplier: 10 * (1 - * 0.9 ^ monsters)

Piercing Arrow:
Per-monster Multiplier: 1.2 ^ (monster# - 1) * (0.5 + 0.5 * (time charged / 3 sec))
Cumulative Multiplier: (5 - 5 * 0.8 ^ monsters) * (0.5 + 0.5 * (time charged/ 3 sec))
Marked in big am I unsure of is correct or not.

I'm aware that the per-monster multiplier is already stated in, but cumulative may be funky to find out if piercing arrow is comparable with other skills. From what I know as well, time charged is rounded to lowest integer, correct?

 Spoiler

Sounds like a confirmation to me. You were using TT no?

*Tries something*
Damage Range 30~50, probability to 2 hit a monster with 80 HP

Let me try to do this via the way you do it with dice.

21^2 = 441 possibilities.

Chances to do 80 damage+ added together:
30/50
31/50
32/50
...
50/50
=20

31/49
32/49
...
50/49
=19

etc etc

49/31
50/31
=2

50/30
=1
= 210 chances, 210/441 = 47.6% chance to 2 hit.
Rawr, that can't be right.

Mm, I'd do a different approach. Instead of that, give the fact that the estimated damage will be 80 damage. Therefore, we know already that you have 0.5 - [exact 80 dmg chance]/2 for doing over 80 damage, and less than 80 damage. Thus, the damage is 0.5 - [exact 80 dmg chance]/2 + [exact 80 dmg chance] = 0.5 + [exact 80 dmg chance]/2.

The chance for having exact 80 dmg is this:

1st	2nd
30	50
31	49
32	48
...	...
48	32
49	31
50	30

That is, 21 different possibilities of getting 80 dmg.
We have in total 21 * 21 different possibilities. 21/((21*21) * 2) equals 1/42, therefore the chance of 2-hkoing is 1/2 + 1/21 = 22/42 chance of 2hkoing.

(Oh, did I ever tell you I love working with fractions?)

Edit: the above written is only exact if the damage range really IS from 30 to 50, and not 30.2 to 50.7 or something.