Pity-adjusted expected value versus player-facing banner claims
Banner EV claims fail when pity is omitted. Synthetic EV lab anchored to JOGA’s expected-amount language.
Banner EV claims fail when pity is omitted from the math. JOGA’s guideline already defines 推定金額 (estimated amount) as the expectation implied by configured rates — use that language, then show what pity does to the same banner.
Definitional anchor
JOGA section 3(1)a (guideline PDF, read from the source 20 September 2026) refers to the estimated amount to obtain a rare item as the amount calculated as an expectation from the configured提供割合. That is a rate-only expectation unless your live system also applies pity.
Illustrative lab
Single-pull price 160 currency units. Featured rare base rate 0.6% without pity. Hard pity guarantees the featured rare at pull 90 if not obtained earlier (teaching rule).
| Model | Approx. pulls to featured (expectation sketch) | Approx. currency EV |
|---|---|---|
| Rate-only geometric (1/0.006) | 166.67 | 26,667 |
| With hard pity at 90 (truncated geometric) | < 90 | < 14,400 |
Exact pity-adjusted expectation needs the full rate table and pity algorithm. The operator point: a banner that quotes only the rate-only EV while the live system has hard pity (or vice versa) is a mismatched claim. Replace synthetic rates with the live banner table before any public math.
Facts vs limits
| Fact | Limit |
|---|---|
| JOGA defines estimated amount from configured rates | This lab’s 0.6% / 90 pity numbers are synthetic |
| Pity changes effective EV vs rate-only | No title’s live banner screenshot is attached here |
| Clarification page supports the EV reading | Not legal advice outside JOGA scope |
