Recruitment Probability Q&A
miyabisun/arona-gacha-calcHow to read the chart and how Recruitment Points and Recruitment Charge are calculated.
How many pulls should I expect to need per banner?
| PUs | Charge | Points |
|---|---|---|
| 1 PU | 90.07 pulls10,809Pyroxene | 107.80 pulls12,936Pyroxene |
| 2 PUs | 180.14 pulls21,617Pyroxene | 192.63 pulls23,116Pyroxene |
| 3 PUs | 270.22 pulls32,426Pyroxene | 274.46 pulls32,935Pyroxene |
| 4 PUs | 360.29 pulls43,235Pyroxene | 357.63 pulls42,916Pyroxene |
Pyroxene is the expected number of pulls multiplied by 120 and rounded to the nearest whole number. An expected value is a long-run average, not a guarantee that every PU will be obtained within that many pulls.
Isn’t the chance of obtaining 2 PUs within 200 pulls using Recruitment Charge 56.34%?
| 1 PU in 100 pulls | 75.06% |
|---|---|
| Two fixed 100-pull windows | 56.34% |
| Exact 200-pull probability | 64.09% |
| Missed by fixed windows | +7.75% |
The 56.34% figure assigns a fixed block of 100 pulls to each PU. If the first PU arrives early, the remaining pulls can be used for the second. Including every such path raises the exact probability to 64.09%.
What does the chart compare?
For a selected number of PUs, the chart compares the cumulative probability of obtaining all of them by each pull count under Recruitment Points and Recruitment Charge. The values are calculated exactly for every pull—not estimated by random sampling—and cross-checked with independent formulas.
What counts as obtaining a PU?
The calculation uses a 0.7% appearance rate for the targeted PU.
Does exact calculation cause a combinatorial explosion?
Recruitment Charge: First, calculate the probability that one PU is obtained on each pull from 1 through 200. Convolve that distribution once per required PU, then sum the probabilities whose total pull count is within the selected limit.
Recruitment Points: For each pull count, calculate the probability distribution of PUs obtained naturally. Add one exchangeable PU per 200 pulls, then sum the probability of meeting or exceeding the required count.
Equivalent states are aggregated instead of enumerating every pull history, so the calculation remains practical for 10 PUs and 2,000 pulls. The implementation is available in scripts/compare.js.