What the stat panel supports
| Luck points | Panel value |
|---|---|
| 0 | ×1.00 baseline |
| 20 | ×1.60 |
| 38 | ×2.14 |
| 183 | ×6.49 |
These observations agree with 1 + 0.03 × Luck points. The Luck calculator calculates this component and its point-to-point difference. It does not turn a “1 in N” card label into a proven effective probability.
Separate sources, separate questions
| Source | Confirmed label | What remains unproven |
|---|---|---|
| Lucky pass | ×1.5 luck | Complete stacking order with all other boosts. |
| VIP | ×1.1 luck and daily chest | Whether every reward or roll type uses the same modifiers. |
| Forge gear | Item-specific +luck% | A universal final multiplier formula. |
| Mastery | Permanent luck bonus and next-roll milestone | A fixed per-rank roll-cost curve. |
| Border Chance stat | +Gold/Rainbow/VOID odds | Exact final border probabilities. |
| Pets and set bonuses | Luck labels in their UI | Full growth and combination formula. |
Do more rolls guarantee the rare card?
No finite roll count observed here is a guaranteed target-card arrival. A printed denominator and a displayed luck multiplier are insufficient to prove independence, pool weights, pity or the transformation used by the game. A generic probability formula would be mathematically tidy but could describe the wrong game model.
Increase the resource you actually lack: rolling time, packs or a gear route. For collection labels use rarities and VOID. Do not buy a pass based on an invented expected-cost-to-Secret figure.