Probability Lab
Standard Banner, dataset national-dex-1025-20260823. These are the exact published odds — the same numbers the pull endpoint samples from, before pity adjusts anything.
Tier odds
| Tier | Species | Pool share | Avg. odds per species |
|---|---|---|---|
| Common | 336 | 52.0000% | 1 in 646 |
| Uncommon | 89 | 28.0000% | 1 in 318 |
| Rare | 413 | 13.0000% | 1 in 3,177 |
| Epic | 52 | 5.0000% | 1 in 1,040 |
| Ultra Rare | 41 | 1.7000% | 1 in 2,412 |
| Legendary | 71 | 0.3000% | 1 in 23,667 |
Expected pulls (no pity applied)
- Expected pulls for any Ultra Rare+: 50 (median 35)
- Expected pulls for any Legendary: 333 (median 231)
- P(no Legendary after 100 pulls): 74.0%
- P(no Legendary after 200 pulls): 54.8%
Real pulls also have soft pity from pull 60 and hard pity at pull 90 (Ultra Rare+) and pull 180 (Legendary), which the numbers above don't include — use the simulator below to see the pity-adjusted effect over many pulls.
Simulate pulls
Simulated pulls — separate from your real account pulls. Uses the same weighted sampling and pity logic as the real pull endpoint, just without touching currency or your collection.