I'm sorry if my writing comes out incomprehendable. I'm mostly using english for science, which makes me compress my writings (a bad thing late at night when I don't bother to look over what I've written). Chesh, feel free to edit if you think it is needed
Let's start from the beginning to get the terms going and everything.
When a weapon is created in the game, the stats are taken from an ingame library of "code-base-stats" and modified. You can see the "code-base-stats" here.
Let's take a koetsu suit as an example
- Code: Select all
|{itArms|Koutetsu|10|60|-20|body|{3|level|26}
So the armor drops with attack = 10, defense = 60, skill = -20, belongs on the body and you need to have a combined character level and fighter guild level of 31 to wear it.
but it also drops as 15a 90d -13s, 21a 126d -10s etc. There are no limits to the drop quality, but you will notice that there seems to be different tiers of quality with set steps inbetween. These steps are determined by a number, so we will call the different tiers by that number. The tier will be in the range of [0.7;inf[ with steps of 0.1
The tier modifies the code-base-stats, such that:
if the code-base-stat is positive, weapon-base-stat=code-base-stat*tier
if the code-base-stat is negative, weapon-base-stat=code-base-stat/tier
Taken the koetsu as example we will calculate the tier 1.3 quality:
attack = 10*1.3 = 13
defense = 60*1.3 = 78
skill = -20/1.3=-15.5==-15 (taking the integer value)
The tier of a weapon is calculated when it first drops and then the weapon-base-stats are frozen. The tier is determined by two probability functions which I will call Rand and Coin.
Rand takes a random integer value between 0 and 3
Coin is a potentially infinite game of "flip a coin." If you get tails the game stops, if you get heads, the game continues. The number of times you get heads is the value that the Coin function returns.
tier=(7+Rand+Rand+Coin)/10
In order to get a tier=0.7 both of the Rand functions and the Coin function must return 0, so that: tier=(7+0+0+0)/10=0.7. The chance to get Rand=0 is 1/4. Getting Coin=0 needs you to get tails on first flip, which has a probability of 1/2, so the chance to get a tier 0.7 weapon is
P(0.7)=1/4*1/4*1/2=3.125%
To make progress a bit easier I invent a bracket notation for these events where the first number is the result of the first Rand function, the second number is the second Rand function and the third number is the Coin function. That makes the above tier=0.7 event a <0,0,0>
Tier=0.8 has three possible events:
<1,0,0><0,1,0>
<0,0,1>
The chance to get Rand=1 is again 1/4, infact getting Rand to be any value will have a chance of 1/4, so the probability of a certain tier is determined by Coin function and the number of events. To get Coin=1 you need to first toss a heads and then tail, that is a probability of 1/2^2. The probability to get a certain Coin value is very easily parametrised as B(Coin=x)=1/2^(x+1)
P(0.
=1/16(2*1/2+1/2*^2)=7.815%
Tier=0.9 has 6 events:
<2,0,0><0,2,0><1,1,0>
<1,0,1><0,1,1>
<0,0,2>
There are three ways of making a tier 0.9 while getting Coin=0, two ways with Coin=1 and one way where Coin=0, so:
P(0.9)=1/16(3*1/2+2*1/2^2+1*1/2^3) = 13.28125
Let's jump to tier=1.3 and tier 1.4
P(1.0)=19.14%
P(1.1)=18.95%
P(1.2)=15.72%
tier=1.3 has 16 events:
<3,3,0>
<3,2,1><2,3,1>
<3,1,2><1,3,2><2,2,2>
<3,0,3><0,3,3><2,1,3><1,2,3>
<2,0,4><0,2,4><1,1,4>
<1,0,5><0,1,5>
<0,0,6>
P(1.3)=1/16(1/2+2/4+3/8+4/16+3/32+2/64+1/128)=10.99%
tier=1.4 has 16 events too!:
<3,3,1>
<3,2,2><2,3,2>
<3,1,3><1,3,3><2,2,3>
<3,0,4><0,3,4><2,1,4><1,2,4>
<2,0,5><0,2,5><1,1,5>
<1,0,6><0,1,6>
<0,0,7>
P(1.3)=1/16(1/4+2/8+3/16+4/32+3/64+2/128+1/256)=5.49%
Since we have used up all combinations of the two Rand functions in both tier=1.3 and tier=1.4, the only difference is that you need Coin to be one bigger for 1.4 than you did for 1.3, which again means that you need to flip heads one extra time, and that has a probability of 1/2. So the chance to get tier=1.4 is half of that to get tier=1.3.
From here on the situation is just like explained above, that for every new tier in line, the chance to get that is halfed. The people who hold the "highest [insert name of fancy weaponry]" in the game is usual around tier=3.0. Try to calculate the chances of that, and get scared
