Trait Calculator | ylxdzsw's blog

Goal

4 Orange + 1 Purple, SS Atk.

Calculation Method

The greedy strategy means locking the trait as soon as it has a color that is needed. opt strategy may reroll purple SS atk if encountered early on.

Let $c$ denote the remaining currency, $o$ and $p$ denote the number of remaining orange and purple traits to get, $r$ the remaining traits rolled but not checked, and $P_{g ree d y} (c, o, p, r)$ and $P_{o pt} (c, o, p, r)$ denote the chance of obtaining $o$ orange and $p$ purple traits with $c$ currency using the greedy and opt strategies, respectively.

$m_{o p}$ is the price of a roll, defined by the game as:

m_{o p} = 5 \times (6 - o - p)

$α$ and $β$ are the probability of SS Atk and specific color. They are defined by the game as:

α = 0.0756% \times \frac{1}{9} β = \frac{1}{5} = 0.000084 = 0.2

$P_{g ree d y} (c, o, p, r)$ can be calculated recursively as:

P_{g ree d y} (c, o, p, r) = ⎩ ⎨ ⎧ 10 P_{g ree d y} (c - m_{o p}, o, p, o + p) P_{g ree d y}^{'} (c, o, p, r) if o + p = 0 if o + p > 0, c < m_{o p}, r = 0 if o + p > 0, c \geq m_{o p}, r = 0 otherwise

P_{g ree d y}^{'} (c, o, p, r) = α \cdot β \cdot 1_{o > 0} \cdot P_{g ree d y} (c, o - 1, p, r - 1) + α \cdot β \cdot 1_{p > 0} \cdot P_{g ree d y} (c, o, p - 1, r - 1) + α \cdot (3 \cdot β + 1_{o = 0} \cdot β + 1_{p = 0} \cdot β) \cdot P_{g ree d y} (c, o, p, r - 1) + (1 - α) \cdot P_{g ree d y} (c, o, p, r - 1)

$P_{o pt} (c, o, p, r)$ is calculated similarly. Instead of locking needed traits right away, it only locks when it provides higher probability.

P_{o pt} (c, o, p, r) = ⎩ ⎨ ⎧ 10 P_{o pt} (c - m_{o p}, o, p, o + p) P_{o pt}^{'} (c, o, p, r) if o + p = 0 if o + p > 0, c < m_{o p}, r = 0 if o + p > 0, c \geq m_{o p}, r = 0 otherwise

P_{o pt}^{'} (c, o, p, r) = α \cdot β \cdot 1_{o > 0} \cdot max {P_{o pt} (c, o - 1, p, r - 1), P_{o pt} (c, o, p, r - 1)} + α \cdot β \cdot 1_{p > 0} \cdot max {P_{o pt} (c, o, p - 1, r - 1), P_{o pt} (c, o, p, r - 1)} + α \cdot (3 \cdot β + 1_{o = 0} \cdot β + 1_{p = 0} \cdot β) \cdot P_{o pt} (c, o, p, r - 1) + (1 - α) \cdot P_{o pt} (c, o, p, r - 1)

Calculator

Remaining currency. E.g. fill in 105000 for 105A trait points.Remaining orange traits to obtain.Remaining purple traits to obtain.Treat blue as purple.Treat any color as purple.