EV Statistics: The Time of Battle
One Piece Card Game • Monte Carlo simulation • model v1
Expected Value by Product
| Product | Price | Mean EV | Median EV | ROI | Std Dev | P5 | P25 | P75 | P95 | P99 | Simulated |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Pack | $6.45 | $8.26 | $1.68 | +28.1% | $45.39 | $1.17 | $1.38 | $3.11 | $25.52 | $110.88 | 1,008,000 |
| Box | $202.06 | $198.50 | $137.61 | -1.8% | $213.54 | $64.41 | $90.35 | $208.86 | $730.3 | $1274.09 | 42,000 |
| Case | $2292.44 | $2382.02 | $2231.79 | +3.9% | $734.66 | $1477.38 | $1810.03 | $2810.16 | $3791.54 | $4645.88 | 3,500 |
Mean EV is skewed upward by ultra-rare chase cards; the median tells you what a typical rip returns. Percentiles show the spread: P5 is a bad rip, P95 is a great one.
Hit Odds (per Booster Box)
| Rarity | Expected / Pack | Expected / Box | Expected / Case | P(≥1 per box) |
|---|---|---|---|---|
| L | 0.5000 | 12.00 | 144.00 | 100.0% |
| Manga Rare | 0.0008 | 0.02 | 0.23 | 1.9% |
| Special | 0.0110 | 0.27 | 3.18 | 26.5% |
| SR | 0.2292 | 5.50 | 66.02 | 99.8% |
| Treasure Rare | 0.0036 | 0.09 | 1.02 | 8.5% |
| SEC | 0.0194 | 0.46 | 5.57 | 46.4% |
| Alt-Art Leader | 0.0105 | 0.25 | 3.02 | 25.2% |
| Alt-Art Rare | 0.0417 | 1.00 | 12.00 | 100.0% |
| Alt-Art Super Rare | 0.0126 | 0.30 | 3.62 | 30.2% |
| Alt-Art Secret | 0.0069 | 0.17 | 2.00 | 16.7% |
| Gold DON!! | 0.0056 | 0.13 | 1.61 | 13.4% |
Active Pull-Rate Model
| Rarity | Finish | Rate / Pack | Odds | Sources |
|---|---|---|---|---|
| L | any | 0.5000 | 1 : 2 packs | Bandai booster structure (12 cards + DON!! topper; leader every other pack) |
| SR | any | 0.2292 | 1 : 4 packs | OP-16 English expected case rates (tcgtalk aggregation + retailer guides) |
| Alt-Art Rare | any | 0.0417 | 1 : 24 packs | OP-16 English expected case rates (tcgtalk aggregation + retailer guides) |
| DON!! | any | 0.0417 | 1 : 24 packs | Bandai booster structure (12 cards + DON!! topper; leader every other pack) |
| SEC | any | 0.0195 | 1 : 51 packs | OP-16 The Time of Battle — documented English 12-box case opening (tcgtalk); OP-16 English expected case rates (tcgtalk aggregation + retailer guides) |
| Alt-Art Super Rare | any | 0.0125 | 1 : 80 packs | OP-16 English expected case rates (tcgtalk aggregation + retailer guides) |
| Special | any | 0.0110 | 1 : 91 packs | OP-16 The Time of Battle — documented English 12-box case opening (tcgtalk); OP-16 English expected case rates (tcgtalk aggregation + retailer guides) |
| Alt-Art Leader | any | 0.0104 | 1 : 96 packs | OP-16 English expected case rates (tcgtalk aggregation + retailer guides) |
| Alt-Art Secret | any | 0.0069 | 1 : 144 packs | OP-16 English expected case rates (tcgtalk aggregation + retailer guides) |
| Gold DON!! | any | 0.0056 | 1 : 179 packs | OP-16 The Time of Battle — documented English 12-box case opening (tcgtalk); OP-16 English expected case rates (tcgtalk aggregation + retailer guides) |
| Treasure Rare | any | 0.0035 | 1 : 288 packs | OP-16 The Time of Battle — documented English 12-box case opening (tcgtalk) |
| Manga Rare | any | 0.0009 | 1 : 1152 packs | OP-16 English expected case rates (tcgtalk aggregation + retailer guides) |
Validation Report
Latest run: PASSED • 45 metrics checked against research data • 0 outside tolerance • 10,000 boxes, 1,000 cases, 100,008 packs
| Metric | Observed | Simulated | Delta | Tolerance | Result |
|---|---|---|---|---|---|
| DON (any) per pack | 0.041667 | 0.041667 | +0% | ±10% | PASS |
| L (any) per pack | 0.5 | 0.5 | +0% | ±10% | PASS |
| DON_GOLD (any) per pack | 0.003472 | 0.00564 | +62.42% | ±200% | PASS |
| SEC (any) per pack | 0.017361 | 0.019548 | +12.6% | ±89.4% | PASS |
| SP (any) per pack | 0.017361 | 0.011409 | -34.28% | ±89.4% | PASS |
| TR (any) per pack | 0.003472 | 0.00331 | -4.68% | ±200% | PASS |
| AA_L (any) per pack | 0.010417 | 0.010699 | +2.71% | ±75% | PASS |
| AA_R (any) per pack | 0.041667 | 0.041667 | +0% | ±75% | PASS |
| AA_SEC (any) per pack | 0.006944 | 0.007439 | +7.13% | ±75% | PASS |
| AA_SR (any) per pack | 0.0125 | 0.012849 | +2.79% | ±75% | PASS |
| DON_GOLD (any) per pack | 0.006944 | 0.00564 | -18.79% | ±75% | PASS |
| MR (any) per pack | 0.000868 | 0.00076 | -12.46% | ±75% | PASS |
| SEC (any) per pack | 0.020833 | 0.019548 | -6.17% | ±75% | PASS |
| SP (any) per pack | 0.006944 | 0.011409 | +64.29% | ±75% | PASS |
| SR (any) per pack | 0.229167 | 0.229662 | +0.22% | ±75% | PASS |
Research Sources
| Source | Type | Sample | Confidence | Data Points |
|---|---|---|---|---|
| Bandai booster structure (12 cards + DON!! topper; leader every other pack) — Bandai | official | — | 100% | 2 |
| OP-16 The Time of Battle — documented English 12-box case opening (tcgtalk) — tcgtalk | case opening | 288 packs / 12 boxes | 85% | 4 |
| OP-16 English expected case rates (tcgtalk aggregation + retailer guides) — tcgtalk / samuraiswordtokyo | estimate | — | 50% | 9 |
Pull rates are never hardcoded: every observation is stored with its source and confidence, merged into a weighted model, then verified by simulating 100,000+ packs and comparing the results back against the research data.