$bonus "twice the sphere button value"
$bonus "Additional spheres: +N"
Frequencies: empirical data from 55,249 observed sphere rolls.
EV: (base × (1 + double_chance) + flat_bonus) × (1 + shop_9_bonus)
| Emoji | Base SP | EV | Frequency |
|---|
Save these settings so the Live P9 Advisor can recommend click/skip for each sphere button as you roll.
Each sphere button color has a base SP value. Your sphere double chance gives a chance to earn twice the base value, and the flat bonus adds a fixed amount on top. Shop 9 level provides a percentage multiplier.
A static strategy picks a fixed set of colors to always click and skips the rest, regardless of how many rolls or clicks remain. The calculator tries every possible threshold (skip the k lowest-EV colors, for each k), then picks the one that yields the highest total SP per day.
Over rMax rolls, the number of potential clicks follows a binomial distribution with probability P(click). The expected number of clicks actually used is capped by cMax (you can't click more than your daily budget). The total expected SP is the per-click EV multiplied by the expected clicks used.
The DP-optimal strategy re-evaluates the click/skip decision at every (rolls left, clicks left) state. We define V(r, c) as the expected total SP from r rolls and c clicks remaining, and work backwards from the base cases: V(0, c) = 0 (no rolls left) and V(r, 0) = 0 (no clicks left). V(1, 1) is simply the expected value of one click.
For other states, V(r, c) is computed by comparing the value of clicking — EV(color) + V(r−1, c−1) — versus the value of skipping — V(r−1, c) — taking the better option for each color and weighting by that color's frequency.
Working backwards this way gives us the optimal threshold at every (r, c) state: click any color whose EV exceeds V(r−1, c) − V(r−1, c−1), which represents the value of saving your click for a later roll. This threshold decreases as rolls run out, and so colors you'd skip early become worth clicking later.